EXPERIMENTAL AND COMPUTATIONAL STUDY OF NOVEL DESALINATION
TECHNOLOGIES FOR INTEGRATION INTO BUILDINGS

By

Mahyar Abedi

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

Mechanical Engineering—Doctor of Philosophy

2024

ABSTRACT

As an inexpensive and environmentally friendly technology, humidification-dehumidification (HDH)

is an ideal candidate for water desalination due to its simple design and low energy requirements.

With the ability to treat various types of compromised waters, the addition of a packed-bed medium

enhances the desalination efficiency and system compactness, making direct-contact packed-bed

HDH desalination systems a perfect fit for geographically distributed water desalination units and

building integration.

The first part of this thesis focuses on modeling the behavior of a desalination unit and its

integration with solar thermal systems, with a one-dimensional mathematical model developed

and validated experimentally. Machine learning regression techniques are used to develop a data-

driven surrogate model, which accurately predicts desalination performance but requires a larger

dataset for high fidelity. A comprehensive assessment is carried out for the integration of an

HDH system with a solar chimney, resulting in solar desalination chimneys. The assessment

suggests that the pressure drop is a critical factor in the system’s performance. A direct-contact

packed-bed condenser shows a prominent desalination capacity. Small-scale configurations are

ideal for household freshwater needs, while the large-scale can be implemented as sporadic water

treatment plants in rural areas. Solar air heater systems are also studied for potential integration

with desalination units, with an experimental flat plate solar air heater built and validated with

3D computational and 1D mathematical models. The investigation suggests that although the

integrated system is more efficient (both thermal and desalination) compared to that of the solar

desalination chimney, the dependency of the system on energy sources for the circulation of water

and air is a significant drawback. This dependency can limit the system’s autonomy and increase

its operational costs.

The second part of this thesis investigates the integration of desalination units with buildings,

specifically greenhouses. The greenhouse is integrated with a transparent solar water heater as a

roof that absorbs the NIR waveband to increase the temperature of used or saline water and then

passes the essential wavebands for plant growth. The hot water then flows through a water treatment

unit to produce potable water. Experimental pilots of the solar water heater are built, and models

are developed to meticulously predict the behavior of the solar water panel. To incorporate the

impact of spectral variation on lettuce as the case study, a dynamic growth model is developed

that quantifies light spectrum variations. Changes in the light spectrum are accounted for via a

new light-use efficiency parameter in the plant growth model. Then, several models are coupled

to predict the behavior of an integrated greenhouse with a transparent solar water heater as a roof,

a water treatment unit, and a spectral-incorporated plant growth model for lettuce in Phoenix,

AZ. The models suggest that the transparent solar water heater on the roof reduces greenhouse

ventilation load by about 30%, and the water treatment unit produces 35-40 kg of potable water

daily, sufficient for single-row cultivation of lettuce. The integrated greenhouse has the potential

to produce an average of 300 kg of fresh lettuce each month during the growth period, according

to the plant growth model.

Copyright by
MAHYAR ABEDI
2024

This thesis is dedicated to my beloved parents and my amazing wife.
Thank you for always believing in me and supporting me through this long journey.

ACKNOWLEDGEMENTS

I am fortunate to have had support and guidance from many people during the pursuit of my

doctorate degree. First and foremost, I would like to thank my advisor, Professor Andre Benard, for

his support, encouragement, and guidance throughout my education at Michigan State University.

Thank you for always believing in me, teaching me how to be an excellent researcher, helping me

to become a better academic writer, and showing me the significance of patience and persistence

in academic research. I never forget even on your busiest day; you were always smiling.

Next, I would like to express my appreciation toward Dr. Xu Tan for his support. We have

worked together on many projects and proposals during my Ph.D. study. we spend a considerable

amount of time developing and investigating numerous experimental setups in the harsh summer

and winter of Michigan. His knowledge of programming and modeling has been so helpful for me

in achieving most of the research goals.

Thanks also go to my dissertation committee. Professor Farhad Jaberi and Professor Junlin

Yuan, whose courses made a significant impact on my research, and their helpful comments and

insights have improved the overall quality of this dissertation.

I would also like to thank my

committee member Professor Erik Runkle for his valuable comments and suggestions on my thesis.

Working with Professor Runkle has been so helpful for me in completing my second journal paper

on spectral-incorporated plant growth modeling and improving the writing quality of the research

paper to be suitable for the horticulture journal. I would also like to thank Professor James Klausner

for his keen insight and helpful comments on different aspects of this dissertation and the published

manuscript.

While machine learning has helped me a lot with different aspects of this dissertation, none of

those could have been achieved without the support of Professor Michael Murillo. Thank you for

teaching me the fundamentals of machine learning and data science, how to implement those tools

to progress this research further, and the significance of proper visualization and presentation for

those works.

I would like to thank my friends at the CFD lab, Dr. Mostafa Aghaei Jouybari, Dr. Ali Akhavan

vi

Safaei, and Dr. Parnab Saha, for their suggestions and help throughout the years.

My final sincere appreciation would go to the three persons whom I loved the most and who

have fully supported me during my Ph.D. endeavor. My beloved parents, I never forgot your support

and the sacrifices you have made to get me to this stage. Thanks for always believing in me, and

helping me to overcome some of the difficulties I have faced, even though we are thousands of

miles away from each other. My beautiful and lovely wife, Afsane, I could never repay what you

have done for me. When I decided to pursue a Ph.D. degree, you accepted my decision without

hesitation and helped me embark on this challenging path. Your support and unconditional love

have been a guiding light for me during this journey, especially during the pandemic. I hope that

someday I can repay a fraction of what you have done for me.

The support of Advanced Research Project Agency-Energy (ARPA-E) of the US Department

of Energy under award no DR-AR0001000 and of the National Institute of Food and Agriculture

(NIFA) under grant number 2018-67003-27407 titled “INFEWS/T3: Advanced Energy Efficient

Greenhouse Systems Employing Spectral Splitting and Solar Water Purification” are gratefully

acknowledged. This work was supported in part through computational resources and services

provided by the Institute for Cyber-Enabled Research (ICER) at Michigan State University.

vii

LIST OF SYMBOLS AND ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . .

xi

TABLE OF CONTENTS

CHAPTER 1

. .

1.1 Context
.
.
1.2 Related Technologies .
1.3 Objective .
1.4 Manuscript Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.

. .

. .

. .

.

.

.

1
1
2
9
9

CHAPTER 2

.

.

.

NUMERICAL MODELING OF DIRECT-CONTACT PACKED-BED
DESALINATION UNITS . . . . . . . . . . . . . . . . . . . . . . . . . 12
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1
.
Introduction .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Experimental Setup .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Mathematical Model
2.4 Methodology .
. 17
. .
2.5 Solver’s Grid Independency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6
. 17
2.7 Mathematical Modeling Validation for a Selection of Mass Transfer Corre-

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Impact of the Interfacial Area Coefficient

. . . . . . . . . . . . . . . . . . .

lations Based on Variable Interfacial Area Correlations . . . . . . . . . . . . . 18

CHAPTER 3

DATA-DRIVEN MODELING OF DIRECT-CONTACT PACKED-
BED DESALINATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 Benefit of Developing Data-Driven Surrogate Model of an HDH Desalination

.

System .

.
3.2 Exploratory Data Analysis
3.3 Machine Learning Tools Implemented to Develop the Data-Driven Surrogate

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
. 21
. . . . . . . . . . . . . . . . . . . . . . . . . . .

. .

. .

.

.

.

. .

. .

Model

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Performance Evaluation for Different Machine Learning Approaches . . . . . . 25
3.5 Sensitivity Analysis .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6 Performance Comparison of the Mathematical Model and Data-Driven Sur-

.

rogate Model

.

.

.

.

3.7 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
. 29

CHAPTER 4

Introduction .

A SELF-SUSTAINING WATER TREATMENT PLANT: INTEGRA-
TION OF SOLAR CHIMNEY AND WATER DESALINATION SYS-
TEM TOWARDS GREEN DESALINATION . . . . . . . . . . . . . . . 34
4.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Description of the solar driven water desalination chimney . . . . . . . . . .
. 38
. 40
4.3 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Methodology for Performance Assessment of a Solar Desalination Chimney . . 45
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5 Simulation Results
. 60
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .
4.6 Summary . .

.
. .

.

.

.

.

CHAPTER 5

MODELING OF SOLAR AIR HEATER INTEGRATED WITH DE-
SALINATION TECHNOLOGIES . . . . . . . . . . . . . . . . . . . . . 62

viii

.

. .

Introduction . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.1
5.2 Review of Related Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
. 67
5.3 Configuration and Description of the Fully-Insulated Experimental SAH . . .
. . 70
5.4 Computational Modeling and Validation of Three-Dimensional SAH Model
5.5 Conceptual Design of an Integrated SAH with Water Desalination System . . . 73
5.6

Impact of Cross-Sectional Area Variation on Thermal Efficiency of a SAH
Under Natural Convection Heat Transfer . . . . . . . . . . . . . . . . . . . . . 74
. 77

5.7 Modeling of the Proposed Integrated Desalination System . . . . . . . . . . .
5.8 Exploring Utilization of a Dual Solar Air-Water Heater as a Replacement for

Conventional SAH .
.

5.9 Summary .

.

.

.

.

.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
. 99

CHAPTER 6

.

.

.

ANALYSIS OF TRANSPARENT SOLAR WATER HEATER WITH
LIGHT SHIFTING MATERIAL: SIMULATION AND EXPERIMEN-
TAL EVALUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.1
.
Introduction .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Literature Review . .
. . . . . . . . . . . . . . . . . . . . 107
6.3 Design of a Semi-Transparent Solar Panel
6.4 Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.5 Experimental Setup .
6.6 Results and Analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.7 Feasibility of Potential Application as Greenhouse Roof . . . . . . . . . . . . . 135
. 140
6.8 Summary . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .

. .

CHAPTER 7

Introduction .

ASSESSING THE IMPACT OF INCOMING LIGHT SPECTRUM
ON INDOOR LETTUCE CULTIVATION . . . . . . . . . . . . . . . . 142
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
. 144

7.1
7.2 Plant Growth Computational Modeling . . . . . . . . . . . . . . . . . . . . .
7.3

Implementation of Regression Methodology to Account for the Impact of
Spectral Distribution and Intensity on Lettuce Growth . . . . . . . . . . . . . . 153
. 166

7.4 Summary and Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

.

.

CHAPTER 8

Introduction .

THE INTEGRATION OF GREENHOUSE AND WATER DESALI-
NATION SYSTEM FOR SUSTAINABLE FOOD AND WATER PRO-
DUCTION .
.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 169
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.1
. 170
8.2 Proposed Integrated Greenhouse . . . . . . . . . . . . . . . . . . . . . . . .
8.3 Methodology for Modeling the Integrated Greenhouse
. . . . . . . . . . . . . 171
8.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
. 183
8.5 Summary . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .

. .

.
.

.

.

CHAPTER 9

9.1 Summary . .
9.2 Remark .
.
.
9.3 Future Works

CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .
. .
.
.
.
. .
.

. 186
. 186
. 186
. 187

ix

BIBLIOGRAPHY . .

. .

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

x

LIST OF SYMBOLS AND ABBREVIATIONS

𝐴 area [𝑚2]

𝑎 albedo

𝑎 𝑝 specific area for packing material [m2 m−3]

𝑎𝑤 specific area for interfacial area [m2 m−3]

𝐴𝑐 surface area for greenhouse cover [m2]

𝐴𝑑 Surface area for greenhouse door [m2]

𝐴𝑔 Surface area for greenhouse ground [m2]

𝐴𝑝 Surface area for greenhouse plant [m2]

𝑐𝛼 conversion rate of CO2 to sugar

𝑐 𝛽 yield factor for lettuce cultivar

𝐶𝑝,𝑎 specific heat for greenhouse air [J kg−1 K−1]

𝐶𝑝,𝐺 specific heat for gas mixture [J kg−1 K−1]

𝐶𝑝,𝐿 specific heat for liquid [J kg−1 K−1]

𝐶𝑝,𝑝 specific heat for plant [J kg−1 K−1]

𝐷 molecular diffusion coefficient [m2 s−1]

𝐷𝑒 hydraulic diameter [m]

𝑑 diameter [m]

𝑑 𝑝 diameter of the packing material [m]

𝐹𝑟 Froude number [ 𝐿2𝑎
𝐿𝑔 ]
𝜌2

𝐸𝜈 energy required for the greenhouse ventilation [kW.hr]

𝑓 friction factor

𝑓𝑝ℎ𝑜𝑡 gross canopy photosynthesis mass rate [kg m−2 s−1]

𝑓𝑟𝑒𝑠𝑝 maintenance respiration mass rate [kg m−2 s−1]

𝐺 air mass flux [kg m−2 s−1]

𝐺𝑟 Grashof number [𝑔𝛽(𝑇𝑠 − 𝑇𝑎𝑚𝑏)𝛿3/𝜈2]

𝑔 gravity [m2 s−1]

xi

𝐻 height [m]

ℎ thermal coefficient [W m−2 K−1]

ℎ enthalpy [kJ kg−1]

ℎ𝑎 convective heat transfer between greenhouse floor and air [W m−2 K−1]

ℎ𝑏 convective heat transfer between greenhouse floor and the ground beneath it [W m−2 K−1]

ℎ𝑑 convective heat transfer for the greenhouse door to the environment [W m−2 K−1]

ℎ 𝑝𝑟

total convective and evaporative heat transfer coefficient between plant and greenhouse air [W
m−2 K−1]

ℎ𝑟 radiative heat transfer between plant and greenhouse air [W m−2 K−1]

ℎ 𝑓 𝑔 latent heat of vaporization [kJ kg−1]

ℎ𝐿 enthalpy of liquid [kJ kg−1]

ℎ𝑣 enthalpy of vapor [kJ kg−1]

𝐼 solar radiation [W m2]

𝐼𝐷𝐻𝐼 diffuse horizontal irradiance [W m−2]

𝐼𝐷𝑁 𝐼 direct normal irradiance [W m−2]

𝐼𝐺𝐻𝐼 global horizontal irradiance [W m−2]

𝑘 thermal conductivity [W m−1 K−1]

𝑘𝐺 mass transfer coefficient for gas in desalination process [m s−1]

𝑘 𝐿 mass transfer coefficient for liquid in desalination process [m s−1]

𝐿 water mass flux [kg m−2 s−1]

𝑀 molecular weight [kg kmol−1]

(cid:164)𝑚 mass flow [kg s−1]

(cid:164)𝑚𝑤 water mass flow rate for the transparent solar water heater [kg s−1]

𝑀𝑎 overall mass of the greenhouse air [kg]

𝑀𝑝 overall mass of the greenhouse plant [kg]

𝑁𝑏 number of baffles

𝑁𝑢 Nusselt number [ℎ𝐿/𝑘]

𝑃 overall pressure [kPa]

xii

𝑃𝑠𝑎𝑡 saturation pressure [kPa]

𝑃𝑟 Prandtl number [𝜇𝑐 𝑝/𝑘]

(cid:164)𝑄𝑙𝑜𝑠𝑠 loss energy for the transparent solar water heater [W]

(cid:164)𝑄𝑡

transmitted energy for the transparent solar water heater [W]

𝑅 universal gas [kJ kmol−1 K−1]

𝑅𝑎 Rayleigh number [𝐺𝑟 × 𝑃𝑟]

𝑅𝑒 Reynold number [ 𝐿
𝑎𝜇 ]

𝑟 overall reflectivity

𝑟 radius [m]

𝑟𝑔𝑟 growth rate of mass for plant structural material [g m−2 s−1]

𝑟 ∥ parallel component for reflectivity

𝑟⊥ perpendicular component for reflectivity

𝑆𝑡 overall irradiance [W]
𝜇
𝜌𝐷 ]

𝑆𝑐 Schmidt number [

𝑇𝑎 temperature of the gas mixture [◦C]

𝑇𝑎𝑚𝑏 temperature of the ambient [◦C]

𝑇 𝑓

temperature of the greenhouse floor [◦C]

𝑇𝑔 temperature of the greenhouse ground [◦C]

𝑇𝑝 temperature of the plant [◦C]

𝑇𝑝𝑎𝑐𝑘 temperature of the packed-bed medium[◦C]

𝑇𝐿 temperature of the liquid [◦C]

𝑈 heat transfer coefficient [W m−2 K−1]

𝑈𝑎𝑏𝑠 solar collector heat loss coefficient [W m−2 K−1]

𝑢 flow superficial velocity [m s−1]

𝑈𝐺 gas mixture heat transfer coefficient [W m−2 K−1]

𝑈𝐿 liquid heat transfer coefficient [W m−2 K−1]

𝑈𝑡 greenhouse heat transfer coefficient [W m−2 K−1]

xiii

𝑉𝑤 wind velocity [m s−1]

𝑋𝑛𝑠𝑑𝑚 non-structural dry mass for lettuce [g]

𝑋𝑠𝑑𝑚 structural dry mass for lettuce [g]

𝑊 width [m]

(cid:164)𝑊𝑡𝑢𝑟𝑏 Turbine Power Generation [W]

𝑊 𝑒 Webber number [

𝐿2
𝜌𝐿 𝜎𝐿 𝑎 ]

Greeks:

𝛼 overall absorptance

𝛼𝑎 air volume fraction [m3 m−3]

𝛼𝐼 solar collector absorption coefficient

𝛼𝑔 absorptance for greenhouse floor

𝛼𝐿 liquid volume fraction [m3 m−3]

𝛼𝑝 absorptance for plant

𝛼⊥ absorptance for perpendicular component

𝛼∥ absorptance for parallel component

𝛽 inclination angle [◦]

𝛽 thermal expansion coefficient [K−1]

𝛿 declination angle [◦]

𝜀 emissivity of the plant

𝜀 desalination effectiveness

𝛾 heat capacity ratio

𝛾𝑟 relative humidity

𝜇 dynamic viscosity [kg m−1 s−1]

𝜈 kinematic viscosity [kg m−1]

𝜔 hour angle [◦]

𝜔 humidity ratio [kg vapor/kg dry air]

𝜙 viscosity correction factor

xiv

𝜎𝑐 critical surface tension of the packing material [N m−1]

𝜎𝐿 surface tension of liquid [N m−1]

𝜏 overall transmittance

𝜏⊥ perpendicular component for transmittance

𝜏∥ parallel component for transmittance

𝜃𝑖 beam incident angle [◦]

𝜌 overall reflectance

𝜌⊥ perpendicular component of reflectance

𝜌∥ parallel component of reflectance

𝜌𝑎 density of gas mixture[kg m−3]

𝜌𝐿 density of liquid [kg m−3]

𝜌 𝑝𝑎𝑐𝑘 density of packed-bed medium [kg m−3]

Subscript:

𝑎 air

𝑎𝑏𝑠 absorbed

𝑎𝑚𝑏 ambient

𝑏 bottom PCB layer

𝑐𝑜𝑛𝑑 conduction

𝑐𝑜𝑛𝑣 convection

𝑓 air flow

𝑔 air gap

𝐺 air/vapor mixture

𝑔𝑟 ground

𝐿 liquid

𝑖𝑛 inlet

𝑜𝑢𝑡 outlet

𝑝𝑎𝑐𝑘 packed-bed

xv

𝑟𝑎𝑑 radiation

𝑠𝑎𝑡 saturated state

𝑠𝑘 𝑦 sky

𝑡 top PCB layer

𝑣 vapor

xvi

CHAPTER 1

INTRODUCTION

1.1 Context

Water is the most abundant natural substance on our planet. Every element in the earth’s

ecosystem depends on it for its continued survival. Although it covers over three-quarters of

the earth’s surface, around 97% of that is saline water which leaves it almost inaccessible, and

small amounts of freshwater.

In the last couple of decades, due to continuous advancements

in technologies caused by the industrial revolution, escalating material consumption, and world

population growth, freshwater resources have become scarce. In 2012, United Nations Environment

Program (UNEP) published a report regarding worldwide access to freshwater resources (Shatat

et al., 2013). According to the report, at that time, one-third of the world’s population lived in

countries that didn’t have adequate freshwater supply to sustain life, and by 2025, over 66 % of the

population will face water scarcity. The World Health Organization estimated that over one billion

people who live in rural and remote areas lack access to purified clean water (Qiblawey and Banat,

2008). One of the early solutions for the freshwater challenge was the desalination of saline water

since it is distributed more evenly around the world, unlike freshwater where most of the resources

are in the form of icebergs at the earth’s poles.

The amount of attention focused on the desalination solution led to huge improvements for the

existing technologies such as solar still, solar pond, and membrane distillation. Humidification-

dehumidification was one of the technologies that were comprehensively studied as an economically

viable desalination technology. The technology was developed based on the idea of heat exchange

between two different flows. Two of the main advantages of such a system were the possibility of

using solar energy as the heating source and a higher operating range. Several researchers aimed to

improve the performance of HDH through several enhancements, including the addition of a heat

transfer wall between components (Narayan et al., 2011), increasing saturation pressure for water

(Arabi and Reddy, 2003), and utilizing packed beds for direct contact between liquids and gases

within each component (Li et al., 2006). Before the implementation of the packed-bed for the HDH

1

desalination system, most of the experimental setups (Al-Hallaj et al., 1998; Müller-Holst et al.,

1999; Bourouni et al., 2001) were developed based on the idea of thin layer film condensation,

which wasn’t an efficient method. To improve condensation efficiency, Li et al. (2006), and Klausner

et al. (2004) analyzed a direct-contact packed-bed HDH desalination system and came up with the

mathematical governing equation that described the behavior of the system under the steady-state

assumption. Later on, their research group built an experimental setup to validate their numerical

result. Alnaimat et al. (2011) updated the mathematical model to accommodate the transient

behavior of the packed-bed HDH system and performed experimental studies for its validation.

A desalination system usually requires an energy source. For traditional desalination systems,

fossil fuels were commonly used for the preheating of the flow for each component. The environ-

mental threat caused by the consumption of conventional fossil fuels led the researchers to focus

on alternative energy sources for those systems or design new systems capable of utilizing cleaner

energy sources. Solar ponds and solar stills were two categories of desalination systems that utilized

solar energy. In addition, several desalination systems were integrated with solar energy.

1.2 Related Technologies

There are two major categories of integrated desalination systems that use solar energy:

1. The technologies that convert solar energy to electricity and use it in desalination plants fall

under the first group. Membrane distillation systems and reverse osmosis systems are two

examples of this technology. These systems often include solar collectors and desalination

systems as their main components.

2. Solar energy as a heating source is another type of integration. Solar still, solar pond, and

humidification-dehumidification are three examples of this category of technologies. These

technologies work by evaporating water and then condensing it at a later point.

The following is a review of some of the desalination and freshwater production technologies

currently in use worldwide.

2

1.2.1 Membrane Distillation

Membrane distillation (MD) is a relatively novel technology that is being researched globally

as a low-cost, energy-efficient method for separation.

It works by evaporating a brine solution

and condensing the vapor to produce fresh water on the cold side. MD has several advantages

over conventional separation processes, including a lower working temperature and pressure, less

interaction with the membrane, and less space required for vapor.

Bodell (1966) described the earliest version of MD. A brine solution tank and an array of

parallel tabular silicon membranes formed this design. Weyl (1964) presented a novel design to

increase the efficiency of desalination in MD by substituting a porous hydrophobic membrane for the

original membrane and thereby reducing the demand for an external energy source. Additionally,

he developed a multistage MD that is capable of recovering and reusing vaporization heat.

Although defining the MD process is straightforward, there are numerous designs for the

location of condensing surface in the MD process, including direct contact with the membrane

(DCMD), a condensing surface separated by an air gap (AGMD), sweeping gas (SGMD), and a

vacuum on the condensing side of the membrane (VMD), which are presented in Figure 1.1.

1.2.2 Reverse Osmosis

Historically, thermal procedures were the primary method of desalinating water; however, with

the advancement of membrane technology and the extremely high capital and operating costs

associated with such techniques, membrane-based desalination technologies have become more

desirable. Reverse Osmosis (RO) is a cutting-edge technology that is more dependable when

dealing with brackish and seawater (salinity range around 0.5 𝑔/𝐿 up to 30 𝑔/𝐿). At the moment,

approximately half of the world’s desalinated water is produced by RO (Goh et al., 2018).

In reverse osmosis (figure 1.2c), pressure is applied to either stop (external pressure equal to the

difference in osmotic pressure) or force (external pressure greater than the difference) water flow

in the opposite direction overcoming the existing osmotic pressure gradient caused by the chemical

potential gradient of the existing solutes.

The process’s primary advantage is its ease of adapting to the surrounding environment. The

3

(a) Direct Contact Membrane Distillation

(b) Air Gap Membrane Distillation

(c) Sweeping Gas Membrane Distillation

(d) Vacuum Membrane Distillation

Figure 1.1 Different configuration for the membrane distillation process. The hydrophobic mem-
brane allows the system to treat saline water.

primary constraint and greatest obstacle in the RO process is the fouling effect, which reduces the

membrane’s functionality and lifetime. Fouling happens when pores get blocked or when solutes

adsorb (Van der Bruggen et al., 2003). To avoid the fouling effect on the membrane, it is critical to

pre-treat the incoming solution using chemical treatment, filtration, and other separation methods

(Chian et al., 2007). Additionally, the fouling effect can be avoided by raising the feed pressure.

1.2.3 Solar Still

Solar still has unique advantages for use in locations with limited access to fresh water and

supply shortages due to its ease of construction, ease of operation and maintenance, and lack of

environmental impact. On the other hand, the procedure produces significantly less freshwater than

other methods, rendering it inefficient (Velmurugan and Srithar, 2011). Apart from that, solar still

desalination plants demand a significant quantity of space.

4

(a) Original state of the system

(b) Equilibrium through the Osmosis

(c) Reverse Osmosis process

Figure 1.2 Osmosis and Reverse Osmosis Processes. As shown in the figure, the applied pressure
pushes the water through the semi-permeable membrane, thereby removing the salinity from the
water.

Solar irradiation is still used as a sustainable and clean energy source to evaporate saline water

and afterward condense the vapor. As illustrated in figure (1.3a), the saline water in the basin

absorbs solar energy and evaporates. The vapor will rise until it reaches the glass cover’s inner

side. It will then condense and accumulate on the other side of the partition figure 1.3b.

1.2.4 Solar Pond

The primary motivation for developing a solar pond was to create a device capable of collecting

and storing solar energy. The accumulated energy can be used for any desired thermal procedure in

the future (including desalination plants). The solar pond’s mechanism is straightforward. Within

the pond, the flow is often saline water with a salt concentration ranging from 20 % to 30 % at

the bottom to nearly none at the top. To maintain this gradient, fresh and saline water will be

5

(a) Complete

(b) Cropped

Figure 1.3 Basic design for solar still. As shown in the figure, the water evaporates through the
absorption of solar energy.

continuously added from the pond’s top and bottom.

The salt gradient will establish and maintain three distinct zones within the pond: the upper

convective zone (UCZ), the non-convective zone (NCZ), and the lower convective zone (LCZ)

(Figure 1.4). Water salinity is low in the UCZ because the composition is similar to that of

freshwater. The salinity increases with depth in the NCZ, and due to the presence of a salinity

gradient, there is no heat convection. Without heat convection, the temperature will rise uniformly

with depth. The LCZ will have a consistent and high salt concentration, similar to brine water.

This is the zone that stores solar energy. To maximize solar radiation absorption, the inner surface

of the pond is painted black. Typically, the solar pond will retain heat for one day.

1.2.5 Humidification- Dehumidification Process (HDH)

The humidification-dehumidification (HDH) desalination method attempts to recreate the nat-

ural water cycle; thus, the HDH desalination process comprises primarily of a humidifier, a

dehumidifier, and a heat source (for the evaporation process in addition to pre-warming flows). The

humidification process involved contacting water (ideally brine) with unsaturated air, diffusing wa-

ter vapor into the air, and increasing the airflow’s humidity. In the dehumidifier, moist air interacts

6

Figure 1.4 A schematic diagram of salt gradient solar pond (SGSP). As shown in the figure, the
system operates by creating three zones with different levels of salinity.

with cold water, lowering the temperature of the air and causing some water vapor to condense.

Numerous HDH studies were conducted with the objective of examining various process con-

figurations. Due to the preference for air with a higher water vapor absorption capacity (higher

temperature for water or air), humidifier systems can be classed as water- or air-heated. Following

that, these systems can be classified by the open/closed cycle of each flow. Furthermore, the HDH

can be classified into two main classes based on their mode of circulation: natural and forced.

Humidifiers (evaporators) are classified into four distinct categories:

1. Spray tower: consists of a cylindrical cylinder into which water is sprayed from the top

(significant pressure drops caused by the spray nozzle render this configuration inefficient)

and the air is circulated from the bottom (Kreith and Bohem, 1988).

2. Packed-bed: The packed-bed configuration was chosen to minimize pressure drop at the

water’s front (Amer et al., 2009).

3. Wetted-wall tower: Within a pipe, a thin layer of water flows downward and interacts with

the air (could be counter-current or co-current) (Müller-Holst et al., 1998).

4. Bubble-column: The air is injected into a water bed, and the water is trapped inside the air

bubble (El-Agouz and Abugderah, 2008).

A dehumidifier is comparable to a heat exchanger in its function. A study examined the

double pipe and shell and tube heat exchanger designs as possible configurations for the HDH’s

7

Figure 1.5 A schematic diagram of direct contact HDH system (Alnaimat et al., 2011). Within the
scope of this study, the electric heater will be replaced with solar thermal systems.

dehumidifier component (Muthusamy and Srithar, 2015). Another study examined the performance

of a bubble column dehumidifier under a variety of operating circumstances, including pressure

and varying superficial velocity for air and liquid (Sharqawy and Liu, 2015). According to the

result of the study, raising the superficial velocity of air improves heat transfer and dehumidifier

efficiency significantly.

The research focusing on HDH desalination plants provides a clear picture of how to determine

the ideal design and operating parameters for HDH systems. They concentrated mostly on GOR,

mass flow rates, and the fluid’s temperature in order to maximize water output and minimize energy

use. The GOR is defined as the proportion of thermal energy consumed during the desalination

process (Equation (1.1)).

𝐺𝑂𝑅 =

(cid:164)𝑚𝑤Δℎ
𝑄 ℎ𝑒𝑎𝑡

(1.1)

Alnaimat et al. (2021) has reviewed new improvements in the technology of HDH desalina-

tion. He stated that by integrating solar stills/chimneys into the desalination system and using

8

heat recovery technologies, performance and freshwater yield may be increased (multi-stage heat

recovery has the optimum performance but is not economically feasible). Solar air/water heaters

have been suggested as a supplement to the HDH desalination plant in order to pre-heat the flow and

alleviate the process within the humidifier. The solar air heater integrated with HDH was investi-

gated under a variety of operating conditions, including varying solar irradiances, varying ambient

temperatures, and varying inlet conditions, and it was concluded that the mass flow rate of air and

solar irradiation had a significant effect on performance (Ben-Amara et al., 2005). Another study

examined an integrated HDH with a solar air heater and a phase change material energy storage and

discovered consistent performance throughout the day, which increases the desalination plant’s ef-

ficiency (Summers et al., 2012). A cost-benefit analysis of a combined HDH and solar water heater

has determined that this configuration is more suitable for decentralized freshwater production in

dry locations (Zamen et al., 2009). A study has examined an integrated HDH desalination plant

with solar air and water heater as the supplement heat source (Yuan et al., 2011). According to the

study, the efficiency of solar air heaters would be critical in making this setup economically viable.

1.3 Objective

The aim of this dissertation is to design and implement an integrated HDH solar desalination

system. The governing equations for the desalination system were derived based on mass and energy

balances for each component. On the basis of the experimental setup in the Engineering Research

Complex, the HDH mathematical model has been validated. Following the implementation of

the validated model, the performance of desalination under various operating conditions will be

predicted. A number of existing structures have been extensively investigated in order to assess

the feasibility of the integration of solar energy, including solar chimney power plant (SCPP), solar

air heater (SAH), and greenhouse. A number of experimental setups have been constructed for the

SAH and SWH. Data from the experimental platforms have been used to validate numerical models

for those systems.

1.4 Manuscript Organization

The manuscript has been organized in the following order:

9

• Numerical Modeling of Direct-Contact Packed-Bed Desalination Units: Validate the

mathematical model of the HDH using experimental data and try to find the best correlations

that result in accurate prediction.

• Data-Driven of Direct-Contact Packed-Bed Desalination Units: Developing a data-driven

model based on experimental data as a surrogate model for the mathematical model.

• A Self-Sustaining Water Treatment Plant: Integration of Solar Chimney and Water

Desalination System: Using a validated mathematical model for a solar chimney, study-

ing the performance of integrated solar desalination chimney for different solar chimneys

geometries.

• Modeling of Solar Air Heater Integrated with Desalination Technologies: Developing

and validating 1D and 3D models of solar air heater, investigating the desalination perfor-

mance of the proposed configuration, and evaluating the potential of additional water flow to

solar air heater conventional structure for desalination.

• Analysis of Transparent Solar Water Heater with Light Shifting Material: Simulation

and Experimental Evaluation: Experimental and computational analysis are carried out

for a transparent solar water panel coupled with NIR absorbing film. The thermal and optical

models are validated and later used for predicting the behavior of a desalination unit with a

greenhouse.

• Assessing the Impact of Incoming Light Spectrum on Indoor Lettuce Cultivation: The

impact of spectral distribution is quantified on lettuce using an improved dynamic growth

model with a new correlation for a light-use efficiency parameter that is impacted by variation

in irradiance spectra.

• The Integration of Greenhouse and Water Desalination System for Sustainable Food

and Water Production: A model is developed to predict the behavior of the greenhouse for

lettuce cultivation that is coupled with a water treatment unit and a transparent solar water

10

panel with a NIR cut-off film. The system’s behavior is evaluated for a region near Phoenix,

AZ, for indoor cultivation of lettuce.

• Conclusion: This chapter provides an overview of the summary, remarks, and future works

for this dissertation.

11

CHAPTER 2

NUMERICAL MODELING OF DIRECT-CONTACT PACKED-BED DESALINATION
UNITS

The content of this chapter was published in the following conference proceeding:

Evaluation of Mass Transfer and Interfacial Area Correlations in Direct Contact Packed-

Bed: Comparison of Correlations, by Mahyar Abedi, Parnab Saha, Xu Tan, James F. Klaus-

ner, and André Bénard, submitted to the 2nd International Conference on Fluid Flow and Thermal

Science (ICFFTS’21), Nov. 24-26, 2021, https://doi.org/10.11159/icffts21.118.

2.1

Introduction

According to the United Nations Environment Programme (UNEP), the global water crisis is

set to worsen in the coming years (Shatat et al., 2013), and by the year 2050, over a quarter of the

earth population will experience difficulties in accessing freshwater resources for at least one month

a year. In order to address the world freshwater deficiency challenge, desalination technologies

provide the capability to harness the 97 percent saline water resources and produce fresh water.

Humidification-dehumidification (HDH) with direct-contact packed-bed material is one of the most

cost-effective water treatment and desalination approaches. Significant advantages of direct contact

HDH are low operating or capital costs, minimal pressure drop, and the utilization of low-grade

heat sources. The addition of the packed-bed media to an HDH system would further improve the

desalination performance by augmenting the interfacial area between air and water flows.

Several researchers have studied HDH systems, including Goosen et al. (2003) and El-Dessouky

(1989), who introduced a mathematical model validated by experiments. These models are primar-

ily based on the assumption of film condensation. However, more recent research has developed

distinct mathematical models based on fundamental heat and mass transfer principles, such as the

work of Alnaimat et al. (2011) and Li et al. (2006). These models employ empirical correlations

to estimate the mass transfer coefficient of liquid and air within the packed bed. The use of em-

pirical correlations for various parameters has a drawback of restricting the validity range of the

mathematical model due to the limitations of each correlation.

12

The first part of this chapter focuses on examining the impact of various empirical correlations

for mass transfer and interfacial area on the precision of the mathematical model. To this end,

an experimental setup was meticulously built to validate the simulated outcomes for a direct-

contact packed-bed dehumidifier. Subsequently, several data-driven models are developed utilizing

different regression methods, and their accuracies are compared with the validated mathematical

model to determine whether a high-fidelity data-driven model could be considered as a substitute

for the studied mathematical model.

2.2 Experimental Setup

To comparatively study the mass transfer coefficients and interfacial area, an experimental

device was set up for a direct contact condenser using a packed bed (Figure 2.1). Cooling water

with a temperature range of 20 − 22 ◦𝐶 was sprayed from the top with sprinklers. An “Aquatec”

pump was placed to provide the condenser with the desired flow rate of around 23 𝑔/𝑠 from a water

tank to the condenser chamber made of the CPVC pipe. The total height of the CPVC pipe was 1 𝑚,

and 0.5 𝑚 of its height was filled with packed-bed. The packed-bed was made of a 3D regular array

of square-printed polycarbonate material. The specific area was 267 𝑚2/𝑚3. The packed-bed had

an inner diameter of 0.14 𝑚, and its effective diameter was 17 𝑚𝑚 when orientation was vertical.
Other required properties of the packing material include the specific heat capacity is 1.12 𝑘 𝐽

𝑘𝑔𝐾 ,
𝑘𝑔
𝑚3 , and the void fraction is 87.8%. Finally, inlet air was pushed through the

the density of 1200

packed bed. Two valves were used to control the flow rate of air. Several T-type thermocouples

were used to measure temperatures at different locations of the packed-bed. To provide steam, a

steam generator was utilized. To prevent heat loss from the setup, the inlet of air vapor has been

covered with insulation. A Labjack data acquisition system, along with LabVIEW, was used for

the temperature measurements.

2.3 Mathematical Model

The mathematical model developed by Alnaimat et al. (2011) for direct contact packed-bed

humidification-dehumidification desalination system. Through considering mass balance for water

vapor, and energy balance for liquid, gas, and packed-bed resulted in governing equations for the evo-

13

Figure 2.1 Schematic diagram of a direct-contact packed-bed dehumidifier utilized for validation
of the mathematical model.

lution of humidity (Equation (2.1)), liquid temperature (Equation (2.2)), air temperature(Equation

(2.3)), and packed-bed temperature (Equation (2.4)), respectively.

𝜕𝜔
𝜕𝑧

=

𝜕𝑇𝑎
𝜕𝑧

𝑃
𝑃 − 𝑃𝑠𝑎𝑡 (𝑇𝑎)

(cid:16)

𝜔

𝑏 − 2𝑐𝑇𝑎 + 3𝑑𝑇 2
𝑎

(cid:17)

𝜕𝑇𝐿
𝜕𝑡

=

𝐿
𝜌𝐿𝛼𝐿

𝜕𝑇𝐿
𝜕𝑧

−

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 − ℎ𝐿(cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝,𝐿

+

𝑈𝑎𝑤 (𝑇𝑎 − 𝑇𝐿)
𝜌𝐿𝛼𝐿𝐶𝑝,𝐿

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝐿(cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝,𝐿

+

(2.1)

(2.2)

𝜕𝑇𝑎
𝜕𝑡

=

−𝐺
𝜌𝑎𝛼𝑔

𝜕𝑇𝑎
𝜕𝑧

−

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 (𝑇𝐿) − ℎ𝐿 (𝑇𝑎)(cid:1)
𝜌𝑎𝛼𝑔𝐶𝑝,𝐺 (1 + 𝜔)

−

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑎 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌𝑎𝛼𝑔𝐶𝑝,𝐺 (1 + 𝜔)

−

𝑈𝑎𝑤 (𝑇𝑎 − 𝑇𝐿)
𝜌𝑎𝛼𝑔𝐶𝑝,𝐺 (1 + 𝜔)
(2.3)

14

𝜕𝑇𝑝𝑎𝑐𝑘
𝜕𝑡

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑎 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝,𝑝𝑎𝑐𝑘

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝐿(cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝,𝑝𝑎𝑐𝑘

−

=

(2.4)

In the Equation (2.1), 𝑏, 𝑐, and 𝑑 are constants used for the empirical correlation of water
saturation pressure in the form of 𝑃𝑠𝑎𝑡𝑇𝑎 = 𝑎exp (cid:0)𝑏𝑇𝑎 − 𝑐𝑇 2
(cid:1) where 𝑎 = 0.611379 (𝑘 𝑃𝑎),
𝑏 = 0.0723669 (cid:0)𝐾 −1(cid:1), 𝑐 = 2.78793 × 10−4 (cid:0)𝐾 −2(cid:1), and 𝑑 = 6.76138 × 10−7 (cid:0)𝐾 −3(cid:1). The overall heat
transfer coefficient for gas was approximated through 𝑈𝐺 = 𝑘𝐺 (cid:0)𝜌𝐺𝐶𝑝𝐺
(cid:16)

(cid:1) 1/3 (cid:16) 𝐾𝐺
𝐷𝐺

, while the heat

transfer coefficient for liquid was calculated according to 𝑈𝐿 = 𝑘 𝐿

. Using these

𝑎 + 𝑑𝑇 3
𝑎

(cid:17) 1/2

(cid:17) 2/3

𝜌𝐿𝐶𝑝 𝐿

two correlations, the total heat transfer coefficient was computed using 𝑈 =

𝐾𝐿
𝐷 𝐿
(cid:16) 1
𝑈𝐿

(cid:17) −1

+ 1
𝑈𝐺

. Most

of the parameters are well-defined; however, the value for the mass transfer coefficient (𝑘 𝐿, 𝑘𝐺)

and the interfacial area (𝑎𝑤) were approximated based on empirical correlations. The correlations

investigated for the mass transfer coefficient include Onda et al. (1968) (Equations (2.5) - (2.6)),

Van Krevelen and Hoftijzer (1948) (Equations (2.7) - (2.8)), Shi and Mersmann (2011) (Equations

(2.9) - (2.10)), Billet and Schultes (1993) (Equations (2.11) - (2.12)), and Zech and Mersmann

(1979) (Equations (2.13) - (2.14)).

𝑘 𝐿 =

0.0051
(cid:0)𝑎 𝑝𝑑 𝑝(cid:1) −0.4

(cid:18) 𝜇𝐿𝑔
𝜌𝐿

(cid:19) 1/3 (cid:18) 𝜌𝐿𝑢𝐿
𝑎𝑤 𝜇𝐿

(cid:19) 2/3

𝑆𝑐−0.5
𝐿

𝑘𝐺 = 𝑐𝐺

(cid:32) 𝐷𝐺
𝑎 𝑝𝑑2
𝑝

(cid:33) (cid:18) 𝜌𝐺𝑢𝐺
𝑎 𝑝 𝜇𝐺

(cid:19) 0.7

𝑆𝑐1/3
𝐺

𝑘 𝐿 = 0.015

(cid:19) 2/3

(cid:18) 𝜌𝐿𝑢𝐿
𝑎𝑤 𝜇𝐺

𝑆𝑐1/3
𝐿

𝐷 𝐿

(cid:105) 1/3

(cid:104) 𝜇2
𝐿
𝐿𝑔
𝜌2

𝑘𝐺 = 0.2

(cid:19) 0.8

𝐷𝐺
𝑑𝑐

(cid:18) 𝜌𝐿𝑢𝐿
𝑎 𝑝 𝜇𝐿

𝑆𝑐1/3
𝐺

√︄

𝑘 𝐿 = 0.86

6𝐷 𝐿
𝜋𝑑 𝑝𝑒

(cid:118)(cid:116)𝑢1.2

𝐿 𝑔1.3𝜎1.2

𝐿 𝜀1.2 (1 − 0.93 cos 𝜃)2
𝐿 𝜌0.3
𝜈1.4

𝐿 𝑎2.4
𝑝

𝑘𝐺 = 𝑐𝐺

𝐷𝐺
𝑑 𝑝𝑒

(cid:18) 𝜌𝐺𝑢𝐺 𝑑 𝑝𝑒
𝜇𝐺

(cid:19) 2/3

𝑆𝑐1/3
𝐺

15

(2.5)

(2.6)

(2.7)

(2.8)

(2.9)

(2.10)

𝑘 𝐿 = 𝑐𝐿

(cid:18) 𝜌𝐿𝑔
𝜇𝐿

(cid:19) 1/6 (cid:18) 𝐷 𝐿
𝑑ℎ

(cid:19) 0.5 (cid:18) 𝑢𝐿
𝑎 𝑝

(cid:19) 1/3

𝑘𝐺 = 𝑐𝐺

𝑎0.5
𝑝 𝐷𝐺
√︁𝑑ℎ (𝜀 − 𝑙ℎ)

(cid:18) 𝜌𝐺𝑢𝐺
𝑎 𝑝 𝜇𝐺

(cid:19) 3/4

𝑆𝑐1/3
𝐺

𝑘 𝐿 = 𝑐𝐿

√︄

6𝐷 𝐿
𝜋𝑑 𝑝𝑒

(cid:32) 𝜌𝐿𝑔𝑑2
𝑝𝑒
𝜎𝐿

(cid:33) −0.15 (cid:18) 𝑢𝐿𝑔𝑑 𝑝𝑒

(cid:19) 1/6

3

𝑘𝐺 = 𝑐𝐺

𝐷𝐺
𝑑 𝑝

𝜀 + 0.12
𝜀 (1 − 𝜀)−1

(cid:18) 𝜌𝐺𝑢𝐺 𝑑 𝑝
(1 − 𝜀) 𝜇𝐺

(cid:19) 2/3

𝑆𝑐1/3
𝐺

(2.11)

(2.12)

(2.13)

(2.14)

Moreover, several correlations for the interfacial area are investigated to see the impact of

interfacial area value on the numerical result and include Onda et al. (1968) (Equation (2.15)),

Puranik and Vogelpohl (1974) (Equation (2.16)), Kolev (1976) (Equation (2.17)), Bravo and Fair

(1982) (Equation (2.18)), and Billet and Schultes (1993) (Equation (2.19)).

(cid:32)

(cid:34)

𝑎𝑤 = 𝑎 𝑝

1 − exp

−1.45

(cid:19) 0.75

(cid:18) 𝜎𝑐
𝜎𝐿

𝑅𝑒0.1

𝐿 𝐹𝑟 −0.05

𝐿 𝑊 𝑒0.2
𝐿

(cid:35) (cid:33)

𝑎𝑤 = 1.045𝑎 𝑝

(cid:18) 𝜌𝐿𝑢𝐿
𝜇𝐿𝑎 𝑝

(cid:19) 0.041 (cid:32) 𝜌𝐿𝑢2
𝐿
𝜎𝐿𝑎 𝑝

(cid:33) 0.133 (cid:18) 𝜎𝑐
𝜎𝐿

(cid:19) 0.182

𝑎𝑤 = 0.583𝑎 𝑝

(cid:32) 𝜌𝐿𝑔
𝑝𝜎𝐿
𝑎2

(cid:33) 0.49 (cid:32) 𝑢2
𝐿𝑎 𝑝
𝑔

(cid:33) 0.196

(cid:0)𝑎 𝑝𝑑 𝑝(cid:1) 0.42

𝑎𝑤 = 0.498𝑎 𝑝

(cid:18) 𝑢𝐿 𝜇𝐿
𝜎𝐿

6𝜌𝐺𝑢𝐺
𝑎 𝑝 𝜇𝐺

(cid:19) 0.392 𝜎0.5
𝐿
𝑍 0.4
𝑡

𝑎𝑤 = 1.5 (cid:0)𝑎 𝑝𝑑ℎ(cid:1) −0.5

(cid:18) 𝜌𝐿𝑢𝐿 𝑑ℎ
𝜇𝐿

(cid:19) −0.2 (cid:32) 𝜌𝐿𝑢2
𝐿 𝑑ℎ
𝜎𝐿

(cid:33) 0.75 (cid:32) 𝑢2
𝐿
𝑔𝑑ℎ

(cid:33) −0.45

16

(2.15)

(2.16)

(2.17)

(2.18)

(2.19)

2.4 Methodology

To solve the system of governing equations for the direct-contact packed-bed dehumidifier,

a finite differences scheme is employed. Specifically, a second-order approximation is used to

discretize the partial differences in Equations (2.1) – (2.4) throughout the entire domain. To simplify

the calculations, the quasi-steady state assumption is utilized. A MATLAB program is developed

to calculate the various parameters used in the equations and to solve the coupled non-linear

ordinary differential equations, which allows for efficient and accurate numerical simulations of the

dehumidifier’s behavior for various operating conditions. Next, the solver’s grid independency is

investigated, and the mathematical model is validated using experimental data.

2.5 Solver’s Grid Independency

The dependence of the solver on the grid resolution is examined first. The simulation findings

are almost independent of the number of nodes, based on Table 2.1, and the insignificant change in

outlet temperature for varied grid resolutions is observed.

Interfacial area correlation Mass transfer coefficient

Nodes Number

Onda
Onda
Onda
Onda
Onda
Bravo
Puranik
Kolev
Billet

Onda
Van Krevelen
Shi
Billet
Zech
Van Krevelen
Shi
Zech
Billet

51

201

51
201
101
Liquid temperature
29.98 29.98 29.98
29.10 29.10 29.10
29.97 29.97 29.96
29.97 29.97 29.97
29.98 29.97 29.97
29.10 29.10 29.10
29.97 29.97 29.96
29.98
29.97 29.97 29.97 22.41

101
Air temperature
22.23 22.21 22.20
34.75 34.74 34.73
22.49 22.47 22.46
22.41 22.39 22.39
22.38 22.36 22.36
34.75 34.74 34.73
22.49 22.47 22.46
29.97 29.97 22.38 22.36 22.36
22.39 22.39

Table 2.1 Summary of mesh independence study performed for 𝐿 = 1.4𝑘𝑔/𝑚2𝑠, 𝐺 = 0.1𝑘𝑔/𝑚2𝑠,
𝑇𝐿,𝑖𝑛𝑙𝑒𝑡 = 21◦𝐶 and 𝑇𝑎,𝑖𝑛𝑙𝑒𝑡 = 68◦𝐶

2.6

Impact of the Interfacial Area Coefficient

Equations (2.15) - (2.19) and (2.5) - (2.6) were used for interfacial area and mass transfer

coefficient to study the effect of interfacial area on the resulting temperature of the liquid and air,

respectively. The interfacial area varies across the packed bed, as seen in Figure 2.2. Because the

liquid and gas velocities are not very high, the interfacial area values change greatly depending on

17

which correlation is used. However, based on the numbers in Table 2.2, we can observe that the

change in the interfacial area value has no effect on the outlet temperature.

Correlation Average 𝐴𝑤 Liquid (◦𝐶) Error for liquid (%) Air (◦𝐶) Error for air (%)

Onda
Bravo
Puranik
Kolev
Billet

126.99
4.37
81.91
27.45
45.86

29.985
29.984
29.985
29.985
29.985

—-
0.003
0.003
0.001
0.000

21.654
21.663
21.652
21.653
21.653

—-
0.040
0.051
0.006
0.002

Table 2.2 Outlet temperature values found for different interfacial area correlations. As illustrated
above, the significant variation in the average value of the interfacial area has a minimal impact on
the outlet temperature of water or air.

Figure 2.2 Variation of the interfacial area value using different correlations (Equations (2.15)-
(2.19)). Based on the result of Table 2.2, it is stated the value of the interfacial area has a small
impact on the thermal behavior of a direct-contact packed-bed dehumidifier.

2.7 Mathematical Modeling Validation for a Selection of Mass Transfer Correlations Based

on Variable Interfacial Area Correlations

When comparing simulation and experiment results, it is clear that Onda and Billet’s correlations

predict air temperature (5 % error) and liquid temperature (9 % error) more precisely than others

(Table 2.3). Furthermore, while Shi and Zech’s correlations aren’t as accurate as Onda’s, their

18

errors are within 10 % of one another. Furthermore, Figure 2.3 shows that Van Krevelen performs

better for almost half of the liquid experimental data, but there are large inaccuracies when the

correlation is used to predict air temperature; this can be seen in Figure 2.4. Moreover, it can be

seen that as the air temperature at the input rises, so does the error in estimating liquid temperature.

Non-uniform flow, water bridging, heat losses to the surroundings for experimental setup, and

misrepresentation of packed-bed geometry are some of the potential reasons for the numerical

error of the mathematical model. Within the rest of this chapter or the following chapters, Onda’s

correlation for mass transfer coefficient (Equations (2.5)-(2.6)) and interfacial area (Equation (2.15))

for predicting the performance of a desalination unit through utilizing the investigated mathematical

model developed by Alnaimat et al. (2011).

Figure 2.3 Comparison of experimental data for different correlations for values of liquid outlet
temperature obtained by varying the inlet air temperature (inlet temperature for water is constant).
Most correlations predicted adequate measured values except for the Van Krevelen correlation.

19

Figure 2.4 Comparison of predicted outlet air temperature with experimental data for varying inlet
air temperature. Most correlations predicted adequate measured values except for the Van Krevelen
correlation.

Onda Van Krevelen

Liquid % 9.39
5.15

Air %

14.65
68.00

Shi Billet Zech
9.45
9.40
9.49
6.10
5.42
6.59

Table 2.3 Average numerical error for predicting gas and liquid temperature considering different
mass transfer correlations.

20

CHAPTER 3

DATA-DRIVEN MODELING OF DIRECT-CONTACT PACKED-BED DESALINATIONS

The content of this chapter was published in the following conference proceeding:

A Comparison of the Performance of a Data-Driven Surrogate Model of a Dehumidifier

with Mathematical Model of Humidification-Dehumidification System, by Mahyar Abedi,

Xu Tan, James F. Klausner, Michael S. Murillo, and André Bénard, submitted to the AIAA

SciTech 2023 Forum, Jan. 23-27, 2023, https://doi.org/10.2514/6.2023-2329

3.1 Benefit of Developing Data-Driven Surrogate Model of an HDH Desalination System

Let’s once more take a look at the performance of the mathematical model. Figures 3.1a and

3.1b represented the mathematical model prediction for water and air temperature at the outlet of the

condenser. Comparing the prediction of the model with experimental data, it could be concluded

that the model could predict the air temperature in good accordance with experimental data (less

than 5 percent average uncertainty), while the uncertainty for the water outlet temperature would

be much higher (average error of 10 to 15 percent). The issue with the mathematical model was

that the empirical correlations were developed based on the experimental data and thus subjected

to the experimental conditions. The mass transfer coefficients and interfacial area correlations

each have a specific temperature range that its prediction was validated; however, the uncertainty

would escalate outside of the range leading to considerable differences between experimental data

and mathematical model. As shown in Figure 3.1b where the air inlet temperature reached values

higher than 60◦𝐶, the difference for water temperature also increased considerably. On the other

hand, a data-driven surrogate model based on the experimental would not have the same limitation

or be bound to simplifying assumptions to develop the mathematical model. Now, the potential

of such a model would be investigated for predicting the behavior of condensers in a desalination

system.

3.2 Exploratory Data Analysis

The dataset used for developing a surrogate model includes physical and thermodynamic features

obtained from the aforementioned experimental setup for direct contact packed-bed dehumidifier

21

(a) Water Outlet Temperature

(b) Air Outlet Temperature

Figure 3.1 Comparison of the predicted outlet temperature with the experimental outlet temperature
at varying inlet air temperature (inlet temperature for water is constant). Water and air mass flow
rates varied from 20 − 30 𝑔/𝑠 and 1 − 3 𝑔/𝑠.

22

in addition to accurate data obtained from the mathematical model. The measured features include

temperature and mass flow of air and water at the inlet and at the outlet, packed-bed height,

porosity, and diameter. The data used for the preliminary investigation of a surrogate model based

on machine learning techniques were comprised of approximately 50,000 samples. Table 3.1

represented statistical information of the dataset. Before implementing regression approaches, the

data needed a transformation using a scalar due to the difference in the order of the magnitude for

their numerical values. The input features included inlet temperatures of water and air, mass flows

of water and air, packed-bed height, diameter, and porosity, while the output features comprised

of the outlet temperatures of the water and air. With the exception of linear regression, the dataset

was split into 80% training and 20% testing data.

𝑇𝐿,𝑖𝑛
29.85
6.87
20.00
40.00

𝑇𝑎,𝑖𝑛 𝐻𝑝𝑎𝑐𝑘 𝐷 𝑝𝑎𝑐𝑘
0.23
0.75
59.93
0.077
0.25
7.54
0.14
0.50
25.27
0.35
1.00
98.41

(cid:164)𝑚 𝐿
0.035
0.0099
0.020
0.054

(cid:164)𝑚𝑎
0.0037
0.0022
0.00034
0.0080

𝜀 𝑝𝑎𝑐𝑘
0.85
0.050
0.8
0.9

𝑇𝑎,𝑜𝑢𝑡
𝑇𝐿,𝑜𝑢𝑡
34.85
38.47
5.49
10.24
20.65
21.52
89.24 80.42

mean
std
min
max

Table 3.1 Statistical summary of the dataset used for training and testing the surrogate model. The
statistics showed that most of the investigated parameters have a normal distribution. It also showed
the existence of outlier entries for different features, and the mathematical model showed some level
of uncertainty for its prediction.

3.3 Machine Learning Tools Implemented to Develop the Data-Driven Surrogate Model

3.3.1 Linear Regression

The multi-variable linear regression is based on an estimation of the unknown parameter(s)

using different coefficients for the weight of known variables. the Scikit-learn built-in function

LinearRegression() was used to develop a multi-output linear model that minimizes the resid-

ual sum of squares (RSS) as the criteria for an accurate model (Pedregosa et al., 2011). RSS

measured the difference between the actual value (𝑦𝑖) and the approximated value ( ˆ𝑦𝑖) using
𝑅𝑆𝑆 = (cid:205)𝑛
ent features ˆ𝑦 = 𝜔0 + (cid:205)𝑛
𝑖=1

𝑖=1 (𝑦𝑖 − ˆ𝑦𝑖)2 while approximated value was estimated based different weights for differ-
𝜔𝑖𝑥𝑖. The linear regression was used to develop a basic and simple

model that would behave as the baseline for the rest of the machine-learning techniques.

23

3.3.2 Gaussian Process Regression

Gaussian process regression (GPR) is based on Gaussian distribution for random features. In

GPR, instead of first-order statistics (mean or variance), the second-order statistics (covariance)

define the process (Schulz et al., 2018). GaussianProcessRegressor(), which is a built-in function

in the Scikit-learn, was utilized to develop training model (Pedregosa et al., 2011). The

function had several hyper-parameter which could be optimized to improve the accuracy. The

hyper-parameter tuning was carried out for the kernel variable, which defined the function to

calculate the covariance matrix. Several options were investigated, including RBF (Radial Basis

Function), DotProduct, and RationalQuadratic. Each of the machine learning techniques had a

specific advantage for implementation. While linear regression predicted a line fitted over the data,

GPR introduced uncertainty in the surrogate model. GPR defined a confidence interval around its

prediction, which showed different accuracy in different regions of the dataset.

3.3.3 Support Vector Regression

The built-in function in the SVM (Support Vector Machine) of Scikit-learn library was used

for training (Pedregosa et al., 2011). The RBF was implemented to compute the kernel matrix. The

only hyper-parameter tuning performed for support vector machine regression (SVR) function was

epsilon, which represented the acceptable difference from the actual data to the prediction without

any penalty for training the model. The SVR has the benefit of good accuracy for the data with

outliers which was the issue with the mathematical model due to low accuracy for the prediction

of those outliers.

3.3.4 Deep Neural Network Regression

A Standard feed-forward deep neural network (DNN) was developed to develop a surrogate

regression model. The architecture of the neural network was a multi-layer perceptron. MLPRe-

gressor() which is a built-in function in the Scikit-learn was implemented for modeling. The

investigated DNN architectures were comprised of two and three hidden layers with a varying num-

ber of neurons from 1 to 9 in each layer. The number of trainable weights for the DNN varied from

8 to 243. The impact of hyper-parameters on the algorithm was studied. Comparing DNN with

24

GPR and SVR, the DNN has the distinctive benefit that the trained model could make predictions

without using training data which is quite different for GPR and SVR.

3.4 Performance Evaluation for Different Machine Learning Approaches

The Scikit-learn built-in functions could use several methods to calculate the accuracy

of each model. In this study, the R2 and mean squared error (MSE) criteria were utilized for a

comparison between different methods. The R2 score was calculated using 𝑅2 =

𝑖=1 ( ˆ𝑦𝑖− ¯𝑦)2
𝑖=1 (𝑦𝑖− ¯𝑦)2 , While
𝑖=1 (𝑦𝑖 − ˆ𝑦𝑖)2. In the aforementioned correlations, 𝑦𝑖 and
ˆ𝑦𝑖 represented the true and predicted value for the i𝑡ℎ sample, and ¯𝑦 is the average of the actual

MSE was estimated through 𝑀𝑆𝐸 = 1
𝑛

(cid:205)𝑛

(cid:205)𝑛
(cid:205)𝑛

values.

First, the optimization of DNN hyper-parameters was investigated. As shown in Figure 3.2,

three solvers for weight optimization and three activation functions were investigated. According

to our optimization study, the rectified linear unit activation function (relu) combined with lbfgs

quasi-newton weight optimizer solver led to an accurate DNN surrogate model. These values were

utilized later for modeling.

Considering the optimized values, different architectures of DNN were investigated to find the

optimal configuration of DNN, including the number of hidden layers and neurons. According

to Figures 3.3 and 3.4, the number of neurons in the first hidden layer had a considerable impact

on the accuracy of the surrogate model. The input layer had 7 neurons representing 7 features of

the input data. Interaction between the input layer and the first hidden layer played a crucial role

in developing an accurate model. A considerable decrease in the number of neurons of the first

hidden layer compared to the input layer (1 or 2 neurons) would lead to unintended dimensionality

reduction for the model and decrease its accuracy. Figures 3.3 and 3.4 also showed that there were

several choices for optimal architecture, which would lead to an accurate surrogate model.

Next, different regression tools were compared to find the convenient approach to developing

the surrogate model for the condenser. Figure 3.5 showed different criteria to compare the studied

approaches. Modeling employed 40 AMD EPYC 7H12 processors with 2.595 GHz clock time and

128 GB of RAM. According to Figure (3.5c), the linear model had the lowest training time with

25

Figure 3.2 Hyper-parameters optimization of the surrogate model based on DNN regression for
two hidden layers with 6 and 3 neurons. Hyper-parameter tuning was carried out for the activation
function of the neurons, solver for the weight optimization, and learning rate initial values. Twenty-
seven distinctive deep neural networks were trained to find the optimal choice for the aforementioned
hyper-parameters.

less than 1 second; however, the linear model based on the original features has an accuracy of

75%, which was less than the accuracy of the mathematical model. Investigating other regression

approaches showed that DNN with two and three hidden layers could lead to an accurate surrogate

model (97 ∼ 98% precision). When comparing DNN’s accuracy with respect to different criteria,

the DNN surrogate model was more accurate than other approaches. On the other hand, due to

the dependency of SVR and GPR techniques on calculating the kernel matrix and dependency

on the whole training dataset for a prediction, given the number of samples in the dataset, the

computational cost for developing a model based on these techniques was much higher compared

to DNN, leading to considerable time investments for developing an accurate model.

3.5 Sensitivity Analysis

The primary purpose of developing and training a surrogate data-driven model based on the

dehumidifier is to optimize the performance of a desalination unit. Sensitivity analysis is an essential

tool for identifying the features that significantly impact the output variables, which include the

outlet pressure and outlet temperature of water and air. Sensitivity analysis involves changing the

26

Figure 3.3 Accuracy of DNN with two hidden layers surrogate model. The rectified linear unit was
used for the activation function (relu), while the quasi-Newton method (lbfgs) was used to optimize
weights for the neurons. The solver iterated for 40000 iterations over training data to find optimized
weights.

input variables of the surrogate model one at a time and observing how the output variables respond.

The sensitivity indices are calculated to quantify the impact of the input variables on the output

variables. The results of the sensitivity analysis can provide valuable insights into the system’s

behavior, allowing for the optimization of the dehumidifier’s performance.

To further investigate the impact of different features, several features in the form of 𝑋 −1

𝑖 or 𝑋𝑖 𝑋 𝑗

are engineered, and surrogate models are trained based on a new dataset with artificial features.

Figure 3.6 represents how the accuracy score of the linear model is affected by introducing artificial

features and how the score is altered by dropping features with less importance on the linear

regression model considering the ranking visualized in Figure 3.7. Figure 3.8 illustrates sensitivity

indices for surrogate models trained on a dataset with artificial features. X1, X2, X3, X4, X5, X6,

X7, and X8 in Figures 3.7 and 3.8 are liquid inlet temperature, air inlet temperature and pressure,

packed-bed height, the diameter of the packed-bed media, inlet mass flows of water and air, and

porosity of the packed-bed medium, respectively. A sensitivity analysis is a valuable tool, but it

27

Figure 3.4 Accuracy of DNN with three hidden layers surrogate model. The rectified linear unit
was used for the activation function (relu), while the quasi-Newton method (lbfgs) was used to
optimize weights for the neurons. The solver iterated for 40000 iterations over training data to find
optimized weights.

must be accompanied by comprehensive information if it is to provide reliable results. For this

case, Figure 3.8 describes how the dataset might affect sensitivity analysis. Based on these figures,

one might conclude that packed-bed geometrical properties (height, diameter, and porosity) are the

most important factors, but it is worth mentioning that this might be due to the fact that limited

numerical investigations were carried out for the value of these properties which could create a bias

in the surrogate models toward these features, whereas parameters such as mass flows and inlet

temperatures for air and water were assigned lower sensitivity indices due to through analysis of

their numerical values.

3.6 Performance Comparison of the Mathematical Model and Data-Driven Surrogate Model

Now, we are going to compare the accuracy of the DNN surrogate model with the mathematical

model developed by Alnaimat et al. (2011) and validated by Abedi et al. (2021). The data that is

presented in Figure 3.1 is once again used for the performance comparison. Figure 3.9 visualizes

the neural network architecture for an accurate data-driven surrogate model, which is used for

28

(a) Accuracy performance based on R2 criteria

(b) Accuracy performance based on MSE criteria

(c) Training time for a surrogate model

Figure 3.5 Performance comparison for each of the machine learning regression approaches. As
shown, deep neural networks with 2 and 3 hidden layers show prominent performance compared
to other approaches.

performance comparison with the validated mathematical model.

Figures 3.10 and 3.11 compare the surrogate model prediction with that of the mathematical

model prediction. The results suggest that the surrogate model outperforms the mathematical

model in predicting air and water temperature, as the error in surrogate model predictions is lower

than that of the mathematical model. Specifically, the average error in surrogate model predictions

for air and water temperature is found to be between 2.5 to 4 percent, which is significantly lower

than the 5 to 10 percent error observed in predictions made by the validated mathematical model.

3.7 Summary and Conclusion

In this study, we studied the accuracy of a data-driven surrogate model based on the MLP

regressor of a direct-contact packed-bed condenser as the replacement of the mathematical model

for the condenser in the desalination system. While the solver based on the mathematical model

Alnaimat et al. (2011) illustrated an average of 5 to 10 percent error for predicting air and water

temperature, the surrogate model shows an improved overall accuracy (3 to 5 percent, respectively).

29

Figure 3.6 Variation of the linear model regression performance for a different number of features.
As expected, by reducing the number of features, the accuracy of the linear model will drop.

On the other hand, the surrogate model displays fluctuating behavior for the prediction of air and

water temperature, which could be addressed by collecting additional experimental data. Numerous

configurations of MLP regressors with distinct hyperparameters are examined to determine the best-

performing surrogate model, which includes architectures with different numbers of hidden layers

and perceptrons, activation functions, weight optimization methods, and learning rates. After that,

we examined the sensitivity of the surrogate model to identify prominent features of the condenser’s

performance. In addition to MLP, we also implemented random forest and linear regression models

to compare the sensitivity indices of various surrogate models. While each of the models suggested

distinct physical or hypothetical features as prominent cofactors with a high sensitivity index, the

most consistent finding amongst these models was the high impact of the inverse of packed-bed

diameter and porosity, and the interaction between air and water thermodynamic properties at the

inlet of system. Future studies should focus on developing a surrogate model with higher fidelity,

trained on experimental data, with more focus on the conditions that limit the behavior of the

mathematical model. Further investigation on more complex architecture with 4 or even higher

hidden layers and perceptrons for the MLP architecture could lead to a precise surrogate model.

30

Figure 3.7 Features importance investigation ranking for linear regression models. Based on the
linear model ranking, the square of the packed-bed diameter has a significant impact on the system’s
performance.

Figure 3.8 Features importance investigation for deep neural network considering R2 score. As
illustrated, the inverse of packed-bed height has a significant impact on the system’s performance.

31

𝑥1

𝑥2

𝑥3

𝑥4

𝑥5

𝑥6

𝑥7

𝑥8

𝑦1

𝑦2

Figure 3.9 DNN architectures with 3 hidden layers and accuracy of 98% which is used for perfor-
mance comparison with mathematical model.

Figure 3.10 Accuracy comparison between the mathematical model and data-driven surrogate
model based on deep neural network regression for the air temperature of a dehumidifier.

32

Figure 3.11 Accuracy comparison between the mathematical model and data-driven surrogate
model based on deep neural network regression for the water temperature of a dehumidifier.

33

CHAPTER 4

A SELF-SUSTAINING WATER TREATMENT PLANT: INTEGRATION OF SOLAR
CHIMNEY AND WATER DESALINATION SYSTEM TOWARDS GREEN
DESALINATION

This chapter was published in Journal of Renewable Energy, Vol 202, by Mahyar Abedi, Xu Tan,

James F. Klausner, and André Bénard, titled as Solar Desalination Chimneys: Investigation on

the Feasibility of Integrating Solar Chimneys with Humidification-Dehumidification Systems,

pages 88-102, Copyright Elsevier (2023). https://doi.org/10.1016/j.renene.2022.11.069.

4.1

Introduction

The concept of using solar energy to heat air and create a buoyant airflow for the purpose of

ventilation and power generation has been investigated since early 1900 with the introduction of

solar chimneys (Cabanyes, 1903). Although the original design of the solar chimney demonstrates

its capacity for power generation, the low heat transfer coefficient of air, the presence of a boundary

layer, and the non-ideal orientation of the solar collector lead to a relatively low thermal efficiency.

By adding functionality to a solar chimney, such as the desalination of water, the value proposition

of the solar chimney changes, which makes it more appealing. Desalination can be achieved by

using the space within the chimney to host a desalination unit. Of all the existing desalination tech-

nologies, direct-contact packed-bed desalination is the preferred choice due to its simple compact

configuration and high effectiveness. Studies on solar chimneys and desalination technologies are

reviewed below. Next, a description of the integrated solar desalination chimney configuration is

presented. Following that, the mathematical models and the methodology to obtain the numerical

solution for various configurations and the estimated conditions suitable for power generation and

desalination are provided.

4.1.1 Solar Chimney

The first design of a solar chimney was proposed which was capable of harnessing solar energy

to provide heat and power for an entire household (Cabanyes, 1903). A solar chimney is commonly

comprised of a solar collector, a turbine, and a chimney. The absorption of solar energy increases

34

the air temperature and creates a buoyancy-driven flow. The flowing air then interacts with the

turbine and produces power; and through the chimney, the air moves out. Several experimental

solar chimney setups were examined to study their potential and their performance. A team of

scientists led by Haaf et al. (1983) proposed and built the world’s first solar chimney power plant

(SCPP) in 1982, which remained operational for eight years. A solar panel with a radius of 122 m

and a height of 1.85 m was part of the Manzanares power plant, as was a chimney with a radius of

5 m and a height of 194.6 m that generated 50 kW for 8 years. Krisst (1983) designed and built a

small-scale SCPP in West Hartford, Connecticut, with a 10 W electrical output. Another pilot setup

was developed in Florida by Pasumarthi and Sherif (1998). The researchers studied the effect of

collector configuration on system performance and found that expanding the collector’s base could

significantly increase the temperature gradient. Zhou et al. (Zhou et al., 2007a,b; Zhou and Yang,

2008) constructed a small-scale pilot in Wuhan, China, with a 10 m diameter collector, an 8 m

height chimney, a 5 W output, and a 10◦𝐶 temperature increase at the collector. Maia et al. (2009)

built an SCPP with a height of 12.3 m and a diameter of 2 m for the chimney, a diameter of 25 m,

and a temperature increase of 8 degrees Celsius in the collector in Brazil. In addition, several SCPP

prototypes have been constructed in various locations around Iran for research purposes. Kasaeian

et al. (2011) built a solar chimney with a 10 m diameter collector and 12 m height chimney to

investigate the impact of air quality on its performance. Najmi et al. (2012) developed a small-scale

solar chimney to optimize performance based on different parameters such as the height of the

collector, construction material of the surface beneath the collector, and geographical coordination.

A number of proposals for large-scale solar chimney power plants were also submitted. In Australia,

the government has proposed a plan to build a solar chimney capable of meeting the energy needs

of 200,000 households with a height of 1000 m and diameter of 7000 m (Nizetic et al., 2008). The

project was later canceled due to technological constraints for building a chimney with the proposed

height. For tourism and energy generation, the construction of a large-scale solar chimney in China

was suggested, and the chimney height would extend over 1000 m (Zhou et al., 2010). Another

proposal for a 40 MW solar chimney in Spain was presented with 3.5 km2 collectors and a 700 m

35

chimney (Kasaeian et al., 2017). In 2008, Namibia’s government approved the construction of a

400 MW SCPP (known as the Green Tower), which would be comprised of a chimney with a height

of 1500 m and a diameter of 280 m, and a collector area that would extend to 37 km2, which was

also suggested to serve as a greenhouse (Cloete, 2008).

Researchers also developed mathematical and analytical models to simulate the behavior of

the SCPP alongside experimental tests. Mullett (1987) conducted an extensive analysis in order

to determine the effectiveness (ratio of mechanical or electrical energy generation to input solar

energy) of an SCPP. Padki and Sherif (1999) developed a differential equation that describes

the chimney and an analytical model capable of predicting the chimney’s operating parameters

consistently within a 5 percent accuracy. A new mathematical model had been developed by Lodhi

(1999) which demonstrated the relationship between collector heat transfer, chimney efficiency,

and cost analysis of electricity generated by the SCPP. In an analytical model, Chitsomboon (2001)

summarized the air flow’s behavior inside the SCPP. The study by Dai et al. (2003) explored the effect

of various system characteristics on power production and concluded that as plant size increases,

production increases nonlinearly. Kreetz (1997) proposed a numerical model for predicting the

behavior of water-filled tubes embedded underground beneath the collector of SCPPs as a thermal

energy storage device, which allowed the continuous daily performance of the design. To gain

a deeper understanding of the plant’s daily operating cycle, Hurtado et al. (2012) examined the

transient behavior of the Manzanares power plant. dos Santos Bernardes et al. (1999) carried out a

numerical investigation to measure the impact of a cross-section between the collector and chimney

on system’s overall efficiency. Chitsomboon (2000) investigated an SCPP model and concluded

that the plant’s efficiency was constant regardless of the size of the tower, the roof type, or the level

of insolation and that there was a linear relationship between power and efficiency with chimney

height. Gannon and von Backstro¨ m (2000) conducted an analysis on the ideal cycle for the air

within a solar chimney to calculate different variables depending on geometrical configuration and

other characteristics of the airflow and validated their analysis based on the Manzanares pilot.

Based on the principles of continuity, momentum, energy, and equation of state, Koonsrisuk (2012)

36

developed a mathematical model of an inclined solar chimney. As a complement to analytical

models, several numerical two and three-dimensional models were developed with the objective of

providing an accurate prediction and improving understanding of the SCPP (Pastohr et al., 2004;

Xu et al., 2011; Gholamalizadeh and Kim, 2016). In spite of these modeling efforts, the efficiency

of a solar chimney is relatively low (for a system similar to the Manzanares power plant, with 50

kW power generation, a solar intensity of 850 𝑊/𝑚2, and absorptivity of 0.65, the ratio of electrical

power generation to incoming solar energy is only about 0.2 %), which indicates that using these

systems for clean water production would increase their value proposition.

4.1.2 Humidification-Dehumidification Desalination System

Sharon and Reddy (2015) reviewed several desalination systems integrated with solar energy as

an energy source to determine the most prominent integrated desalination technology. According

to the study, intermittent desalination units could be powered by solar energy. It should be noted

that the humidification-dehumidification desalination process, which consists of an evaporator and

a condenser connected together, is one of those technologies that may be widely employed due to

their simplicity and low investment cost. In the HDH system, solar energy is used but to heat up

air or water coming into the desalination system rather than directly evaporate water. Al-Hallaj

et al. (1998) designed an experimental HDH set up to investigate the performance of the unit.

In order to enhance the performance of the HDH system, Müller-Holst et al. (1999) have used

numerical simulations. An experimental HDH was completed by Abdel-Salam et al. (1993) in

order to evaluate the effect of various parameters. El-Dessouky (1989) suggested that the HDH

system could take advantage of the waste heat from a gas turbine. citebourouni2001water created

a system for humidification and dehumidification of water that could desalinate water. A further

study conducted by Hou et al. (2005) examined the performance of the HDH system with an analysis

of energy conservation to determine the minimum temperatures of the two rejected flows and the

maximum mass flow ratio of the system.

In spite of the advantages of HDH systems, a financial analysis carried out by Narayan et al.

(2010) indicated that the cost of freshwater production was high, and further study should focus

37

on increasing its efficiency. There have been several suggestions for improving the efficiency

of such a system including adding a heat transfer wall between the components (Narayan et al.,

2011), increasing saturation pressure for water (Arabi and Reddy, 2003), and utilizing packed

beds for direct contact between liquids and gases within each component (Li et al., 2006). Aside

from the direct contact method with a packed bed, other proposed modifications will elevate the

sophistication of the system, which undermines one of the advantages of the HDH approach. The

objective of direct contact HDH employing a packed bed was to provide a high surface area per

volume for mass and heat transfer. Klausner et al. (2006) and Li et al. (2006) developed a one-

dimensional steady-state mathematical model of the HDH system with a packed bed. Following

that, Alnaimat et al. (2011, 2013) carried out a comprehensive investigation of the HDH system to

develop a transient model that would accommodate transient inlet conditions.

4.2 Description of the solar driven water desalination chimney

The proposed integrated water desalination system consists of several components, including a

solar collector, a chimney, a counter-current evaporator and condenser, a water tank, a pump, and a

turbine. An illustration of the solar-driven water desalination process is shown in Figure 4.1. The

temperature of the air between the solar collector and the ground increases through the absorption

of solar energy. Hot air induces a buoyancy-driven air flow, which moves within the system. Using

a pump, water is circulated through the evaporator and condenser. The evaporator is filled with

packed bed material in order to allow direct interaction between the hot air flow and saline water

flow. Through the use of nozzles, the saline water is distributed over the packed bed. The heated

airflow passes through the evaporator in the opposite direction to that of the saline water. The

saline water absorbs the heat from hot air, causing the water to evaporate, which creates a humid

airflow. Humidified air exits the evaporator in a higher humidity compared to inlet conditions

and enters the condenser. With the aid of a pump, cold saline water flows from the top of the

condenser. The water interacts with the saturated air, decreasing the temperature of the airflow

and resulting in the condensation of a portion of water vapor within the airstream. The produced

fresh water is collected from the bottom of the condenser.

In the following stages, rejected air

38

from the top of the condenser passes through a turbine, which keeps the pumps operating and is

responsible for the autonomous performance of the integrated system. For the condenser, there

is the option of using direct or indirect interactions between two streams. The direct interaction

utilizes a direct-contact packed-bed condenser, while the indirect interaction employs a shell and

tube (SHT) condenser. Interaction between flows in the condenser affects the configuration and

performance of the proposed integrated system. Implementation of direct interaction results in the

employment of brine and freshwater tanks to circulate through the evaporator and the condenser

filled with packed-bed material. In addition, the circulation of two different flows of water requires

two water tanks and two pumps with higher power requirements, as it is represented in Figure

4.1. The implication of using an indirect interaction condenser leads to a simpler design with

fewer components and less required power for the pump, but likely to reduce the efficiency of the

desalination process. The two suggested configurations will be investigated in detail for the purpose

of comparison and the feasibility of an autonomous desalination process.

Figure 4.1 A possible configuration of an HDH water desalination process integrated with a solar
chimney. A direct contact evaporator and a condenser with packed-bed material are used for
desalination purposes.

39

4.3 Governing Equations

Since we would like to investigate the feasibility of an integrated solar chimney and HDH

water desalination system, it is necessary to discuss the methodology to numerically simulate the

behavior of the integrated solar desalination chimney. One-dimensional models for a solar chimney

and direct contact packed-bed are used in this study.

4.3.1 One-Dimensional Mathematical Model for Solar Chimney based on Original Design

Assuming the specific environmental and operational characteristics of the SCPP, it is possible

to calculate thermodynamic variables, such as temperature and pressure, using the one-dimensional

mathematical model developed and validated by Koonsrisuk et alKoonsrisuk (2012). The general

assumptions for the validated model are uniform one-dimensional steady-state airflow with a low

Mach number, neglecting the boundary layer effects in the collector and chimney, ideal gas behavior

for air, and isentropic behavior in the turbine and the chimney.

Figure 4.2 Schematic outline used for mathematical modeling of solar chimneys to assess the
desalination potential of the integrated system.

The energy balance for the collector is derived using uniform flow with a low Mach number

assumption, and neglecting the friction effect on the flow within the solar collector.

40

𝑞′′ = 𝛼𝐼 𝐼 − 𝑈𝑎𝑏𝑠Δ𝑇 = (cid:164)𝑚𝑐 𝑝

Δ𝑇
𝐴𝑟

(4.1)

In Equation (4.1), Δ𝑇 in (cid:164)𝑚𝑐 𝑝

Δ𝑇
𝐴𝑟 is the temperature rise across the collector (𝑇2 − 𝑇1); while for
𝛼𝐼 𝐼 − 𝑈𝑎𝑏𝑠Δ𝑇, it represents temperature difference between the inside and outside of the collector,

which is approximated to the collector temperature riseDuffie and Beckman (2013) and set to

(𝑇2 − 𝑇1). 𝛼𝐼 is the absorptivity, 𝐼 is the solar irradiation intensity at the location, 𝑈𝑎𝑏𝑠 is the

average heat loss coefficient across the collector, (cid:164)𝑚 is the air mass flow within the solar chimney,

and 𝐴𝑟 is the solar collector surface area. The collector outlet temperature (𝑇2) is estimated using

the energy balance for the collector and air inlet temperature (𝑇1), and is found to be

𝑇2 = 𝑇1 +

𝛼𝐼 𝐼
𝑈𝑎𝑏𝑠 + (cid:164)𝑚𝑐 𝑝
𝐴𝑟

(4.2)

The collector outlet pressure is approximated using continuity, momentum, and energy equation

and the assumption of low Mach number air flow within the collector, i.e,

𝑃2 = 𝑃1 +

(cid:164)𝑚𝑞′′
𝑟 𝜌1𝑐 𝑝𝑇1

2𝜋𝐻2

ln

𝑟𝑟
𝑟𝑐

−

(cid:164)𝑚2
2𝜌1

(cid:32)

−

1
𝐴2
2

(cid:33)

1
𝐴2
1

(4.3)

In Equation (4.3), 𝜌1 is the inlet density of air, 𝑟𝑟 and 𝑟𝑐 are the collector and chimney radiuses

respectively, 𝐻𝑟 is collector height, 𝐴1 and 𝐴2 are cross sectional areas at the inlet and the outlet of

the collector, and 𝑃1 and 𝑃2 are pressure at the inlet and the outlet of the collector. The chimney

outlet temperature (𝑇4) is calculated using the dry adiabatic temperature lapse rateCalvert (1990),

𝑇4 = 𝑇3 −

𝑔
𝑐 𝑝

𝐻𝑐

(4.4)

In Equation (4.4), 𝑇3 represents the temperature at the outlet of the turbine, and 𝐻𝑐 is the height

of the chimney. The model assumes that air behaves as an ideal gas,

𝜌2 =

𝑃2
𝑅𝑇2

, 𝜌3 =

𝑃3
𝑅𝑇3

, 𝑎𝑛𝑑 𝜌4 =

𝑃4
𝑅𝑇4

(4.5)

41

Assuming ideal gas behavior for air and hydrostatic equilibrium for the ambient air, chimney

outlet pressure (𝑃4) is calculated through the following equation,

𝑃4 = 𝑃∞

𝑐𝑝
𝑅

(cid:19)

(cid:18)

1 −

𝑔
𝑐 𝑝𝑇∞

𝐻𝑐

(4.6)

In Equation (4.6), 𝑇∞ and 𝑃∞ are the ambient temperature and pressure respectively. The outlet

temperature of the turbine is estimated using the isentropic assumption for the power generation

within the turbine, i.e,

(cid:18) 𝑃3
𝑃2
The outlet pressure for the turbine (𝑃3) is approximated through continuity and momentum

𝑇3 = 𝑇2

(4.7)

(cid:19)

𝛾−1
𝛾

equations for the flow and a chimney with a constant cross-sectional area, i.e,

𝑃3 = 𝑃4 +

1
2

(𝜌3 + 𝜌4) 𝑔𝐻𝑐 +

(cid:18) (cid:164)𝑚
𝐴𝑐

(cid:19) 2 (cid:18) 1
𝜌4

−

(cid:19)

1
𝜌3

(4.8)

In Equation (4.8), 𝐴𝑐 is the chimney cross sectional area, 𝜌3 and 𝜌4 are air densities at the outlet

of turbine and the outlet of chimney. Additionally, for the calculation of the wind turbine power, the

pressure drop through the turbine will be determined from the turbine’s pressure difference. The

power output can then be calculated using the turbine pressure drop,

(cid:164)𝑊𝑡𝑢𝑟𝑏 =

(cid:164)𝑚
(𝜌2 + 𝜌3) /2

(𝑃2 − 𝑃3)

(4.9)

While these equations are relatively simple and neglect many aspects of flow behavior, they

provide a close approximation of thermodynamic properties for the operating points of a solar

chimney.

4.3.2 One-Dimensional Transient Model for Direct Contact Packed-Bed HDH Desalination

System

The mathematical model for the direct contact packed-bed HDH desalination system is devel-

oped by Alnaimat et al. (2011) using mass and energy balances within a packed-bed system.

42

Evaporator: The evaporator energy balance for the liquid phase, gas phase, and the packed-bed,

and the mass balance for water vapor result in the following equations for the temperature of the

liquid (𝑇𝐿), the air (𝑇𝑎), the packed-bed (𝑇𝑝𝑎𝑐𝑘 ), and the humidity (𝜔), respectively,

𝜕𝑇𝐿
𝜕𝑡

=

𝐿
𝜌𝐿𝛼𝐿

𝜕𝑇𝐿
𝜕𝑧

−

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 − ℎ𝐿(cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

−

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝐿 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

−

𝑈𝑎𝑤 (𝑇𝐿 − 𝑇𝑎)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

(4.10)

𝜕𝑇𝑎
𝜕𝑡

=

−𝐺
𝜌𝑎𝛼𝑎

𝜕𝑇𝑎
𝜕𝑧

−

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 (𝑇𝐿) − ℎ𝑣 (𝑇𝑎)(cid:1)
𝜌𝑎𝛼𝑎 (1 + 𝜔)𝐶𝑝𝐺

+

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝑎(cid:1)
𝜌𝑎𝛼𝑎 (1 + 𝜔) 𝐶𝑝𝐺

+

𝑈𝑎𝑤 (𝑇𝐿 − 𝑇𝑎)
𝜌𝑎𝛼𝑎 (1 + 𝜔) 𝐶𝑝𝐺

𝜕𝑇𝑝𝑎𝑐𝑘
𝜕𝑡

=

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝐿 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝 𝑝𝑎𝑐𝑘

−

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝑎(cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝 𝑝𝑎𝑐𝑘

(4.11)

(4.12)

The humidity is obtained using mass balance for water vapor in the packed bed which brings

about Equation (4.13),

𝜕𝜔
𝜕𝑧

=

𝑘𝐺 𝑎𝑤
𝐺

𝑀𝑣
𝑅

(cid:18) 𝑃𝑠𝑎𝑡 (𝑇𝑖)
𝑇𝑖

−

(cid:19)

𝜔
𝜔 + 0.622

𝑃
𝑇𝑎

(4.13)

Condenser: Same as the evaporator, the condenser energy balance for the liquid phase, gas

phase, and the packed-bed, and the mass balance for water vapor result in the following equations

for the temperature of the liquid (𝑇𝐿), the air (𝑇𝑎), the packed-bed (𝑇𝑝𝑎𝑐𝑘 ), and the humidity (𝜔),

respectively,

𝜕𝑇𝐿
𝜕𝑡

=

𝐿
𝜌𝐿𝛼𝐿

𝜕𝑇𝐿
𝜕𝑧

−

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 − ℎ𝐿(cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

+

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝐿(cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

+

𝑈𝑎𝑤 (𝑇𝑎 − 𝑇𝐿)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

(4.14)

𝜕𝑇𝑎
𝜕𝑡

=

−𝐺
𝜌𝑎𝛼𝑎

𝜕𝑇𝑎
𝜕𝑧

−

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 (𝑇𝐿) − ℎ𝑣 (𝑇𝑎)(cid:1)
𝜌𝑎𝛼𝑎 (1 + 𝜔)𝐶𝑝𝐺

−

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑎 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌𝑎𝛼𝑎 (1 + 𝜔) 𝐶𝑝𝐺

−

𝑈𝑎𝑤 (𝑇𝑎 − 𝑇𝐿)
𝜌𝑎𝛼𝑎 (1 + 𝜔) 𝐶𝑝𝐺

(4.15)

43

𝜕𝑇𝑝𝑎𝑐𝑘
𝜕𝑡

=

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑎 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝 𝑝𝑎𝑐𝑘

−

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝐿(cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝 𝑝𝑎𝑐𝑘

(4.16)

The only difference lies in the characteristic of the condensation process. While in the evap-

orator, air humidity gradually increases until it becomes humid, for the condenser, the relative

humidity of air during the condensation will remain the same. So, the humidity equation is quite

different from the evaporator, i.e,

𝜕𝜔
𝜕𝑧

=

𝜕𝑇𝑎
𝜕𝑧

𝑃
𝑃 − 𝑃𝑠𝑎𝑡 (𝑇𝑎)

(cid:16)

𝜔

𝑏 − 2𝑐𝑇𝑎 + 3𝑑𝑇 2
𝑎

(cid:17)

(4.17)

In Equation (4.17) 𝑏, 𝑐, and 𝑑 are constants used for the empirical correlation of water sat-
uration pressure in the form of 𝑃𝑠𝑎𝑡 = 𝑎 exp (cid:0)𝑏𝑇𝑎 − 𝑐𝑇 2
(cid:1) where 𝑎 = 0.611379 (𝑘 𝑃𝑎),
𝑏 = 0.0723669 (cid:0)𝐾 −1(cid:1), 𝑐 = 2.78793 × 10−4 (cid:0)𝐾 −2(cid:1), 𝑑 = 6.76138 × 10−7 (cid:0)𝐾 −3(cid:1), and 𝑇𝑎 is the air

𝑎 + 𝑑𝑇 3
𝑎

temperature in Kelvin.

The heat transfer coefficient for gas is estimated through 𝑈𝐺 = 𝑘𝐺 (cid:0)𝜌𝐺𝐶𝑝𝐺

(cid:1) 1/3 (cid:16) 𝐾𝐺
𝐷𝐺

(cid:17) 2/3

, while

the heat transfer coefficient for liquid is calculated according to 𝑈𝐿 = 𝑘 𝐿

(cid:16)

these two correlations, the total heat transfer coefficient is computed using 𝑈 =

𝜌𝐿𝐶𝑝 𝐿
(cid:16) 1
𝑈𝐿

(cid:17) 1/2

𝐾𝐿
𝐷 𝐿

. Using

(cid:17) −1

+ 1
𝑈𝐺

. Most

of the parameters are well-defined; however, the value for the mass transfer coefficient and the

interfacial area is approximated based on empirical correlations. Several existing correlations were

previously investigated to find appropriate correlations for the investigated packed-bed configuration

(Abedi et al., 2021). Liquid and gas mass transfer coefficients are calculated using empirical

correlations 𝑘 𝐿 =

0.0051
(𝑎 𝑝 𝑑 𝑝) −0.4

(cid:16) 𝜇𝐿𝑔
𝜌𝐿

(cid:17) 1/3 (cid:16) 𝜌𝐿𝑢𝐿
𝑎𝑤 𝜇𝐿

(cid:17) 2/3

𝑆𝑐−0.5
𝐿

and 𝑘𝐺 = 𝑐𝐺

(cid:16) 𝐷𝐺
𝑎 𝑝 𝑑2
𝑝

(cid:17) (cid:16) 𝜌𝐺𝑢𝐺
𝑎 𝑝 𝜇𝐺

(cid:17) 0.7

𝑆𝑐1/3

𝐺 , while

the interfacial area is estimated based on the following empirical correlation (Onda et al., 1968).

(cid:32)

(cid:34)

𝑎𝑤 = 𝑎 𝑝

1 − exp

−1.45

(cid:19) 0.75

(cid:18) 𝜎𝑐
𝜎𝐿

𝑅𝑒0.1

𝐿 𝐹𝑟 −0.05

𝐿 𝑊 𝑒0.2
𝐿

(cid:35) (cid:33)

(4.18)

In equations (4.13) and (4.17), 𝑃 represents the absolute pressure of air at the point of the

investigation, which is estimated through pressure loss calculation across the packed-bed for air

(Alnaimat and Klausner, 2012), which was numerically validated using a 3D numerical simulation

of the packed-bed (Roy et al., 2021).

44

(cid:34)

Δ𝑃
𝐻

=

𝐺1.4
𝜌𝑎

0.054 + 654.48

(cid:19) 2

(cid:18) 𝐿
𝜌𝐿

+ 1.176 × 107

(cid:35)

(cid:18) 𝐿
𝜌𝐿

(cid:19) 4 𝐺4
𝜌2
𝑎

(4.19)

4.4 Methodology for Performance Assessment of a Solar Desalination Chimney

4.4.1

Initial and Boundary Conditions

The considered solar irradiation is varied from 600 to 1000 𝑊/𝑚2 in this study.

It is also

assumed that the temperature of air coming into the collector, which in turn is also equal to the

ambient temperature, is varied from 20◦𝐶 to 30◦𝐶 depending on the experimental setup location.

For the desalination system, each component has six boundary conditions that include temperature,

pressure, mass flow, humidity for the incoming air, and temperature and mass flow of water. The

relative humidity for the air coming into the desalination unit is set to 30%. As shown in Figure

4.1, the arid air comes to the evaporator and will then move to the condenser. Therefore, the

boundary condition for air coming into the evaporator is the same as the collector output. The

water inlet temperature for the evaporator could be determined based on water outlet temperature

of the condenser (shell and tube configuration), or independent of it (packed-bed configuration).

For the condenser, the inlet water temperature is fixed and differs from the ambient temperatures to

30◦𝐶 higher. However, the temperature, humidity, and pressure of the air coming into the condenser

depend on the evaporator’s performance. To simplify the solution, the incoming water mass flow

rate for both the condenser and evaporator is assumed to be equal to the air mass flow rate.

4.4.2 Solver Configuration for Direct Contact Packed-Bed HDH

A MATLAB code was developed to solve the partial differential equations provided in section

4.3.2. The finite difference method has been adopted to solve the systems of equations. The height

of the packed-bed is set to 0.5 𝑚 for Florida and Kerman solar chimneys, while for Manzanares,

each desalination component has a packed-bed with 1 𝑚 height. The central second-order finite-

difference has been utilized for the discretization of the partial differential terms, while on the

boundaries, a forward or backward scheme is implemented. The Gauss-Seidel method proved to

be reliable and simple to solve systems of equations for the counter-flow configuration. A uniform

45

grid was developed to discretize the mathematical model. A sensitivity study of grid sizes 2000,

5000, and 10000 was carried out to find the optimized mesh size.

4.4.3 Solver Configuration for Shell and Tube Heat Exchanger Condenser

To perform a preliminary analysis of the shell and tube heat exchanger condenser configuration,

the ASPEN commercial solver was utilized. Figure (4.3) shows the schematic of vertical shell and

tube heat exchanger. The input for the ASPEN model includes the shell geometry, tube diameter

and pattern, and flow properties and locations. Hot flow (air) flows through the tube-side, while

cold flow (water) is on the shell-side.

Figure 4.3 Schematic diagram of a vertical shell and tube condenser. The humid air coming out
of the evaporator passes through the tube, while water fills the shell. The baffles ensure that water
flows through the whole domain and condensation happens for air within each tube.

The output of the model includes possible water condensation, outlet pressure and temperature,

and cost analysis of the investigated configurations. The pressure drop within the shell and tube is

a parameter that we will investigate comprehensively due to its considerable impact on the energy

performance of the integrated design. The shell and tube pressure drop in ASPEN is estimated

using the following correlations (Kakac et al., 2002),

46

Δ𝑝𝑠 =

𝑓 𝐺2

𝑠 (𝑁𝑏 + 1) 𝐷 𝑠
2𝜌𝐷𝑒𝜙𝑠

(4.20)

In the above equation, 𝐺 𝑠 is the shell-side mass flux, 𝑁𝑏 is the number of baffles, 𝐷 𝑠 is inner

diameter of shell-side, 𝐷𝑒 is the hydraulic diameter for the shell-side, and 𝜙𝑠 is the viscosity
correction factor for shell-side which is calculated based on (𝜇𝑏/𝜇𝑤)0.14 where 𝜇𝑤 is the flow

dynamic viscosity at the wall temperature, and 𝜇𝑏 is the flow dynamic viscosity at the bulk

temperature.

𝑓 represents friction factor for the shell-side which is approximated using 𝑓 =

exp (0.576 − 0.19 ln 𝑅𝑒𝑠) that 𝑅𝑒𝑠 = 𝐺 𝑠𝐷𝑒/𝜇.

Although pressure drop on the shell-side could have some impact on the integrated solar

desalination chimney, the pressure drop due to friction on tube-side determines functionality of the

system which can be evaluated using the following equation,

Δ𝑝𝑡 =

(cid:18)

4 𝑓

𝐿𝑁 𝑝
𝑑𝑖

+ 4𝑁 𝑝

(cid:19) 𝜌𝑢2
𝑚

2

(4.21)

In Equation (4.21), 𝐿 is effective length of tube, 𝑁 𝑝 is number of tube passes (which is one

for the investigation), 𝑑𝑖 is the inner diameter of tube, and 𝑢𝑚 is the average velocity inside tube.

Friction factor for tube-side is approximated using empirical correlation 𝑓 = (1.85 ln 𝑅𝑒𝑡 − 3.28)−2

and 𝑅𝑒𝑡 is Reynolds number for tube-side flow.

4.5 Simulation Results

Several experimental solar chimney setups are examined below to investigate the potential of

the proposed integrated solar desalination chimney designs. The investigated experimental setups’

dimensions are shown in Table 4.1. Figure 4.4 shows the flowchart of the methodology used

for calculating thermodynamic variables at different sections of the integrated solar desalination

chimney based on the condenser configurations. Table 4.2 compares the experimental data for

investigated solar chimneys with the prediction of one-dimensional mathematical model of the

solar chimney.

47

Start

Choose air mass flow rate

Calculate 𝑇2, 𝑃2, 𝜌2 using
equations (4.2),(4.3),(4.5)

Choose water mass flow rate

Condenser configuration

Shell and Tube

Packed-Bed

Solve evaporator PDEs
(4.10), (4.11),(4.12), (4.13)

Solve condenser PDEs
(4.14), (4.15),(4.16), (4.17)

Guess water inlet temperature for the evaporator

Solve evaporator PDEs
(4.10), (4.11),(4.12), (4.13)

Use evaporate outlet condition as
the inlet for shell and tube condenser

Model the Shell and Tube condenser

(cid:12)
(cid:12)𝑇𝐿,𝑔𝑢𝑒𝑠𝑠 − 𝑇𝐿,𝑠𝑖𝑚

(cid:12)
(cid:12) ≤ 𝜀

Yes

No

Update guess
temperature for
water

Use air outlet condition from
condenser as the input for the wind turbine

Guess turbine outlet pressure

Calculate 𝑇3, 𝜌3, 𝑇4, 𝜌4, 𝑃3 using equations (4.7),(4.5),(4.4),(4.5),(4.8)

Calculate turbine work
using Equation (4.9)

Yes

(cid:12)
(cid:12)𝑃3,𝑔𝑢𝑒𝑠𝑠 − 𝑃3,𝑠𝑖𝑚

(cid:12)
(cid:12) ≤ 𝜀′

No

Update 𝑃3

Stop

Figure 4.4 Flowchart of the procedure used to solve the coupled equations and mathematical model
for both types of heat exchanger.

48

Experimental Setup Collector radius (m) Collector height (m) Chimney radius (m) Chimney height (m)
1.85
0.2∼1.08
0.3∼1.3

Manzanares
Florida
Kerman

5.08
0.305∼1.22
1.5

122.0
4.6
22.6

194.6
7.92
60

Table 4.1 Geometrical dimensions used to investigate the performance of the proposed desalination
system.

Figure 4.5 Annotated schematics for the proposed solar-driven water desalination systems based
on a) Manzanares, b) Florida, and c) Kerman solar chimneys.

Experimental Setup
Manzanares
Florida
Kerma

𝐼 (cid:0)𝑊/𝑚2(cid:1)
1000
650
800

(cid:164)𝑊𝑒𝑥 𝑝 (𝑊)
48400
5
400

(cid:164)𝑊𝑡 ℎ (𝑊) 𝑇1 (◦𝐶) 𝑇2,𝑒𝑥 𝑝 (◦𝐶) 𝑇2,𝑡 ℎ (◦𝐶)
48250
4.83
399.28

37.78
29.86
39.27

18.5
20
27

38
30
40

Table 4.2 Comparison of a one-dimensional mathematical model of the solar chimney with the
(cid:164)𝑊𝑒𝑥 𝑝 and 𝑇2,𝑒𝑥 𝑝 are experimental power generation
experimental data for the investigated setups.
(cid:164)𝑊𝑡ℎ and 𝑇2,𝑡ℎ are model predictions for power
and temperature at the collector outlet; while,
generation and collector outlet temperature.

49

4.5.1 HDH Mesh Independency and Validation

In order to verify the accuracy of the numerical results, solver dependency from the grid

resolution is investigated. Based on Figure 4.6 which represents the impact of grid resolution

on the HDH solver, it appears that there is a negligible change (less than 0.2 percent) in outlet

temperature and humidity for different grid resolutions.

Component Test

Evaporator

Condenser

I
II
I
II

𝑇𝑎
30.00
28.00
50.00
60.00

Inlet
𝑇𝐿
60.00
55.00
25.00
22.00

𝜔
0.016
0.0118
0.0863
0.1525

Table 4.3 Inlet conditions utilized for mesh independency investigation for L = 1 𝑘𝑔/𝑚2𝑠, G = 0.5
𝑘𝑔/𝑚2𝑠. The temperature values are represented in Celsius.

Figure 4.6 Mesh independency investigation based on the inlet boundary conditions of Table 4.3.
The results indicate that the solution is almost independent of grid resolution for mesh number
higher than 5000.

Figure 4.8 compares the numerical solution for the desalination unit with the experimental

data. The condenser data is obtained from our experimental setup with specifications mentioned in

Table 4.4, while evaporator experimental data is extracted from an experimental study on a direct

contact packed-bed desalination Alnaimat et al. (2011). Figure 4.7 presents the schematic diagram

and experimental setup of the direct-contact packed-bed condenser utilized for the validation of

50

dehumidifier component. Evaporator experimental data were obtained under a transient condition;

however, using the quasi-steady state assumption and due to the slow system behavior, all experi-

mental data are assumed to be separate case studies. It can be inferred that the solver is capable of

close prediction compared to experimental data (average of 2 to 3◦𝐶 difference) within the validity

range of empirical correlations.

Feature
pipe material
pipe height
packing material
packed-bed height
packed-bed inner diameter
packed-bed effective diameter
packed-bed specific area
packed-bed density
packed-bed void fraction

Description
CPVC
1 (𝑚)
Polycarbonate
0.5 (𝑚)
0.14 (𝑚)
0.017 (𝑚)
267 (cid:0)𝑚2/𝑚3(cid:1)
1200 (cid:0)𝑘𝑔/𝑚3(cid:1)
87.8 (%)

Table 4.4 Experimental direct contact packed-bed condenser setup specifications for the validation
of the mathematical model.

Figure 4.7 Schematic diagram and experimental setup of the direct-contact packed-bed condenser
used for validity evaluation.

51

Figure 4.8 Evaluating the accuracy of numerical solver for the HDH mathematical model consider-
ing the experimental data for a condenser with L = 1.2∼1.8 𝑘𝑔/𝑚2𝑠, and G = 0.06∼0.18 𝑘𝑔/𝑚2𝑠,
and evaporator with L = 1 𝑘𝑔/𝑚2𝑠, and G = 0.5𝑘𝑔/𝑚2𝑠. The experimental data were extracted
from a study by Alnaimat et al. (2011), while the experimental data for the condenser was obtained
from a setup with the specification of Table 4.4

4.5.2

Integrated Solar Chimney Desalination System with Packed-Bed Condenser

4.5.2.1 Power Generation

Among the factors that have a considerable effect on turbine performance, is the overall pressure

drop within the desalination unit, and other components that air passes through, before entering the

turbine which has the most impact. The pressure drop indicates whether the integrated design can

operate under given conditions.

The pressure drop within a packed-bed desalination system is obtained using Equation (4.19);

while for shell and tube, ASPEN provides an approximation for the amount of pressure drop for

shell and tube sides using Equations (4.20) and (4.21). Table 4.5 presents the pressure distribution at

different sections of the integrated design according to Figure 4.2 for normal operating conditions,

while 𝑃5 represents the region between condenser outlet and turbine inlet. If 𝑃5 has a value smaller

52

than the chimney or the turbine outlet pressures, the pressure gradient in the chimney disrupts the

performance of the integrated design and prevents the air from moving out.

Setup

(𝑃𝑎/𝑚)

Manzanares

Air Mass Flow (𝑘𝑔/𝑠)
1200
2400
3600
2
28

𝑃4 (𝑃𝑎)
N/A
99043.33
99043.33
101321.63 101231.41
100617.54
Table 4.5 Pressure distribution at various sections of integrated design. 𝐷𝐶/𝐷𝐶,0 is the ratio of
chimney diameter to its value for the experimental setup. The pressure gradient between 𝑃5,𝑃3,
and 𝑃4 determines whether the system can function or not.

𝑃3 (𝑃𝑎)
𝑃5 (𝑃𝑎)
N/A
N/A
99748.01
101232.44
101283.24 101255.53
101324.65
101313.14 101300.68

𝑃2 (𝑃𝑎)
101244.05
101306.05
101318.76
101324.69
101307.75

Δ𝑃𝐻 𝐷𝐻
𝐻
525475.71
779.02
17.76
0.06
5.39

𝐷𝐶
𝐷𝐶,0
1
2
3
1
1

Florida
Kerman

According to Table 4.5, for the Manzanares case study, there is a considerable pressure drop

within the packed-bed desalination unit, which prevents the air from passing through the chimney.

For this reason, we investigated a design based on the Manzanares setup with a modification in the

chimney diameter. Based on a study, there is a linear correlation between the air mass flow and the

chimney diameter if the rest of the geometrical dimensions remain the sameGholamalizadeh and

Mansouri (2013). Using this guidance, for an arbitrary solar chimney with the same geometrical

dimensions as the Manzanares chimney, but with a larger chimney diameter (three times the original

diameter), the pressure drop becomes smaller which allows the possibility of air moving out of the

chimney. For the Florida and Kerman solar chimneys, the pressure gradient inside the chimney for

the original design allows the air to move out and indicates its functionality.

Figures 4.9 and 4.10 show the potential of the integrated design for desalination without utilizing

an external energy source. As mentioned earlier, the Manzanares setup is incapable of operation

due to considerable pressure loss within the desalination system; however, based on Figure 4.9, the

arbitrary design of Manzanares plant with a chimney diameter three times the original diameter,

in an area with abundant access to solar energy, is capable of autonomous water desalination. On

the other hand, based on the results for the Florida solar chimney, which is shown in Figure 4.10,

although the systems remain operational for the investigated conditions, the turbine only generates

a portion of the required power to circulate water through the desalination unit. However, for

the given experimental setup, increasing the height of the chimney enhances the system power

53

generation and ensures a self-sustaining desalination operation.

Figure 4.9 Comparison of solar chimney power generation with the required power to circulate
water through the desalination unit based on a) Manzanares and b) Kerman solar chimneys.

Based on Figures 4.9 and 4.10, it can be inferred that the wind turbine within the solar chimney

is capable of producing enough power under various operational conditions and geometries to

operate a desalination unit that unveils the potential of the solar chimney integrated design to be

deployed in the arid regions to produce freshwater without an additional energy source.

4.5.2.2 Performance of the Desalination System

After studying the capacity of a solar chimney for self-sustainable desalination, we investigate

the performance of the desalination system. There are several criteria to compare the efficiency

of these systems. The first measure is the effectiveness of a condenser, which is calculated by

comparing the condenser’s thermal performance to an ideal counter-current heat exchanger. For

an ideal counter-current heat exchanger, with a sufficient length between different streams for

exchanging heat, the temperature at the outlet of one stream would be equal to the inlet temperature

of the other stream. The effectiveness of the condenser is the ratio of the humidity difference

to the humidity difference in the case that the air outlet temperature is equal to the water inlet

temperature. It is calculated using 𝜀 =

𝜔𝑖𝑛,𝑐𝑜𝑛𝑑−𝜔𝑜𝑢𝑡 ,𝑐𝑜𝑛𝑑
𝜔𝑖𝑛,𝑐𝑜𝑛𝑑−𝜔𝑡 ℎ,𝑐𝑜𝑛𝑑 where 𝜔𝑡ℎ,𝑐𝑜𝑛𝑑 is the humidity at the inlet

temperature of the water which is the same as the theoretical outlet temperature of air for an ideal

condenser. Figure 4.11 shows that for the studied geometries, the integrated desalination system is

capable of producing freshwater at around 50 percent of the theoretical expectation. In addition,

54

Figure 4.10 Comparison of solar chimney turbine power generation with the required power to
circulate water through the desalination unit based on Florida setup. A chimney height of 30 m
and above would allow the proper operation of the pump.

the desalination is slightly more efficient in the region with a higher level of solar intensity; but

with higher solar insolation the mass flow increases, which reduces the effectiveness. For a fixed

cross-sectional area, higher mass flow corresponds to a higher superficial velocity for each flow,

which decreases the interaction between air and water stream.

The second criteria is the gain output ratio (GOR) which is based on the thermal performance

of the desalination system and represents the heat recovery of a desalination procedure. The

GOR is defined as the rate of energy gained from water condensation to the incoming energy

and it is calculated through 𝐺𝑂𝑅 =

(cid:164)𝑚𝑤 ℎ 𝑓 𝑔
(cid:164)𝑄𝑖𝑛

. Figure 4.11 represents the variation in GOR for the

investigated case studies. Although the GOR for the integrated design has a smaller value than other

existing desalination techniques, we should consider that the amount of heat loss in the collector is

55

considerable. In addition, the air heat transfer coefficient is smaller compared to other gases which

in turn has a negative impact on GOR. It is also worth mentioning that the GOR improves in higher

air mass flow which is expected because, at a higher flow rate, airflow shows turbulent behavior

which increases the heat transfer coefficient of air. The solar insolation has the same impact on the

GOR value as the mass flow; however, for Manzanares with the arbitrary chimney, GOR decreases

as the solar intensity increases.

The height of the packed-bed is set to 0.5 and 1 𝑚, while the porosity is set to 0.878. Although

the effectiveness may seem small, it is worth mentioning that increasing the height of the packed-

bed could improve the efficiency of desalination which means higher effectiveness and GOR for

the integrated design. Preliminary investigation shows that for Manzanares, increasing the height

of packed-bed to 2 𝑚, would increase the effectiveness to 0.7.

After studying the efficiency of the desalination unit, the amount of freshwater production is

calculated. Figure 4.12 shows the amount of water production for different geometries. For a large-

scale design based on Manzanares with the modified chimney, the system is capable of producing

up to 14 𝑘𝑔/𝑠 freshwater in areas with higher solar insolation, which for an average daylight of

12 hours is around 600 tons of fresh water, which can satisfy the average freshwater needs for an

approximate 800 to 1000 households, assuming 600 liters of water for daily usage. It is important

to consider, despite the high amount of water production, the integrated solar desalination chimney

based on Manzanares occupies a large surface area (46,800 m2). On the other hand, looking at

the amount of water production for a small-scale solar chimney such as Florida, which requires a

small area (66 m2), the amount of freshwater production per day is around 610 liters which are

around the average daily water consumption of a household. Comparing the amount of freshwater

production per unit of area for the two setups, we can see that Manzanares (12.82 𝑙𝑖𝑡𝑒𝑟 𝑠/𝑚2) has

a higher amount of freshwater production than Florida (9.24 𝑙𝑖𝑡𝑒𝑟 𝑠/𝑚2). However, a small-scale

solar chimney such as Florida’s has the distinct advantage of a smaller surface footprint, which

makes it an ideal choice to be placed on the roof of a building and satisfy the freshwater needs of

its households.

56

Figure 4.11 Investigation of desalination performance based on GOR and effectiveness criteria for
integrated solar chimney based on a) Manzanares b) Kerman, and c) Florida.

57

Figure 4.12 Fresh water production of the integrated design for a) Manzanares, b) Kerman, and c)
Florida solar chimney.

4.5.3

Integrated Solar Chimney Desalination System with Shell and Tubes Condenser

Before investigating the desalination performance, we studied the pressure distribution across

the solar chimney. ASPEN Exchanger Design and Rating has some limitations for geometry and

mass flow rate of the condenser that prevents implementation of the shell and tube model for

Manzanares with a modified chimney; however, the model is useful for the Kerman solar chimney.

Table 4.6 shows the pressure distribution at the outlet of the condenser and turbine and the freshwater

production. Even though the condenser is able to produce freshwater, the integrated design-based

shell and tube condenser is disregarded due to a considerable pressure drop through the condenser.

Comparing the linear pressure drop for the packed-bed unit in Table 4.5 with the same value for

shell and tube in Table 4.6, we can observe that generally, a shell and tube condenser has higher

pressure loss per unit of length than a packed-bed condenser. The higher pressure drop is expected

because of changes in the cross-sectional area for air to flow. The substantial pressure drop leads

58

to a positive pressure gradient as the air moves through the turbine, which prevents the flow of air.

Even with a modification of the chimney height, the flow is unable to move out of the chimney.

Tube Diameter Tube Pitch

(m)

0.1
0.1
0.1
0.05
0.05
0.05
0.05
0.025
0.025
0.0125
0.0125

(m)

0.2
0.15
0.125
0.2
0.15
0.1
0.063
0.05
0.031
0.025
0.016

Tube Number

Δ𝑃𝑆𝐻𝑇
𝐻

(cid:0) 𝑃𝑎
𝑚

(cid:1) 𝑃5 (𝑃𝑎)

𝑃3 (𝑃𝑎)

160
300
400
500
300
600
1710
2700
7000
11000
28000

3030
2573.33
2136.67
12983.33
6011.67
3116.67
2490
3493.33
2566.67
3980
2563.33

99437
99711
99973
93519
97648
99385
99761
99159
99721
98867
99663

101280.87
101281.63
101111.62
101047.11
101089.43
101109.23
101116.79
101118.03
101098.98
101135.15
101154.79

Freshwater

(cid:17)

(cid:16) 𝑘𝑔
𝑠

Production

0.0018
0.0084
0.0124
0.0031
0.0128
0.0297
0.05
0.0858
0.1235
0.1794
0.231

Table 4.6 Performance of integrated desalination unit using indirect interaction condenser based
on Kerman solar chimney. Air mass flow is considered 28 𝑘𝑔/𝑠, while the evaporator and the
condenser have 0.5 and 0.6 𝑚 height packed-bed.

4.5.4 Performance comparison for various solar desalination chimney configurations

In the previous section, we investigated the theoretical performance of our proposed desalination

system for three geometries. Although the proposed system is novel in using an HDH desalination

unit for the production of freshwater, there are several other existing systems that integrated solar

chimneys with different types of desalination technologies (Maia et al., 2019). Zuo et al. (2011)

proposed an integrated solar desalination chimney comprised of a collector, a chimney, a turbine,

an energy storage layer, and a solar still. The proposed system had a chimney height of 200 m and

a 5 m radius. It also had a collector of 125 m radius and 2 m height, and a storage layer of 20

m radius. It was suggested that the proposed system was capable of generating 2.83 × 105 𝑘𝑊 ℎ

power (approximately 100 𝑘𝑊) and producing 69500 tons (an average of 8.81 𝑘𝑔/𝑠) of freshwater

annually. In a similar study, Zuo et al. (2012) built a small-scale experimental setup based on the

previously investigated design, and measured a maximum freshwater production of 180 𝑔/𝑠, for

a solar chimney with a height of 3.25 m and collector length of 2.25 m, at the absence of solar

irradiation. Asayesh et al. (2017) suggested another system similar to the aforementioned system;

59

however, in the proposed design the desalination system which was a solar pond, didn’t cover the

entire surface of the collector ground. Preliminary analysis for a chimney with a height of 200 m

and a collector with a radius of 125 m, with a solar pond radius between 85 and 125 m, indicates

that the system was capable of producing electricity and treating saline water at rates of 18.5 𝑘𝑊

and 6.5 𝑘𝑔/𝑠, respectively. Table 4.7 presents a summary for performance comparison of various

studied solar desalination chimneys with the proposed configuration in this study.

Reference

Zuo et al. (2011)
Zuo et al. (2012)
Asayesh et al. (2017)
Current study (Manzanares)
Current study (Florida)
Current study (Kerman)

Chimney
radius (𝑚)
5
0.04
5
5.08
0.305∼1.22
1.5

Chimney
height (𝑚)
200
3.25
200
194.6
7.92
60

Collector
radius (𝑚)
125
2.25 (length)
125
122.0
4.6
22.6

Collector
height (𝑚)
2
0.15
2
1.85
0.2∼1.08
0.3∼1.3

Freshwater
production (𝑘𝑔/𝑠)
8.82
5 × 10−5
6.5
14.75
0.014
0.09

Table 4.7 Comparison of freshwater production between the investigated solar chimney geometries
in this study with suggested solar desalination chimney in the literature.

Based on Table 4.7, it can be inferred that the theoretical desalination potential of the pro-

posed system is at the same level as the other studied integrated solar chimney with desalination

technologies.

4.6 Summary

In this chapter, the potential of integrating a desalination unit with a solar chimney, resulting

in a solar desalination chimney being employed in areas with abundant access to solar energy

and saline water, was investigated. Two distinctive configurations for the desalination unit were

examined to find the performance of the integrated designs. A mathematical model of a solar

chimney coupled with a mathematical model for an HDH packed-bed desalination system and

a commercial model for the shell and tube condenser were used to predict the behavior of the

integrated system. Numerical investigations, as anticipated, show that the pressure drop within the

desalination unit had a considerable impact on the performance of the integrated design. For the

Manzanares solar chimney with the original dimensions, the pressure drop prevents the proposed

system from working. However, changing the diameter of the chimney allows for the identification

60

of favorable operating conditions for the integrated desalination system. Increasing the diameter of

the chimney, which in turn increased the mass flow of air, reduced the pressure loss (for modified

Manzanares design with chimney diameter three times the original, pressure loss in desalination

system is about 17.76 Pa per unit area, leads to following pressures 101.28 and 101.25 𝑘 𝑃𝑎 in

the inlet and the outlet of wind turbine) and allowed autonomous desalination. For the Kerman

chimney, which is a smaller system than Manzanares, the proposed system appears capable of

circulating up to 25 𝑘𝑔/𝑠 of water for desalination based on solar irradiation of 1000 𝑊/𝑚2. On

the other hand, modifying the chimney height for Florida from 7.92 m to 20 m or greater would

increase power generation up to 20 W, thus allowing potential autonomous operation for several

conditions. Numerical investigations for the studied geometries also show that the integrated system

based on packed-bed desalination could treat contaminated or brine water. Furthermore, based on

the freshwater production for the packed-bed configuration, the large-scale solar chimney such as
Manzanares in a region with abundant solar irradiation (cid:0)𝐼 = 1000 𝑊/𝑚2(cid:1) could provide 600 tons

of freshwater which can satisfy the freshwater needs of approximately 1000 households, while the
small-scale system such as Florida in a region with abundant solar irradiation (cid:0)𝐼 = 1000 𝑊/𝑚2(cid:1)

that could be placed on the roof of a residential building, and has the potential to produce 604

kg of freshwater and sustain the freshwater requirement of a residential building. Integrated solar

chimney with a packed-bed desalination system shows the capability of producing freshwater in

the amount of 9 to 12 liters per unit of area for the collector of the solar chimney. Despite

the performance of the packed-bed integrated design, a solar chimney coupled with a shell and

tube condenser and packed-bed evaporator is not capable of producing freshwater due to even

higher pressure loss for the shell and tube condenser (for shell and tube, pressure drop per unit

of tube length is about 2500 Pa while for the packed-bed component is around 5 to 20 Pa). The

proposed desalination system with solar chimney needs further and more comprehensive numerical

and experimental investigation to gain a better understanding of parameters that could improve

efficiency.

61

CHAPTER 5

MODELING OF SOLAR AIR HEATER INTEGRATED WITH DESALINATION
TECHNOLOGIES

This chapter was published in Journal of Applied Thermal Engineering, by Mahyar Abedi,

Xu Tan, Parnab Saha, James F. Klausner, and André Bénard, titled as Design of a solar air

heater for a direct-contact packed-bed humidification-dehumidification desalination system,

Copyright Elsevier (2024). https://doi.org/10.1016/j.applthermaleng.2024.122700.

5.1

Introduction

Desalination technologies encompass a wide range of methods to treat contaminated or brack-

ish water resources. These include reverse osmosis as one of the most widely used techniques

(Goh et al., 2018), to humidification-dehumidification (HDH) methods, which thermally treats

water through an evaporation and condensation process (Al-Hallaj et al., 1998). HDH systems

offer several advantages, including a low cost of materials, the capacity to treat a wide range of

water resources and zero-discharge treatment. Recent research and reviews on HDH systems have

introduced innovative approaches to further enhance their performance (Faegh et al., 2019; Mo-

hamed et al., 2021). One approach to enhance the performance of HDH systems involves direct

interaction between air and water, which in turn leads to lower pressure drop and higher heat

transfer (Niroomand et al., 2015). Moreover, experimental assessments suggest that the system

performed better in multi-stage configuration (Wu et al., 2017). One of the parameters that tend

to significantly enhance the yield of the HDH system is the humidifier pressure that impacts the

freshwater production (Rahimi-Ahar et al., 2018). The performance of the HDH systems can also

be improved by increasing the air-water interfacial area, which is achieved through the addition of

packed-bed media in the evaporator and condenser (Li et al., 2006).

Among various parameters, the inlet temperature of air and water are often considered to

have a substantial impact on the performance of the evaporator and condenser (Niroomand et al.,

2015). For this purpose, HDH systems are often used in conjunction with preheating chambers to

increase the temperature of air or water or even both, based on the desired output (Alnaimat and

62

Klausner, 2013). Among the various options, solar-driven thermal systems, that cover a variety of

technologies, stand out as a prominent environmental-friendly choice. Solar air heaters (SAHs),

which typically are comprised of a transparent glass cover, an absorbing plate, insulation, and

inlet/outlet ducts, have the merits of low capital costs, simple construction, and flexible operating

conditions, are one of the subcategories that most importantly deliver green renewable thermal

treatment under natural convection. Their integration with HDH systems is a logical step in

developing a low-cost solar desalination system, especially for warmer climates.

While the implementation of solar collectors in conjunction with an HDH system for pretreat-

ment purposes has been comprehensively studied (Nawayseh et al., 1999; Houcine et al., 2006;

Yamalı and Solmuş, 2007; Li et al., 2014; Al-Sulaiman et al., 2015; Siddiqui et al., 2016) (as this

will be discussed in Section 5.7.10), the impact of solar heaters integration lacks in-depth analysis

and requires further investigation to fully understand its potential benefits and drawbacks in the

context of overall system efficiency and performance. Even though several studies assessed the

performance of SAHs for performance optimization through flow passage modification and the

introduction of artificial roughness (Section 5.2), there is a literature gap in studying a possible

configuration where thermal insulation layers fully surround the flow passage in the SAHs.

This study aims to investigate the potential of using SAHs with insulation layers all around

the flow passage as a green, sustainable, and cost-effective pretreatment method for desalination

based on HDH. The main objective is to assess the feasibility and benefits of this approach

in comparison to other pretreatment methods and determine its performance under both natural

and forced convection modes. The utilized experimental setup comprised of an SAH designed

and constructed with insulation layers cover the flow passage. A combination of experimental,

computational, and numerical methods is employed to evaluate the efficiency of the system. The

performance of the SAH is assessed under different modes of convection. Additionally, the

study explores the potential of a dual solar air-water heater system for treating saline water. The

performance of the dual system is compared with the solar air-only heater system. By providing

insights into the feasibility, efficiency, and benefits of SAHs for desalination pretreatment, this

63

study aims to contribute to the development of sustainable and cost-effective methods for water

desalination. The findings of this study have potential implications for policy and industry practices

and could inform future research in this area.

With that in mind, the rest of the manuscript is organized as follows: a review of relevant

studies on SAHs is given in Section 5.2, followed by a detailed description of an experimental

SAH equipped with additional insulation layers in Section 5.3. Subsequently, the modules utilized

for developing a 3D computational model of a SAH based on the experimental setup in ANSYS

Fluent are examined, and the validation of the computational results is then presented in Section 5.4.

Following the 3D model, a conceptual design for an integrated SAH with an HDH water desalination

system is suggested in Section 5.5. Several configurations for HDH systems have been proposed

and validated by our group in the literature and are not described here for brevity. Section 5.6

studied the impact of cross-sectional area variation on the thermal efficiency of the proposed SAH

configuration under natural convection. Furthermore in Section 5.7, a 1D mathematical model of

the SAH is developed and coupled with a transient model of direct-contact packed-bed desalination

to evaluate the potential of the system under forced convection airflow at different geographical

locations. The potential of an integrated dual solar air-water heater with a desalination unit is

explored in Section 5.8, which is followed by a conclusion and remarks.

5.2 Review of Related Research

The concept of utilizing solar energy for heating purposes has been around for several centuries

(Mazria, 1979); however, the inventions of modern flat-plate solar air and water heaters are dated

back to the latter half of the seventeenth (Ackermann, 1915) and nineteenth (Morse, 1882) centuries,

respectively. Even though SAH is a comparatively recent invention, trivial SAHs are often consid-

ered at a disadvantageous position to water heaters in spite of natural convection operation, due to

the notable difference in the heat capacity of water compared to air. To increase the viability of

the SAHs, numerous studies have been conducted to explore various configurations and investigate

parameters to enhance the performance of SAHs.

The first category of these studies has focused on enhancing the optical properties of SAHs.

64

For that purpose, a variety of materials for the absorber plate and the transparent cover, along with

innovative system designs are examined. Given the significant role of the absorber plate material

in influencing the system’s input energy, enhancing SAH efficiency necessitates the use of specific

alloys like Al2O3, TiO2, and SiO2 for creating blackened absorbing surfaces, thereby optimizing

absorption and reducing thermal emittance (Mammadov, 2012). One such advancement includes

the utilization of Teflon film on the absorber plate, to reduce the emissivity losses without affecting

its capacity to absorb solar radiation (Rhee and Edwards, 1981). Another modification involves

incorporating reflective fins with low thermal conductivity and emissivity (Issacci et al., 1988),

or using transparent glass (Deubener et al., 2009), to enhance the thermal efficiency of SAHs.

An alternative path to improve the optical behavior of the system is to improve the intensity of

solar irradiation which can be achieved by incorporating booster mirrors (Prasad and Sah, 2014) or

concentrators (Khalil et al., 2012; Kasperski and Nemś, 2013).

Although enhancing the optical properties has improved the thermal performance, SAH remains

thermally inefficient. The second group of studies focuses on optimizing heat transfer efficiency

and minimizing heat losses to the environment. To prevent or reduce heat losses, the addition of the

insulation layer seems like the next logical step, as a proper layer with sufficient thickness would

greatly enhance thermal performance (Bahadori and Vuthaluru, 2010). The use of a translucent

insulation layer is a particularly effective modification as it simultaneously enhances optical prop-

erties and provides thermal insulation (Platzer, 1987). Moreover, modifying the flow passage’s

geometry/configuration has been shown to significantly enhance SAH performance. For instance,

the implementation of a double-pass SAH design, where air flows above and below the absorber

plate, has demonstrated a notable increase in thermal efficiency (Tyagi et al., 2014). The perfor-

mance of double-pass SAH will further improve if a porous absorber plate is deployed (Abo-Elfadl

et al., 2021). Examination of various cross-sectional geometries, including circular, semicircular,

and triangular shapes, has suggested that circular shape passage results in a substantial heat transfer

improvement (Abdullah et al., 2017), while triangular cross-section has a smaller surface footprint

(Akhbari et al., 2020).

65

An alternative approach to improve heat transfer in the SAH involves introducing roughness

to surfaces in contact with airflow, particularly on the absorber plate (Whillier, 1964). This can

be achieved through different methods, such as adding ribs and fins or even modifying the flat

configuration of the absorber plate, which can improve heat transfer by creating turbulence in

the airflow and disrupting the formation of a stagnant boundary layer. An experimental study

suggested that the implementation of a wavy absorber enhances the natural convection heat transfer

to the airflow (Varol and Oztop, 2008). Computational tools, such as ANSYS Fluent, have

shown remarkable capabilities to assess the behavior of SAH, and optimize the heat transfer

through roughness flow (Chaube et al., 2006). Computational assessments suggested that a conical

roughness rib significantly increases the thermal efficiency of SAH Alam and Kim (2017). Other

configurations that seem to impact the thermal performance of the system are V-shaped staggered

ribs (Ravi and Saini, 2018), arc staggered ribs (Agrawal et al., 2022), and broken arc staggered ribs

(Gill et al., 2021), whereas the V-shaped configuration tends to be effective with low air mass flow,

while higher mass flow rate resulted in a significant pressure drop and renders the configuration

impractical.

Aside from the literature reviewed above, further studies have explored enhancing system

performance through various innovative methods. The integration of honeycomb phase-change

material energy storage (PCM) in the SAH is one of these solutions that moderately enhance

thermal performance (Abuşka et al., 2019). Another solution involves the integration of a blackened

cylindrical copper tube that results in significantly higher thermal efficiency (Saxena et al., 2020).

Additionally, the introduction of nanoparticles with high thermal conductivity has proven effective

in improving heat transfer from the absorber plate to the airflow (Menni et al., 2019).

Table 5.1 offers a more comprehensive summary of several studies discussed in this section.

The literature review, while thorough, only investigates a subset of numerous studies aimed at

improving the performance of the SAH systems. The next section focuses on describing the

proposed configuration of SAH, which is one of the contributions of this study, addressing the gap

in the existing literature regarding the fully-insulated flow passage.

66

Modification
Optical Enhancement

Reference
Togrul et al. (2004)

Year Methodology Key Findings
2004

Experimental Using conical concentrator in SAH; exit temperature reaches up to

150◦𝐶; up to 12% thermal efficiency reported.

Flow Passage and Ge-
ometry Modification

Mammadov (2012)

2012

Experimental Examining various compounds for selective solar receiver; the absorp-
tance and emittance of the surface reaches 96% and 4%.

and Nemś

Kasperski
(2013)
Prasad and Sah (2014)

2013 Mathematical Developing a 1D model for a SAH with multiple fin arrays, solar con-

2014

Experimental

centrator and receiver; 13-14% improvement in thermal efficiency.
Integrating booster mirrors into an artificially roughened SAH; 40%
improvement on the input solar irradiation; around 90-135% and 10-
15% increase for thermal performance parameter of system with both
and roughened configuration without booster compared to smooth SAH,
respectively.

Tyagi et al. (2014)

2014

Experimental Analyzing the performance of double-pass SAH; 40% thermal efficiency

Abdullah et al. (2017)

2017

Experimental

reported for double-pass configuration.
Investigating the impact of three cross-sectional geometry for flow pas-
sage; between circular, semi-circular, and half-circle, 80% thermal effi-
ciency observed for circular configuration.

Jia et al. (2019)

2019

Experimental Examining the impact spiral and serpentine flow passage in SAH; 60%
thermal efficiency observed for spiral passage, indicating higher thermal
efficiency than serpentine.

Akhbari et al. (2020)

2020 Mathematical Assessing the performance of SAH with triangular channel and U-turn
flow passage; new configuration has 25% smaller footprint to compared
to flat plate SAH; 78% thermal efficiency was estimated when wind
velocity was around 1 m/s.

Abo-Elfadl et al. (2021)

2021

Experimental Analyzing the impact of porous media in single-pass and double-pass
SAH; around 4-6% increase in temperature rise for SAH with porous
media; energy efficiency increased by about 4 and 9% for single- and
double-pass, respectively.
Investigating the impact of wavy and flat absorber on SAH; wavy ab-
sorber facilitates heat transfer to air.

Artificial Roughness

Varol and Oztop (2008)

2008 Numerical

Alam and Kim (2017)

2017

Computation Studying the impact of conical rib roughness on SAH performance; 70%
thermal efficiency predicted by the computational model for roughened
SAH.

Ansari
(2018)

and Bazargan

Ravi and Saini (2018)

2018 Mathematical Analyzing the impact of rectangular rib on the performance of SAH; 9%
improvement observed in thermal efficiency for low mass flow rate; ribs
render system inefficient in high mass flow rate due to pressure losses.
Experimental Examining double-pass SAH with multi V-shaped and staggered rib
roughness; Nusselt number increased up to 5 times compared to smooth
configuration.

2018

Gill et al. (2021)

2021

Computation Assessing the impact of broken arc and staggered rib on heat transfer in

Innovative Solution

Abuşka et al. (2019)

2019

Experimental

Menni et al. (2019)

2019 Numerical

SAH; proposed roughness increases Nusselt number by a factor of 3.
Integrating SAH with PCM and honeycomb energy storage; 9% im-
provement reported for the thermal efficiency of the new configuration.
Conducting a review on the implementation of nanofluids in SAH; small
concentration of higher conductivity nanoparticles further enhances heat
transfer from the absorber plate.

Saxena et al. (2020)

2020

Experimental Examining the performance of SAH by integrating it with a blackened
cylindrical copper tube; experimental data suggested 80% thermal effi-
ciency for the integrated system.

Table 5.1 Comprehensive summary of examined literature with a focus on improving the thermal
efficiency of SAHs.

5.3 Configuration and Description of the Fully-Insulated Experimental SAH

After reviewing some of the ideas intended to improve the thermal performance of the SAH,

in this section, we describe the proposed SAH configuration, which is designed to cover a gap in

the literature regarding the fully-insulated flow passage. We thus propose a configuration where

the flow passage is surrounded by an absorber plate and insulation layer on the lower side, wooden

panels on the side walls, and a transparent polycarbonate air gap on the upper side of the flow

passage. The additional thermal insulation through the introduction of a sealed air gap further

67

decreases the convection heat losses from the system.

For the comprehensive evaluation of the proposed configuration, we have developed an experi-

mental setup and a 3D computational model, which give us the capability to investigate a broader

range of boundary conditions through a validated model. The SAH experimental prototype used

in this study consists of thin aluminum plates, insulation foam, a wooden frame, and a two-layered

air-filled polycarbonate sheet. The wooden frame with a dimension of 316 cm × 122 cm × 7 cm is

filled with 312 cm × 118 cm × 4 cm insulation foam. On top of this, a 0.025 cm thick aluminum

sheet, acting as an absorbent, is placed and coated with black paint to enhance absorption. The

polycarbonate (PCB) sheet with a size of 316 cm × 122 cm × 0.6 cm is placed on top of the absorber

and is separated from it by a flow passage with 2.5 cm thickness. Figure 5.1a provides a visual

representation of the 3D geometry of the SAH experimental setup, while Figure 5.1b shows the

experimental prototype implemented in this study.

(a) Front and isometric view

(b) Experimental setup

Figure 5.1 Visualization of SAH 3D geometrical model and experimental prototype constructed
based on the 3D design.

During the experimental study, key characteristic properties of the airflow, such as the tem-

perature and the velocity of the flow at the inlet and outlet boundaries of the flow passage, were

monitored using a high-precision anemometer, more specifically Digi-Sense WD-20250-16 hot

wire thermo-anemometer, that measures the velocity and temperature with ±0.005 m/s and ±0.05

68

◦C uncertainties, respectively. Ambient temperature and ground temperature were obtained using

type T thermocouples with a typical error of ±0.5 ◦C. Apogee quantum sensors (SQ-512-SS) and

pyranometers (SP-510-SS) were employed to measure the ambient solar irradiation, which deter-

mines the irradiation with less than 3% uncertainty. During the experiment, a handheld digital

anemometer wind speed meter was utilized to measure the average wind velocity of the site. Figure

5.2 describes the measurement system implemented to monitor different thermodynamic properties

of the air as it passes through the flow passage of the proposed fully-insulated SAH, in addition

to thermocouples and pyranometers/quantum sensors for the measurement of the ambient solar

irradiation.

Figure 5.2 Description of monitoring apparatus implemented to evaluate the performance of a
fully-insulated SAH configuration.

The experiments were conducted during the months of June and July 2021, in East Lansing,

Michigan. Measurements included air temperature and velocity at both the inlet and outlet of the

flow passage, as well as ambient solar irradiation and temperature, all captured and logged using a

National Instrument data acquisition module. After recording this data, it was meticulously analyzed

to evaluate the system’s performance. Due to the variable nature of environmental conditions, the

data was considered a representation of steady-state only when variations in the sensors’ readings

stabilized and remained within a predefined threshold, specifically a narrow margin of 3%.

69

5.4 Computational Modeling and Validation of Three-Dimensional SAH Model

5.4.1 Description of the ANSYS FLUENT Computational Model

To estimate the performance of the SAH, temperature, pressure, and velocity are obtained by

solving the Navier-Stokes and energy balance equations with consideration of specific environmen-

tal and operational conditions. The steady-state assumption was used to simplify the governing

system of equations further. The Boussinesq approximation is utilized to calculate changes in air

density solely based on temperature, using a reference value for density, i.e. the variation in density

is approximated as 𝜌∞𝛽 (𝑇∞ − 𝑇𝑎), where 𝛽 represents the thermal expansion coefficient, 𝑇∞ and

𝜌∞ denote temperature and density at the reference point (ambient condition), and 𝑇𝑎 denotes the

ambient air temperature. Turbulent flow characteristics are observed when the superficial velocity

of air is around 1 m/s. The experimental data indicates the necessity of considering a module to

accommodate turbulence. Among various turbulence models available, the preferred model for

simulating airflow in the SAH is the transition SST model Langtry and Menter (2009), which is

a combination of the 𝑘 − 𝜔 transport model and an equation for intermittency (𝛾). To consider

radiation heat transfer, the non-gray model for discrete ordinate is utilized, solving the radiation

heat transfer equation for a finite number of solid discrete angles. The discrete ordinate model is

linked with the energy equation to facilitate convergence.

A computational geometry consisting of six zones was created to model the thermal performance

of the system accurately. These zones represent various components of the experimental setup,

which include the insulation layer, surrounding wooden frame, polycarbonate panel, trapped air

within the panel, and airflow passage - all of which play an important role in the overall heat transfer

(or heat loss prevention) of the system.

5.4.2 Grid Independency Investigation

In developing the computer model to simulate the 3D behavior of a SAH, a grid-independence

study is carried out to see the impact of the grid resolution on the outlet temperature. Figure 5.3

provides the variation in the SAH outlet temperature as grid resolution improves. As shown in

Figure 5.3, once the grid resolution reaches a specific threshold, the SAH computational model

70

becomes grid-independent, implying that further refining the grid will not significantly affect the

results.

Figure 5.3 Mesh independency investigation for the SAH computational model. No improvement
was observed in the accuracy of a 3D model beyond 6 million elements.

5.4.3 Experimental Validation of the Computational Model

Another equally important step for developing a reliable computational model is experimental

validation which is needed to provide a benchmark for comparison and confirm the accuracy of the

numerical model. The experimental prototype of the SAH with the air gap, which was discussed

in Section 5.3, was utilized for the validation of the computational model. Multiple variables

were monitored during the experimentation process, including the air temperature at the inlet and

outlet of the system in addition to the ambient temperature, wind speed, air outlet velocity, and

ambient spectral irradiance. The inlet temperature and the ambient spectral irradiance were used

as boundary conditions of the model, whereas the outlet temperature and velocity were employed

for the model validation. Table 5.2 presents the experimental data used for the validation of the

SAH 3D model.

Figures 5.4a and 5.4b provide temperature and velocity distribution at the outlet of the SAH

considering 1030 W/m2 solar irradiation, 36◦ inclination angle, and 31 ◦C ambient temperature.

Comparing the predicted outlet temperature and velocity at the center line of the contours with the

experimental data obtained from the anemometer (test number 6 in Table 5.3), it is suggested that the

computational model could predict air thermodynamic properties for the investigated environmental

71

Test
1
2
3
4
5
6
7

𝜃 (◦) 𝑇𝑎𝑚𝑏 (◦𝐶)
45
45
45
45
36
36
26

30
28.5
28
31
31
32
33

𝐼 (𝑊/𝑚2) 𝑇𝑎𝑖𝑟,𝑖𝑛 (◦𝐶) 𝑇𝑎𝑖𝑟,𝑜𝑢𝑡 (◦𝐶) 𝑉𝑎𝑖𝑟,𝑜𝑢𝑡 (𝑚/𝑠)

800
200
1060
1100
1040
1030
1050

31
29
29
32
31
32
34

66
49
64
68
75
70
85

1.7
1.2
1.8
2.5
2
1.8
1.5

Table 5.2 SAH experimental data collected under different environmental conditions utilized for
validation. In this table, 𝜃 represents the inclination angle of the SAH, 𝑇𝑎𝑚𝑏 denotes the ambient
temperature, 𝐼 indicates the ambient spectral irradiance, 𝑉𝑎𝑖𝑟,𝑜𝑢𝑡 is the air outlet velocity, and 𝑇𝑎𝑖𝑟,𝑖𝑛
and 𝑇𝑎𝑖𝑟,𝑜𝑢𝑡 are the air inlet and outlet temperatures, respectively. Although real-time measurements
exhibit transient behaviors, the values presented in each test are averaged for consistency. It is worth
mentioning that during the experiments, the readings from the monitoring apparatus consistently
fell within a 3% margin of these average values.

conditions.

(a) Temperature distribution

(b) Velocity distribution

Figure 5.4 Temperature and velocity distribution at the outlet of SAH for 1030 W/m2 solar ir-
radiation, 36 ◦ inclination angle, and 31 ◦C ambient temperature. Comparing the velocity and
temperature at the center line of the SAH outlet with the experimental data (test number 6, 1.8 m/s
and 70 ◦C), the computational model is capable of predicting the distribution of different parameters
for the given boundary conditions with acceptable error.

Experimental validation of the SAH computational model through the temperature and velocity

contour plots poses a challenge, as it is difficult to compare the obtained values from the anemometer

with the corresponding contours. Therefore, Figures 5.5a and 5.5b are developed to compare the

72

(a) Outlet temperature

(b) Outlet velocity

Figure 5.5 Outlet temperature and velocity validation for the computational model with the exper-
imental data presented in Table 5.2. As shown, the computational model predicts the temperature
and velocity at the air outlet with a 4% average uncertainty.

experimental values with the average values at the center line of contours. Based on Figures

5.5a and 5.5b, it appears that the computational model can predict air velocity and temperature

with a 4 percent average uncertainty within the scope of investigated experimental conditions,

which indicates the reliability of the developed computational model to further assess the thermal

performance of the proposed SAH configuration.

5.5 Conceptual Design of an Integrated SAH with Water Desalination System

The proposed water desalination system integrates several components, such as the SAH, an

evaporator, a condenser, water tanks, photovoltaic water pumps, and a fan. The SAH has the

merit of operating under both natural and forced convection. Although natural convection does

not require external energy, forced convection typically provides improved thermal performance.

Figure 5.6 provides an illustration of the proposed desalination design. In this system, the SAH is

comprised of a wooden frame, a two-layered air-filled polycarbonate sheet, insulation foam, and

thin aluminum plates that act as absorbers and are painted with a black coating to enhance solar

radiation absorption. The wooden frame and insulation foam prevents heat loss from the absorber

plate and airflow to the environment. The two-layered air-filled polycarbonate sheet is placed over

the wooden frame. The sealed air between the two layers of polycarbonate sheet minimizes heat

loss from airflow (refer to Figure 5.7). The temperature of the air between the absorber plate and

73

the polycarbonate sheet increases through convection heat transfer. In the proposed system, hot air

under natural convection induces buoyancy-driven airflow, whereas, in forced convection, which

typically yields better thermal performance, a fan is used to actively move the air, enhancing heat

transfer efficiency.

The evaporator and condenser, collectively referred to as direct-contact packed-bed HDH de-

salination, are filled with packed-bed material. The integrated system requires two pumps and two

water tanks designated for saline and fresh water. Saline water is distributed over the packed bed

of the evaporator using nozzles. Hot air flowing from the SAH allows water evaporation upon

interaction with saline water, which would result in hot air with a higher level of humidity. The

saturated air interacts with fresh water sprayed from the nozzle located at the top of the condenser,

causing the airflow temperature to decrease, and a portion of water vapor condenses from the

airstream. The fresh water that is produced is then collected from the bottom of the condenser. The

saline and fresh water leaving the evaporator and the condenser, respectively, would then return to

the designated water tanks, allowing the system to operate continuously as long the SAH heats the

air and pumps circulate the water.

5.6

Impact of Cross-Sectional Area Variation on Thermal Efficiency of a SAH Under Natural
Convection Heat Transfer

Different geometries for the collector plate of the SAHs are investigated to estimate their impact

on the thermal performance under natural convection. The design of the studied SAH flow passage

or collector plate is illustrated in Figure 5.8.

The geometries that were analyzed are shown in Table 5.3. Figures 5.9a-5.9c illustrate the

changes in different performance parameters of the SAH for natural convection as the area or the

overall length of the flow passage changes.

Considering Figure 5.9b, it seems that there is a reverse correlation between the outlet cross-

sectional area and the air mass flow of the system. Decreasing the outlet area by 50% (from design

numbers 0 to 5) would lead to considerable change in air mass flow (more than 80%). The outlet

cross-sectional area affects thermal efficiency (ratio of heat absorbed by airflow to the overall heat

74

Figure 5.6 Proposed integrated SAH desalination system. The numbering corresponds to the
following components: 1) fan, 2) SAH, 3) pump, 4) fresh water tank, 5) saline water tank, 6)
direct contact packed-bed evaporator, 7) freshwater collector, 8) direct contact packed-bed (or shell
and tube condenser, which resulted in configuration with only one water tank (saline) and pump),
9) wooden frame, 10) insulation with absorber plate, 11) airflow, 12) sealed polycarbonate sheet
with air trapped (air gap). The above symbols (*) and (**) represent air inlets under forced and
natural convection, respectively. While conventional SAHs are comprised of a wide and narrow
flow passage, direct-contact packed-bed HDH systems often have square or circle cross-sectional
areas. Therefore, in the proposed design, we have suggested an intermediate object (colored pink)
connecting the SAH with the HDH system, particularly the evaporator. To mitigate the heat losses
from the system, the proposed intermediate object should be covered with insulation foam.

absorbed by the SAH absorber plate; 𝜂 =

(cid:164)𝑚𝑎𝑖𝑟 𝑐 𝑝,𝑎𝑖𝑟Δ𝑇𝑎𝑖𝑟
(cid:164)𝑄𝑖𝑛
flow (Figure 5.9c). However, the air temperature rise would increase, which could be preferable

) in the same way as it changes air mass

because, in the direct contact packed-bed HDH, a hotter air stream has a higher impact on the

desalination performance than the air mass flow.

The impact of flow passage shape with the same area is considered next (Design numbers 0 and

6-25). By studying Figure 5.9c, it appears that the thermal efficiency of the system drops as the

overall length of the absorber increases. Knowing that the flow passage area remains the same, it

75

Figure 5.7 The cross-sectional schematic of the proposed SAH, which its 3D representation is
outlined in Figure 5.6 through objects (2), (9), (10), (11), and (12). The temperature information
provided in this figure will be later utilized in Section 5.7.1 to develop a 1D mathematical model
of the system.

Figure 5.8 General geometry of the investigated SAH flow passage for integration with a water
treatment unit.

is thus inferred that decreasing the outlet cross-sectional area decreases the air mass flow rate and

thermal efficiency of the system (Figures 5.9b and 5.9c). The SAH temperature rises and enhances

as the flow passage length increases. Looking at the variation caused by changes in flow passage

shape (either by changing the overall area or length), it is assumed that while the natural convection

mode is the desired operating condition, it puts the system at a disadvantage for integration with a

water treatment unit to produce fresh water, due to significantly lower air mass flow rate.

76

Design W1 W2 W3
(𝑚)
(𝑚)
number
0.0
0
1.14
0.65
1
1.14
0.0
2
0.41
0.0
3
0.3
0.0
4
0.19
0.0
5
0.09
1.07
6
1.14
0.99
7
1.14
0.88
8
1.14
1.14
9
0.96
1.14 0.87
10
1.14 0.71
11
1.14 0.18
12
1.14 0.77
13
1.14 0.59
14
1.14 0.31
15
1.14 0.58
16
1.14 0.41
17
1.14 0.28
18
1.14 0.81
19
1.14 0.69
20
1.14 0.53
21
1.14 0.29
22
1.14 0.59
23
1.14 0.14
24
1.14 0.32
25

(𝑚)
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14
1.14

L1
(𝑚)
3.0
0.5
3.0
3.0
3.0
3.0
2.8
2.8
2.8
2.9
2.9
2.9
2.9
1.5
1.5
1.5
2.0
2.0
2.0
2.5
2.5
2.5
2.5
1.0
1.0
0.5

L2
(𝑚)
0.0
2.0
0.0
0.0
0.0
0.0
0.21
0.22
0.23
0.11
0.12
0.13
0.18
1.8
1.99
2.36
1.33
1.48
1.61
0.59
0.63
0.69
0.8
2.65
3.56
3.9

𝜃1
(◦)
0.0
0.0
7.0
8.0
9.0
10.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

𝜃2
(◦)
0.0
7.0
0.0
0.0
0.0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
6.0
8.0
10.0
12.0
14.0
15.0
16.0
20.0
24.0
28.0
6.0
8.0
6.0

Area 𝐴𝑅 (area
(𝑚2)
3.43
2.51
2.32
2.16
2.00
1.84
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43
3.43

ratio)
1.00
0.73
0.68
0.63
0.58
0.54
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00

Table 5.3 The geometrical dimensions of various investigated flat-plate air heater flow passages.
These geometries are categorized into two classes, of which the first considers the same overall
length for flow passages (L1+L2), while the second explores geometries with the same flow passage
area. Areas, angles, lengths, and widths are presented in m2, m, m, and degree (◦), respectively.

5.7 Modeling of the Proposed Integrated Desalination System

5.7.1 SAH One-Dimensional Mathematical Model

Continuity, momentum, and energy equations are used to develop a model for the SAH. A 1-D

model will reduce the complexity of the original model by eliminating the need to solve the other

two momentum equations and removing partial difference terms that are not in the flow direction.

In the SAH, assuming 1-D behavior for the air will make it possible to utilize the thermal resistant

circuit and solve the energy equation for the entire system. Following are the equations used to

calculate the thermal resistance for conduction, convection, and radiation heat transfer (Incropera

et al., 2018).

𝑅𝑐𝑜𝑛𝑑 =

𝐿
𝑘 𝐴

=

1
ℎ𝑐𝑜𝑛𝑑 𝐴

(5.1)

77

(a) Temperature rise

(b) Air mass flow rate

(c) Thermal Efficiency

Figure 5.9 Variation in SAH temperature rise, air mass flow, and thermal efficiency for various
geometrical configurations visualized in Figure 5.8 and with the detailed description provided in
Table 5.3.

𝑅𝑐𝑜𝑛𝑣 =

=

1
ℎ𝐴
𝑇𝑠 − 𝑇𝑠𝑢𝑟
𝑞𝑟𝑎𝑑

1
ℎ𝑐𝑜𝑛𝑣 𝐴
1
ℎ𝑟𝑎𝑑 𝐴

=

(5.2)

(5.3)

𝑅𝑟𝑎𝑑 =

Figure 5.10 represents the thermal resistant circuit developed to study the experimental SAH setup.

As shown in Figure 5.7, the investigated system consists of seven surfaces that interact with each

other and the environment (ambient and ground). For the first surface (upper surface of the top

polycarbonate layer), heat transfer occurs through both radiation and convection. For this layer,

convection heat transfer is affected by wind speed (𝑉𝑤), and the coefficient (ℎ𝑤) is estimated

considering ℎ𝑤 = 2.8 + 3.3𝑉𝑤 (Watmuff et al., 1977). For the same surface, radiation heat transfer

occurs with the earth’s atmosphere; therefore, when applying Equation (5.3), it should be taken

78

into account that the ambient temperature (𝑇𝑎𝑚𝑏) differs from the temperature used in calculating

radiation heat flux. The literature indicates that the sky temperature could be approximated by

𝑇𝑠𝑘 𝑦 = 𝑇𝑎𝑚𝑏 − 6 (Tiwari et al., 2016). The overall emissivity between any two layer 𝐴 and 𝐵 is

calculated through 𝜀𝑡𝑜𝑡 =

1
+ 1
𝜀𝐵

1
𝜀 𝐴

. Given the fact that the emissivity for the atmosphere (sky)

− 1

is approximately around 1, for this surface, the overall emissivity is equal to that of the top PCB

layer (𝜀𝑡).

Figure 5.10 Thermal resistant circuit corresponding to the SAH configuration

ℎ𝑟𝑎𝑑,𝑎𝑚𝑏−𝑡 =

1
𝑅𝑟 𝑎𝑑,𝑎𝑚𝑏−𝑡

=

(cid:17)

𝜎𝜀𝑡

(cid:16)
𝑇 4
−𝑇 4
1
𝑇1−𝑇𝑎𝑚𝑏

𝑠𝑘 𝑦

ℎ𝑐𝑜𝑛𝑣,𝑎𝑚𝑏−𝑡 =

1
𝑅𝑐𝑜𝑛𝑣,𝑎𝑚𝑏−𝑡

= 2.8 + 3.3𝑉𝑤𝑖𝑛𝑑





=⇒

1
𝑅1

=

1
𝑅𝑟𝑎𝑑,𝑎𝑚𝑏−𝑡

+

1
𝑅𝑐𝑜𝑛𝑣,𝑎𝑚𝑏−𝑡

(5.4)

Because of the top PCB layer’s thickness, conduction heat transfer occurred between the two

surfaces on both sides; therefore, thermal resistance between these two surfaces was determined

using Equation (5.1).

𝑅2 = 𝑅𝑐𝑜𝑛𝑑−𝑡 =

1
ℎ𝑐𝑜𝑛𝑑−𝑡

=

=

𝛿𝑡
𝑘𝑡

1
𝑘𝑡
𝛿𝑡

(5.5)

79

In the experimental setup, the air gap within the polycarbonate sheet is sealed. For this enclosed

inclined air gap, the Nusselt number can be calculated based on Equation 5.6 (Cengel and Ghajar,

2020).

𝑁𝑢𝑔 = 1 + 1.44

(cid:20)

1 −

1708
𝑅𝑎𝑔 cos 𝜃

(cid:21) + (cid:32)

1 −

1708 (sin (1.8𝜃))1.6
𝑅𝑎𝑔 cos 𝜃

(cid:33)

(cid:0)𝑅𝑎𝑔 cos 𝜃(cid:1) 1
18

3

+ (cid:169)
(cid:173)
(cid:171)

+

− 1(cid:170)
(cid:174)
(cid:172)

(5.6)

In Equation 5.6, 𝜃 is the inclination angle with respect to the horizontal axis, and 𝑅𝑎𝑔 is the Rayleigh

number for the enclosed air gap, estimated using the following equation,

𝑅𝑎𝑔 =

𝑔𝛽𝑔 (cid:0)𝑇𝑔 − 𝑇∞

(cid:1) 𝛿3
𝑔

𝜈2
𝑔

𝜇𝑔𝐶𝑝,𝑔
𝑘𝑔

(5.7)

In Equation 5.7, 𝑔 is the gravity (m/s2), 𝛽𝑔 is the thermal expansion coefficient for air (1/K), 𝜈𝑔 is

the kinematic viscosity (m2/s), 𝜇𝑔 is the dynamic viscosity (kg/m s), 𝛿𝑔 is the gap thickness (m),

C𝑝,𝑔 is the specific heat capacity of air (kJ/kg K), k𝑔 is the thermal conductivity of air (W/m K), T𝑔

and T∞ are the gap and the ambient temperatures, respectively. With the calculation of the Nusselt

number for the enclosed gap, the convection heat transfer of the gap (ℎ𝑐𝑜𝑛𝑣,𝑡−𝑏) is estimated through
𝑁𝑢𝑔 × 𝑘𝑔
𝛿𝑔

. For the enclosed air gap, heat transfer occurs in both convection (through the air gap)

and radiation (between the lower surface of the top PCB and the upper surface of the bottom PCB

layers).

ℎ𝑟𝑎𝑑,𝑡−𝑏 =

1
𝑅𝑟 𝑎𝑑,𝑡 −𝑏

=

2 )
−𝑇 4

𝜎𝜀1(𝑇 4
3
𝑇3−𝑇2

ℎ𝑐𝑜𝑛𝑣,𝑡−𝑏 =

1
𝑅𝑐𝑜𝑛𝑣,𝑡 −𝑏

=

𝑁𝑢𝑔 𝑘𝑔
𝛿𝑔

=⇒

1
𝑅3

=

1
𝑅𝑟𝑎𝑑,𝑡−𝑏

+

1
𝑅𝑐𝑜𝑛𝑣,𝑡−𝑏

(5.8)





In Equation (5.8), 𝜀1 represents the emissivity between the two poly-carbonate layers of the air gap,
(cid:19)

(cid:18)

which can be calculated based on the emissivity of the top and bottom PCB layers

𝜀1 =

1
𝜀𝑡 + 1
1
𝜀𝑏

.

−1

Similar to the top PCB layer, conduction heat transfer determines the thermal resistance between

two surfaces of the bottom PCB layer.

𝑅4 = 𝑅𝑐𝑜𝑛𝑑−𝑏 =

1
ℎ𝑐𝑜𝑛𝑑−𝑏

=

=

𝛿𝑏
𝑘 𝑏

1
𝑘 𝑏
𝛿𝑏

(5.9)

The thermal resistance between the lower surface of the bottom PCB layer and the insulation layer

is calculated by considering convection (between airflow and the two interacting surfaces) and

80

radiation (between the lower surface of the bottom PCB layer and the insulation layer) heat transfer.

For the air that moves through a duct under forced convection, the value of the Nusselt number is

approximated to 8.24 (Cengel and Ghajar, 2020); however, under natural heat transfer convection,

the Nusselt number is calculated through the following at the average temperature of the surface

and airflow (Incropera et al., 2018).

𝑁𝑢 𝑓 = 0.645

(cid:21) 1

4

(cid:20)

𝑅𝑎𝑠

𝛿 𝑓
𝐿

(5.10)

The convection thermal resistances between the airflow and the interacting surfaces are estimated

using the above Nusselt number from Equation (5.10).

ℎ𝑐𝑜𝑛𝑣,𝑖− 𝑓 =

1
𝑅𝑐𝑜𝑛𝑣,𝑖− 𝑓

=

ℎ𝑐𝑜𝑛𝑣,𝑏− 𝑓 =

1
𝑅𝑐𝑜𝑛𝑣,𝑏− 𝑓

=

𝑁𝑢 𝑓 ,𝑇𝑖 𝑘 𝑓
𝛿 𝑓

𝑘 𝑓

𝑁𝑢 𝑓 ,𝑇𝑏
𝛿 𝑓





ℎ𝑟𝑎𝑑,𝑖−𝑏 =

1
𝑅𝑟 𝑎𝑑,𝑖−𝑏

=

4 )
−𝑇 4

𝜎𝜀2(𝑇 4
5
𝑇5−𝑇4

𝑅𝑐𝑜𝑛𝑣𝑖−𝑏 = 𝑅𝑐𝑜𝑛𝑣,𝑏− 𝑓 + 𝑅𝑐𝑜𝑛𝑣,𝑖− 𝑓

=⇒

1
𝑅5

=

1
𝑅𝑟𝑎𝑑,𝑖−𝑏

+

1
𝑅𝑐𝑜𝑛𝑣,𝑖−𝑏

(5.11)

(5.12)





In Equation (5.12), 𝜀2 represents the emissivity between the bottom poly-carbonate layer and the

absorber plate which can be calculated based on the emissivity of each layer (bottom poly-carbonate
(cid:33)

(cid:32)

layer and the absorber layers)

𝜀2 =

. Due to the black coating layer of the absorber,

1
+ 1
𝜀𝑖

1
𝜀𝑏

− 1

the absorber behaves as a black body surface (𝜀𝑖 = 1); therefore, 𝜀2 is equal to the emissivity of the

bottom PCB layer. The thermal resistance for the insulation layer is calculated using the conduction

resistance equation.

𝑅6 = 𝑅𝑐𝑜𝑛𝑑−𝑖 =

1
ℎ𝑐𝑜𝑛𝑑−𝑖

=

=

𝛿𝑖
𝑘𝑖

1
𝑘𝑖
𝛿𝑖

(5.13)

From the bottom surface of the insulation layer, radiation and convection heat occur in the same

way as in the top PCB layer, but the only difference is that the radiation heat transfer is with the

ground.

ℎ𝑟𝑎𝑑,𝑖−𝑔 =

1
𝑅𝑟 𝑎𝑑,𝑖−𝑔

=

𝜎𝜀𝑖 (𝑇 4
−𝑇 4
6
𝑇6−𝑇𝑔𝑟

𝑔𝑟)

ℎ𝑐𝑜𝑛𝑣,𝑖−𝑎 =

1
𝑅𝑐𝑜𝑛𝑣,𝑖−𝑎

= 2.8 + 3.3𝑉𝑤





81

=⇒

1
𝑅7

=

1
𝑅𝑟𝑎𝑑,𝑖−𝑔

+

1
𝑅𝑐𝑜𝑛𝑣,𝑖−𝑎

(5.14)

After deriving correlations for each of the thermal resistances in Figure 5.10, the conservation

of energy is used for each node (besides the absorber, in which there are incoming and outgoing

energy fluxes).

𝑇1 − 𝑇𝑎𝑚𝑏
𝑅1

=

𝑇4 − 𝑇3
𝑅4

=

𝑇2 − 𝑇1
𝑅2
𝑇6 − 𝑇5
𝑅6

=

𝑇3 − 𝑇2
𝑅3
𝑇𝑔𝑟 − 𝑇6
𝑅7

=

=

𝑇5 − 𝑇4
𝑅5

(5.15)

(5.16)

For the absorber plate, energy flux conservation is a bit different than the rest of the nodes due to

incoming and outgoing heat flux from and to the ambient.

(cid:164)𝑞𝑎𝑏𝑠 = (cid:164)𝑞𝑐𝑜𝑛𝑑,𝑖 + (cid:164)𝑞𝑐𝑜𝑛𝑣,𝑖− 𝑓 + (cid:164)𝑞𝑟𝑎𝑑,𝑖−𝑏

(5.17)

Assuming steady state airflow in the SAH, the energy balance could be written as Equation

(5.18). To calculate other properties, such as velocity and pressure, continuity (Equation (5.19)),

momentum (Equation (5.20)) and Boussinesq approximation (Equation (5.21)) is used between any

two given points.

(cid:164)𝑞 𝑓 = (cid:164)𝑞𝑐𝑜𝑛𝑣,𝑏− 𝑓 + (cid:164)𝑞𝑐𝑜𝑛𝑣,𝑖− 𝑓

,

𝑑𝑇 𝑓
𝑑𝑥

=

(cid:164)𝑞 𝑓 𝑊
(cid:164)𝑚 𝑓 𝑐 𝑝, 𝑓

𝜌1𝑢1 𝐴1 = 𝜌2𝑢2 𝐴2

𝑃1 +

1
2

𝜌1𝑢2

1 + 𝜌1𝑔ℎ1 = 𝑃2 +

1
2

𝜌2𝑢2

2 + 𝜌2𝑔ℎ2

𝜌 = 𝜌∞ (1 − 𝛽 (𝑇 − 𝑇∞))

(5.18)

(5.19)

(5.20)

(5.21)

Darcy-Weisbach Equation (5.22) was used to calculate pressure drop and pressure value at the

different grids for the Equation (5.20).

Δ𝑃𝑙𝑜𝑠𝑠
𝐿

= 𝑓𝐷

𝜌

2

𝑈2
𝐷 ℎ

(5.22)

5.7.2 Computational Methodology for the SAH Heat Transfer

A MATLAB code has been developed to solve the nonlinear system in Equation 5.23, using an

iterative solver. The solver started at the air inlet and moved forward through the domain. At each

iteration, every coefficient was calculated based on the known values from the previous iteration.

82

Since the only known temperature was air temperature at the inlet, arbitrary values were used for

the temperature at different layers in Figure 5.7 to numerically solve Equation (5.23).

(cid:17)

(cid:17)

(cid:17)

(cid:17)

(cid:17)

(cid:16)

(cid:16)

(cid:16)

(cid:16)

(cid:16)

1 + 𝑅1
𝑅2
1 + 𝑅2
𝑅3
1 + 𝑅3
𝑅4
1 + 𝑅4
𝑅5
1 + 𝑅6
𝑅7

− 𝑇2

− 𝑇3

− 𝑇4

− 𝑇5

(cid:17)

(cid:17)

(cid:17)

(cid:17)

(cid:16) 𝑅1
𝑅2
(cid:16) 𝑅2
𝑅3
(cid:16) 𝑅3
𝑅4
(cid:16) 𝑅4
𝑅5

− 𝑇5 = 𝑇𝑔𝑟

= 𝑇𝑎𝑚𝑏

− 𝑇1 = 0

− 𝑇2 = 0

− 𝑇3 = 0
(cid:17)
(cid:16) 𝑅6
𝑅7

𝑇1

𝑇2

𝑇3

𝑇4

𝑇6






(5.23)

This system of equations consists of 5 nonlinear equations and 6 unknowns. A simple approach

to solve this system is assigning a numerical value to one of the unknown variables (in this case,

𝑇5) and solving Equation (5.23). At each iteration, a coefficient matrix was developed based on

the known values of the last iteration to calculate each of the resistances. After a few iterations,

using converged temperatures for all of the nodes besides 𝑇5, Equation (5.24) is used to update the

value of 𝑇5, based on the incoming heat flux through the absorber plate, which is correlated with

the incident angle (𝜃) and the transmissivity of the PCB layers (the incident angle is a function of

inclination, surface azimuth, declination, and hour angles). These loops continue until all of the

temperatures reach convergence criteria. Solving Equation (5.23) in this decoupled manner from

Equation (5.24) provided a faster framework and improved convergence.

𝐼 𝜏𝑡 𝜏𝑏 sin 𝜃 =

𝑇5 − 𝑇6
𝑅6

+

𝑇5 − 𝑇 𝑓
𝑅𝑐𝑜𝑛𝑣,𝑖− 𝑓

+

𝑇5 − 𝑇4
𝑅𝑟𝑎𝑑,𝑖−𝑏

(5.24)

In the next step, using temperature for all of the layers at the inlet and Equation (5.25), the air

temperature at the next node can be calculated using Equation (5.18). A first-order finite difference

forwarding scheme is used to discretize the equation. These loops continue until the solver reaches

the outlet of the system.

𝑇 𝑓 ,𝑖+1 = 𝑇 𝑓 ,𝑖 +

(cid:164)𝑞 𝑓 𝑊Δ𝑥
(cid:164)𝑚 𝑓 𝑐 𝑝, 𝑓

(5.25)

Figures 5.11 and 5.12 represent how the solver obtains the distribution of different thermodynamic

properties across the SAH for the nonlinear governing equations.

83

Figure 5.11 Schematic of the solution procedure for the SAH mathematical model to obtain the
temperature and velocity at different cross-section of the proposed SAH.

Figure 5.12 Flowchart of the procedure used to obtain the developed one-dimensional mathematical
model of the SAH.

5.7.3 Grid Independency Investigation

To investigate the independency of the 1D numerical solution from the grid resolution, the mesh

size was reduced, as shown in Figure 5.13. The variation in the air outlet temperature is negligible

if the length of each element for a uniform grid is less than or equal to 0.006 m.

84

Figure 5.13 Mesh-independence investigation for the SAH mathematical model. For an element
number greater than 5000 (which translates to less than 0.006 m for element size since the length of
SAH is 3 m), the higher grid resolution only increases the computational cost without improvement
in accuracy.

5.7.4 Validation of the SAH Mathematical Model

The validation of the 1D mathematical model is a bit challenging since the model predicts the

average outlet temperature, whereas the experimental data are obtained for the center line of the air

heater outlet. Therefore, the validated 3D model is utilized to investigate the accuracy of the 1D

mathematical model for the experimental data. Figures 5.14a and 5.14b compare the predictions

of the mathematical model with the calibrated 3D model. It is suggested that the mathematical

model estimates the behavior of the system with a 2 to 6 percent error, which is an acceptable level

of error. With the 1D mathematical model implemented, it is possible to assess the desalination

capacity of the proposed integrated system.

5.7.5 Mathematical Model of a Direct-Contact Packed-Bed HDH

A transient mathematical model developed by Alnaimat et al. (2011) is utilized to model the

behavior of the HDH water treatment system. By considering the balance of energy for different

subcomponents of the treatment system, which includes air, water, and porous medium, and

the mass balance for the vapor within the air, four nonlinear coupled governing equations are

developed, which predict the evolution of water temperature (Equation (5.26)), air temperature

(Equation (5.27)), packed-bed temperature (Equation (5.28)), and the air humidity (for evaporator

85

(a) Outlet temperature

(b) Outlet velocity

Figure 5.14 Outlet temperature and velocity validation for the mathematical model with the average
data obtained from the calibrated computational model. As shown, the mathematical model predicts
the temperature and velocity at the air outlet with 3% average error for temperature and velocity,
respectively.

and condenser, through Equations (5.29) and (5.30)), respectively.
𝑈𝐿𝑎𝑤 (cid:0)𝑇𝐿 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

𝐺 (cid:0)ℎ 𝑓 𝑔 − ℎ𝐿(cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

𝐿
𝜌𝐿𝛼𝐿

𝜕𝑇𝐿
𝜕𝑡

𝜕𝑇𝐿
𝜕𝑧

𝜕𝜔
𝜕𝑧

−

−

=

−

𝑈𝑎𝑤 (𝑇𝐿 − 𝑇𝑎)
𝜌𝐿𝛼𝐿𝐶𝑝 𝐿

(5.26)

𝜕𝑇𝑎
𝜕𝑡

=

−𝐺
𝜌𝑎𝛼𝑎

𝜕𝑇𝑎
𝜕𝑧

−

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 (𝑇𝐿) − ℎ𝑣 (𝑇𝑎)(cid:1)
𝜌𝑎𝛼𝑎 (1 + 𝜔)𝐶𝑝𝐺

+

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝑎(cid:1)
𝜌𝑎𝛼𝑎 (1 + 𝜔) 𝐶𝑝𝐺

+

𝜕𝑇𝑝𝑎𝑐𝑘
𝜕𝑡

=

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝐿 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝 𝑝𝑎𝑐𝑘

−

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝑎(cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝 𝑝𝑎𝑐𝑘

𝜕𝜔
𝜕𝑧
𝜕𝜔
𝜕𝑧

=

=

𝑘𝐺 𝑎𝑤
𝐺
𝜕𝑇𝑎
𝜕𝑧

𝑀𝑣
𝑅

(cid:18) 𝑃𝑠𝑎𝑡 (𝑇𝑖)
𝑇𝑖

−

(cid:19)

𝜔
𝜔 + 0.622

𝑃
𝑇𝑎

𝑃
𝑃 − 𝑃𝑠𝑎𝑡 (𝑇𝑎)

(cid:16)

𝜔

𝑏 − 2𝑐𝑇𝑎 + 3𝑑𝑇 2
𝑎

(cid:17)

𝑈𝑎𝑤 (𝑇𝐿 − 𝑇𝑎)
𝜌𝑎𝛼𝑎 (1 + 𝜔) 𝐶𝑝𝐺
(5.27)

(5.28)

(5.29)

(5.30)

5.7.6 Validation of a Direct-Contact Packed-Bed HDH Desalination Model

While the majority of the parameters and variables within Equations (5.26)-(5.30) are clearly

defined, there are some parameters that require direct or indirect implementation of empirical

correlations to estimate their numerical values, including 𝑎𝑤 (interfacial area; m2/m3); 𝑘𝐺 and

𝑘 𝐿 (air and water mass transfer coefficients; m/s); and 𝑈𝐺, 𝑈𝐿, and 𝑈 (air, water, and overall

heat transfer coefficients; W/m2 K). Within the scope of this study, we have implemented Onda’s

empirical correlations Onda et al. (1968) to approximate the values of 𝑎𝑤, 𝑘𝐺, and 𝑘 𝐿, through

Equations (5.31), (5.32), and (5.33), respectively.

86

𝑘𝐺 = 𝑐𝐺

(cid:32) 𝐷𝐺
𝑎 𝑝𝑑2
𝑝

(cid:33) (cid:18) 𝜌𝐺𝑢𝐺
𝑎 𝑝 𝜇𝐺

(cid:19) 0.7

𝑆𝑐1/3
𝐺

𝑘 𝐿 =

0.0051
(cid:0)𝑎 𝑝𝑑 𝑝(cid:1) −0.4

(cid:18) 𝜇𝐿𝑔
𝜌𝐿

(cid:19) 1/3 (cid:18) 𝜌𝐿𝑢𝐿
𝑎𝑤 𝜇𝐿

(cid:19) 2/3

𝑆𝑐−0.5
𝐿

(cid:32)

(cid:34)

𝑎𝑤 = 𝑎 𝑝

1 − 𝑒𝑥 𝑝

−1.45

(cid:19) 0.75

(cid:18) 𝜎𝑐
𝜎𝐿

𝑅𝑒0.1

𝐿 𝐹𝑟 −0.05

𝐿 𝑊 𝑒0.2
𝐿

(5.31)

(5.32)

(5.33)

(cid:35) (cid:33)

Examination of Equation (5.31) indicates the presence of a constant, which necessitates ex-

perimental validations to ensure accurate prediction from the empirical correlation. Moreover,

employing such empirical correlations demands meticulous consideration of the experimental con-

ditions, since these correlations are derived under specific circumstances, and deviations from

these conditions can introduce considerable uncertainty in the predicted values. With that in

mind, the values Onda’s empirical correlations are then utilized to approximate air, water, and
(cid:17) 2/3
overall heat transfer coefficients through the following correlations 𝑈𝐺 = 𝑘𝐺 (cid:0)𝜌𝐺𝐶𝑝𝐺

(cid:1) 1/3 (cid:16) 𝐾𝐺
𝐷𝐺

,

𝑈𝐿 = 𝑘 𝐿

(cid:16)

𝜌𝐿𝐶𝑝 𝐿

𝐾𝐿
𝐷 𝐿

(cid:17) 1/2

, and 𝑈 =

(cid:16) 1
𝑈𝐿

(cid:17) −1

.

+ 1
𝑈𝐺

Within the scope of this study, we are going to assume quasi-steady-state conditions to further

simplify Equations (5.26)-(5.30). The simplified forms of these equations are then discretized over

a 1D grid using a second-order finite difference scheme. The Gauss–Seidel method proved to be

accurate and simple to solve systems of equations for the direct-contact counter-flow configuration.

A MATLAB code is developed to solve the simplified discretized equations over the designated

grid and obtain temperatures of air, water, and packed bed, in addition to the humidity ratio within

the evaporator and the condenser. The results obtained from the MATLAB solver are then validated

with the experimental data obtained from direct-contact packed-bed condenser, visualized in Figure

5.15 with properties provided in Table 5.4, and data extracted from a study by Alnaimat et al. (2011)

for a direct-contact packed-bed evaporator, to obtain the constant value for calculation of air mass

transfer coefficient and ensure a higher fidelity in the HDH solver’s predictions.

The experimental observations for the evaporator were carried out for water and air mass fluxes

of 1 and 0.5 𝑘𝑔/𝑚2𝑠, while the data for the condenser are obtained for water and air mass fluxes

87

Figure 5.15 Experimental setups utilized for the validation of direct-contact packed-bed condenser
mathematical equations Abedi et al. (2023a).

Property
pipe material
pipe height
packing material Polycarbonate packed-bed density

Property
packed-bed height
packed-bed specific area

Value
CPVC
1 𝑚

Property
packed-bed inner diameter

Value
0.5 𝑚
267𝑚2/𝑚3 packed-bed effective diameter
1200𝑘𝑔/𝑚3 packed-bed void fraction

Value
0.14 𝑚
0.017 𝑚
87.8%

Table 5.4 Experimental direct contact packed-bed condenser setup specifications for the validation
of the mathematical model.

of 1.2∼1.8 𝑘𝑔/𝑚2𝑠, and 0.06∼0.18 𝑘𝑔/𝑚2𝑠, respectively. For both systems, the packed-bed void

fraction is set to 87.8%, while the density and specific heat capacity for the evaporator is set to

850 𝑘𝑔/𝑚3 and 2.35 𝑘 𝐽/𝑘𝑔 𝐾, whereas, for the condenser, those values are set 1200 𝑘𝑔/𝑚3 and

1.12 𝑘 𝐽/𝑘𝑔 𝐾, respectively. The packed-bed specific diameter and specific area are 17mm and 267

m2/m3. Figure 5.16 outlines the experimental validation analysis for the direct-contact packed-bed

evaporator and condenser. As illustrated, the validated mathematical model can predict various

operational parameters (humidity ratio, air and water temperatures at the outlet boundaries) of the

direct-contact packed-bed evaporator and condenser with an uncertainty range of 5 to 10 percent.

5.7.7 Water Treatment Capacity for the Proposed Integrated Configuration

The water treatment potential of an integrated SAH with a desalination unit is assessed for

different locations within the US and around the world. To estimate annual desalination capacity,

real-time environmental data obtained from NREL datasets Sengupta et al. (2018); Habte et al.

(2017) are utilized, including direct normal irradiance (DNI), diffuse horizontal irradiance (DHI),

temperature, relative humidity, and wind speed. Since different datasets provide environmental

88

(a) Water temperature for the
evaporator

(b) Air temperature for the evap-
orator

(c) Humidity ratio for the evap-
orator

(d) Water temperature for the
condenser

(e) Air temperature for the con-
denser

(f) Humidity ratio for the con-
denser

Figure 5.16 Experimental validation for the direct-contact HDH mathematical model considering
the experimental data for a condenser with L = 1.2∼1.8 𝑘𝑔/𝑚2𝑠, and G = 0.06∼0.18 𝑘𝑔/𝑚2𝑠, and
evaporator with L = 1 𝑘𝑔/𝑚2𝑠, and G = 0.5𝑘𝑔/𝑚2𝑠. The experimental data for the evaporator is
obtained from the study by Alnaimat et al. (2011), while the experimental data for the condenser is
obtained from the experimental pilot visualized in Figure 5.15 with the geometrical specification
provided in Table 5.4.

data at various locations for different time periods, all ambient data are obtained for the year

2019 to ensure consistency and facilitate comparisons. For a given country, if annual solar

energy varies significantly among its states, desalination potential is calculated for every state. In

this study, for most of the countries, average ambient data is used for modeling. However, for

Argentina, Australia, Bolivia, Brazil, Chile, China, Colombia, Mexico, Peru, the United States, and

Venezuela, we collected ambient data from different states, resulting in a total of 500 geographical

points considered for modeling. Figures 5.17, 5.18, 5.19, and 5.20 provide the annual average of

overall irradiation, ambient temperature, relative humidity, and wind speed, respectively.

The SAH geometry for the integrated system considered for this worldwide study is the same as

the experimental setup built for model validation. The inclination angle for the flow passage is set

to 45◦. The condenser and evaporator have a diameter of 0.15 m, and the height of each component

is set to 1 m. The packed bed specific area is set to 267 m2/m3, with an inner diameter of 0.14 m,

an effective diameter of 17 mm for vertical orientation, a specific heat capacity of 1.12 𝑘 𝐽/𝑘𝑔 𝐾, a

density of 1200 𝑘𝑔/𝑚3, and a void fraction is 87.8% Abedi et al. (2021). The SAH mass flow rate

89

Figure 5.17 Annual average of solar irradiation at various geographical locations within the scope
of this study. The NREL datasets Sengupta et al. (2018) are utilized to develop the solar irradiation
distribution map.

Figure 5.18 Annual average of ambient temperature at various geographical locations within the
scope of this study. The NREL datasets Sengupta et al. (2018) are utilized to develop the temperature
distribution map.

of dry air is set to 0.1 kg/s, while the water mass flow rates within the condenser and the evaporator

are assumed to be the same as dry air mass flow. The SAH inlet conditions are the same as ambient

conditions. The temperature of the water flowing through the evaporator is considered the same

as the ambient temperature. In contrast, the temperature of water flowing through the condenser

is assumed to be lower than the ambient temperature, and it can be achieved by providing proper

shading.

Based on the aforementioned specifications, simulations are carried out for 500 geographical

sites using real-time environmental data from 2019, to examine the water treatment capacity of the

proposed system. Figure 5.21 illustrates the global distribution of annual water treatment capacity.

90

Figure 5.19 Annual average of relative humidity at various geographical locations within the scope
of this study. The NREL datasets Sengupta et al. (2018) are utilized to develop the relative humidity
distribution map.

Figure 5.20 Annual average of wind speed at various geographical locations within the scope of this
study. The NREL datasets Sengupta et al. (2018) are utilized to develop the wind speed distribution
map.

Referring to the figure, within the geographical scope considered in this study, the average amount

of water treated by the system ranges from 0.3 to 1.6 grams per second when the system operates

with an air mass flow rate of 0.1kg/s. Comparing Figure 5.21 with Figure 5.17, it becomes evident

that the desalination capacity exhibits a strong correlation with the incoming solar irradiation. This

relationship is expected since higher solar intensity translates to increased energy available for

heating the air, resulting in warmer air and allowing for a higher humidity ratio limit.

The ambient temperature and solar intensity have a strong correlation with water treatment

capacity (comparing the solar irradiation map (Figure 5.17) and the ambient temperature map

(Figure 5.18) with the water treatment capacity map (Figure 5.21)). However, it would be hard to

91

Figure 5.21 Annual water desalination capacity (Ton/year) at different countries and states. As
shown, an SAH with a 3.5 m2 solar collector could theoretically treat around 5 to 30 tons of
contaminated, used, or saline water annually. These numbers could translate to approximate values
of 0.3 to 1.6 grams of produced water per second if the air mass flow is around 100 grams per
second.

evaluate the impact of wind speed and relative humidity on the system’s performance. In developing

the mathematical model, the effect of the wind speed on the thermal performance of the SAH was

considered through the convection heat transfer coefficient in the form of ℎ𝑤 = 2.8 + 3.3𝑉𝑤 Watmuff

et al. (1977), whereas V𝑤 is wind velocity. This parameter is one of the indicators of the system’s

heat losses to the surroundings (higher average wind results in higher anticipated loss); however,

since the variation in the wind speed is usually accompanied by changes in ambient temperature, a

comprehensive evaluation of its impact on the system’s performance remains challenging. Similar

to wind speed, higher relative humidity results in a greater specific heat capacity for the air passing

through the SAH, leading to a smaller temperature rise during the pretreatment process. However,

due to the interdependence of relative humidity and ambient temperature, evaluating the precise

impact of this parameter on the proposed system becomes more intricate.

5.7.8 Special Case Study: Water Treatment Capacity of the Proposed Integrated SAH for

East Lansing, Michigan

Now that we have examined the overall potential of the proposed integrated SAH, we shift

our focus to a more detailed analysis of the daily water treatment capacity, specifically for a case

study in East Lansing, Michigan. Figure 5.22 illustrates the system’s performance in terms of daily

treated water, capturing the changes in environmental conditions across different days and seasons,

92

whereas subfigures 5.22a, 5.22b, 5.22c, and 5.22d outlines the possible correlation between the

average ambient solar irradiation, temperature, relative humidity, and wind speed with the treatment

capacity, respectively.

(a) Daily average solar irradiation impact

(b) Daily average ambient temperature impact

(c) Daily average relative humidity impact

(d) Daily average wind speed impact

Figure 5.22 A detailed assessment of the daily variation in the ambient environmental conditions
for the proposed integrated SAH for a case study at East Lansing, Michigan, based on the daily
treated water production. As illustrated, each visualization represents the daily fluctuation for a)
solar irradiation, b) ambient temperature, c) relative humidity, and d) wind speed, while the color
bar outlines the variation observed in the daily treated water production.

First, we evaluate the case study behavior by examining the correlation between solar irradiation

variation and daily treated water production. As outlined in Figure 5.22a, the produced treated

water tends to increase as the daily average solar irradiation increases (the noticeable presence of

green bars in the July and August regions indicates peak performance during summer, correlating

with higher solar irradiation levels and extended daylight hours). Moving on to the average

ambient temperature trends, based on Figure 5.22b, there is a positive relationship between ambient

temperature and treated water production, with higher temperatures leading to increased output.

This trend is likely attributed to the enhanced ability of warmer air to absorb vapor when it comes

into contact with saline water in the evaporator. While ambient solar irradiation and temperature

have been shown to positively impact treated water production, the influence of relative humidity

variations is more ambiguous. As depicted in Figure 5.22c, there is no clear correlation between

fluctuations in average relative humidity and the daily treated water production, suggesting a more

93

complex interaction of factors. The final step of the case study analysis involves evaluating the

effect of average wind speed on system performance. Figure 5.22d reveals an inverse relationship

between average wind speed and daily treated water production. This trend is anticipated, as

higher wind speeds likely enhance convective heat losses from the system, thereby impacting the

desalination potential.

5.7.9 Carbon Dioxide Reduction Potential of the Proposed Integrated SAH Desalination

System

Having thoroughly explored the desalination potential of the integrated system and analyzed the

influence of various environmental parameters, the next step is to evaluate the environmental impact

associated with the deployment of such a system by quantifying the changes in CO2 resulting from

its implementation. Considering reverse osmosis as the conventional water treatment technology,

treating one cubic meter of water in RO technology consumes 3.5 to 5.6 kWh of energy Ludwig

(2010). Looking at the CO2 emissions associated with electricity production None (2013), it

appears that the emission based on the energy consumption of the RO system for one cubic meter

of water translates to 1.6 to 2.5 kg of CO2 emissions for electricity generated from natural gas, and

3.6 to 5.6 kg for electricity generated from coal. As a result, the implementation of the proposed

integrated system has the potential to reduce CO2 emissions by approximately 100 to 150 kg per

year. While this figure may seem relatively small on an individual household level, it becomes

significant when considering a scenario where these systems are deployed in numerous households.

For instance, in a small province with 1000 households, the collective CO2 reduction could amount

to 150 tons per year.

5.7.10 Performance Comparison with the Previously Studied Configurations

After investigating the theoretical global water treatment potential and assessing the envi-

ronmental merits of the proposed integrated SAH, it is worth evaluating the performance of the

proposed system with other similar existing systems, which may incorporate different desalination

technologies. Nawayseh et al. Nawayseh et al. (1999) developed a pilot solar-driven desalination

system used to preheat the air, and achieved a notable result with the system capable of producing

94

up to 4 kg of fresh water per hour. Houcine et al. Houcine et al. (2006) conducted a detailed

study on a solar desalination system with 5 dehumidification stages and a solar collector for heating

air, and observed a 4 liters per collector unit of area daily water treatment capacity. In a similar

study, Yamali and Solmus Yamalı and Solmuş (2007) performed a theoretical analysis on an HDH

desalination system integrated with a double-pass flat plate SAH, and reported a 4 kg per day water

production per unit of area of the collector for Ankara Turkey. Li et al. Li et al. (2014) examined

the performance of a small-scale integrated HDH desalination system and SAH with evacuated

tubes, and observed a maximum of 21 g of water per 1 kg of air flowing through the SAH, while

the solar intensity is around 850 W/m2. Al-Sulaiman et al. Al-Sulaiman et al. (2015) evaluated

the performance of an integrated HDH desalination system with a parabolic trough collector in

two distinct configurations depending on preheating the air for the evaporator or the condenser.

The study concluded that the SAH placement before the condenser greatly affected the thermal

performance of the system, and such a configuration had a treatment capacity of 11 tons of water

in a year. Siddiqui et al. Siddiqui et al. (2016) proposed a solar-driven HDH desalination system

with two electric water heaters (500 W) in the humidification chamber, a condenser, and a SAH

for pre-heating the air. According to this study, such a system could produce treated water up to

35 liters daily. Table 5.5 provides a comprehensive summary and performance comparison of the

various studied integrated SAH desalination systems, including the proposed configuration in this

study.

By looking at the water production column in Table 5.5, it can be inferred that the proposed

system, with the exception of the system suggested by Siddiqui et al. Siddiqui et al. (2016), performs

on the same level or slightly better. While the system studied by Siddiqui et al. Siddiqui et al.

(2016) had a higher treatment capacity, it is worth mentioning that the proposed system in this

study does not require any external heat sources, whereas the other system utilizes several electrical

heaters to pretreat both air and water before passing through the evaporator and the condenser.

95

Study

Location

Nawayseh et al. (1999) Malaysia

Houcine et al. (2006)

Tunisia

Yamalı
(2007)

and Solmuş

Turkey

Li et al. (2014)

China

Al-Sulaiman
(2015)

et

al.

Saudi Ara-
bia

Collector
Surface
20 m2

127 m2

0.5 m2

14 m2

25 m2

Siddiqui et al. (2016)

Saudi Ara-
bia

2 m2

China

Malaysia

Present study

3.5 m2

Saudi Ara-
bia
Tunisia

Turkey

Specification

Pretreatment

Water Production

Recovering heat in the con-
denser; using electrical heater
5 dehumidification stages

Air

Air

4 kg/hr

4 kg/m2 per day

CO2 Emission

0.5 ∼ 1 kg/hr

Zero emission (no elec-
trical heater)
1.5 ∼ 3 kg/hr

double pass solar collector; 3
finned tube condenser; using
electrical heater
SAH with glass evacuated
tubes
Parabolic trough solar collec-
tor; preheating before or after
the evaporator using electric-
ity
Shell and tube heat exchanger
with copper tubes; transparent
evaporator to use solar energy;
using electrical heater
Fully-insulated
air
heater (air gap on top side,
wooden
sides,
insulation foam on the bottom
side); direct-contact packed-
bed humidifier and dehumidi-
fier

panel

solar

on

(might pre-

Air
treat water)

4 kg/m2 per day (for pretreated
water and air)

Air

Air

maximum of 0.021 kg of wa-
ter per unit of air mass flow
11 × 103 kg per year

Zero emission (no elec-
trical heater)
Electrical heater prop-
erties missing

Air and water

up to 35 L/m2 per day

0.75 ∼ 1.5 kg/hr

Air

3 g water per 100 g of air mass
flow (during July) ≈ 0.03 kg
per kg of air mass flow

18 tons of water per year ≈
3.42 kg/hr (for 3.5 m2 collec-
tor)
28 tons of water per year ≈ up
to 27 L/m per day
20 tons of water per year ≈
15.7 kg/m2 day
18 tons of water per year ≈ 14
kg/m2 per day

Zero emission (no elec-
trical heater)

Table 5.5 Comparison of freshwater production between the proposed configuration in this study
with the similar in the literature.

5.8 Exploring Utilization of a Dual Solar Air-Water Heater as a Replacement for Conven-

tional SAH

The main drawback of SAHs is the utilization of air as the working fluid. The low thermal

conductivity and heat capacity, in addition to the resistance of the laminar viscous layer, limits

thermal efficiency in these solar thermal systems. A common solution to the SAH’s inefficient

thermal performance is introducing artificial roughness into the system, which has been investigated

extensively. Artificial turbulence increases the heat transfer coefficient and tries to lessen the effects

of the laminar behavior outside of the boundary layer while increasing the flow pressure drop.

Another solution that has been studied in the past decade is the addition of another flow stream

within the configuration (Assari et al., 2011). An additional flow stream with a higher thermal

capacity and heat transfer coefficient compared to air enhances the thermal performance of the

SAH. Due to its characteristics and potential, the dual-purpose solar heater makes a compelling

option for integration with a desalination system. Rajaseenivasan and Srithar (2017) suggested a

solar collector design that would serve as a heat source for water and air flow simultaneously for the

purpose of water desalination. They developed an experimental desalination system with a solar

96

collector to heat up air and water for the desalination system. The heated air and water would later

interact with each other in a humidifier and dehumidifier to produce fresh water. In another study,

Somwanshi and Sarkar (2020) designed a dual-purpose solar collector with storing capability. They

built an experimental setup based on the design that could be used for the sole purpose of air or

water heating. The setup was later utilized to validate a mathematical model based on the proposed

design. Soomro et al. (2021) conducted a thermodynamic investigation on a desalination system

integrated with a simultaneous solar air and water heater.

In this section, we aim to explore the potential for enhancing the performance of the integrated

SAH by utilizing the absorbed heat from the collector for simultaneous pretreatment of both air

and water. The configuration of the solar thermal system, depicted in Figure 5.23, demonstrates

how it is designed to effectively and simultaneously heat the air and water flows entering the

evaporator. The model developed to analyze the impact of this dual treatment is similar to the

computational model employed in Section 5.4. However, the key distinction lies in the inclusion

of a hypothetical zone situated between the absorber plate and the insulation. This additional

zone serves as a passage for the flow of water and interaction with the absorbed heat. Similarly,

for the computational modeling of the solar air-water heater (SAWH), the distribution of various

thermodynamic properties is obtained by solving the continuity, momentum, energy, and radiation

equations for distinct zones.

Figure 5.23 The geometry of the dual solar air-water heater as a replacement for the proposed SAH.

97

By employing computational models of the SAH and solar air-water heater (SAWH), we con-

ducted simulations for specific boundary conditions at East Lansing, Michigan. These conditions

include an inclination angle (𝜃) of 45◦, an ambient temperature of 30◦C (inlet temperature for both

air and water), and an ambient solar irradiation of 800 W/m2. These simulations allowed us to gain

insights into the potential benefits and improvements that can be achieved by incorporating dual

heating of air and water in the system. Figure 5.24 presents a comparison of the temperature rise

and thermal efficiency between the SAH and SAWH systems, with both configurations operating

under identical boundary conditions.

(a) SAH performance

(b) Dual solar air-water heater

Figure 5.24 Comparison of temperature rise and thermal efficiency for solar air and dual solar
air-water heaters. As anticipated, the introduction of additional flow with better thermal properties
into the proposed configuration of SAH enhances the thermal performance of the system while
pretreating both air and water simultaneously, resulting in an efficient humidification process in the
evaporator.

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Compared to the proposed SAH, the incorporation of water with air heating improved the

thermal efficiency of the system from 40% to an approximate value of 75%. Due to the higher

specific heat capacity of water compared to air (approximately four times greater), the SAWH

system operates with lower mass flow rates than the SAH, in order to achieve sufficient temperature

rise. Therefore, in the SAH simulations, we varied the air mass flow rate from 0.01 to 0.2kg/s,

while in the SAWH simulations, the air mass flow rate ranged from 0.01 to 0.02kg/s, and the water

mass flow rate varied from 0.01 to 0.03kg/s. The outlet temperatures of air and water of the SAWH

are used as the inlet condition for the humidifier component of the HDH direct-contact packed-bed

desalination. Using the values depicted in Figure 5.24 as inputs for the HDH mathematical model,

it is observed that despite the lower mass flow rate, the SWAH exhibits a significant improvement

in water production. Specifically, it can generate up to 76 g of water per kg of dry air, which is

a substantial enhancement compared to the 30 g reported in Table 5.5. This improvement can be

attributed to the influence of water pretreatment on the HDH system’s performance. With water’s

higher specific heat capacity, it becomes the dominant factor in determining the outlet temperature

of the air, leading to a higher humidity ratio. As a result, the SWAH system achieves a higher water

production capacity per unit of air mass flow rate, highlighting the importance of simultaneous

pretreating of both air and water in optimizing the performance of the overall integrated desalination

system. Future research will look into the comprehensive exploration of a dual solar air and water

heater system for the pretreatment stage of HDH desalination, aiming to assess its feasibility and

efficiency in greater detail.

5.9 Summary

In this study, we examined the potential of an integrated SAH with a direct-contact packed-

bed HDH desalination system that can be applied globally. We explored a novel design for the

SAH, deviating from the conventional configuration, by incorporating insulation layers around the

flow passage and absorber plate. This design aimed to minimize heat loss to the surroundings and

improve the system’s thermal efficiency. To experimentally investigate this concept, we constructed

a setup consisting of a wooden frame, insulation foam, a black-coated absorber plate, and a sealed

99

polycarbonate sheet serving as an air gap. The wooden frame, air gap, and insulation foam were

utilized to reduce heat loss from the solar thermal system. Computational and mathematical models

were developed based on the SAH’s geometry, and their accuracy was validated using experimental

data from a pilot setup. These models were then employed to evaluate the system’s performance

under various conditions and configurations. By coupling the validated mathematical model with

the HDH mathematical model, we were able to assess the system’s annual water treatment capacity

worldwide.

While the natural convection mode was initially preferred for the system’s operation, reducing

the cross-sectional area of the SAH led to a significant decrease in the air mass flow rate, neces-

sitating a shift to the forced convection mode, which proved to be more suitable for the integrated

water treatment system. The analysis demonstrated that the proposed system, equipped with a 3.5

m2 solar collector surface, had the capacity to treat an annual volume of water ranging from 5 to

30 tons across different locations worldwide. The treatment capacity was primarily influenced by

solar irradiation intensity and ambient temperature. Moreover, it was estimated that the system

could achieve a reduction of up to 150 kg of CO2 emissions per year compared to using reverse

osmosis (RO) technology to treat the same amount of water. While this reduction may appear

relatively small, when considering a scenario with 1000 of these systems, the cumulative reduction

in CO2 emissions would reach approximately 150 tons per year. Moreover, the assessment of an

alternative configuration that pretreats both air and water suggested that simultaneous pretreatment

enhances both the thermal efficiency (from 40% to 75%) and the treatment capacity of the system

per unit of air mass flow rate (from 30 to 60 g of water per kg of air mass).

While the preliminary analysis of the proposed integrated SAH desalination system showed

promising results, further investigation and research are needed to fully understand and optimize

its performance, as well as to assess its long-term reliability, cost-effectiveness, and environmental

impact. Additionally, studies focusing on system scalability and integration with existing infras-

tructure would be valuable in advancing the practical implementation of this innovative technology.

Furthermore, continued research into the development of advanced materials, enhanced heat trans-

100

fer mechanisms, and improved system designs would contribute to the ongoing refinement and

optimization of the integrated SAH desalination system for widespread deployment and maximum

efficiency.

101

CHAPTER 6

ANALYSIS OF TRANSPARENT SOLAR WATER HEATER WITH LIGHT SHIFTING
MATERIAL: SIMULATION AND EXPERIMENTAL EVALUATION

This chapter was published in Journal of Applied Energy, by Xu Tan, Mahyar Abedi, James

F. Klausner, and André Bénard, titled as Modeling and Experimental Validation of Light-

Splitting Semi-Transparent Solar Water Heater Using NIR Cut-Off Film as the Rooftop of a

Greenhouse for Arid Regions, Copyright Elsevier (2024).

https://doi.org/10.1016/j.apenergy.2024.123489.

6.1

Introduction

The water-food-energy nexus is a complex interplay among water, food, and energy systems,

where their interdependence shapes the sustainability of human societies (Simpson and Jewitt,

2019). Recognizing and addressing this nexus is vital in order to overcome the growing challenges

of resource scarcity and environmental degradation, as well as ensuring a resilient future for

generations to come. Arid regions, characterized by water scarcity, high temperatures, excessive

solar radiation, and minimal rainfall, face particularly formidable challenges when it comes to

sustaining agricultural practices under such circumstances (Mahmood and Al-Ansari, 2022; Abdel-

Ghany et al., 2012).

In this context, this paper presents a novel potential solution: a semi-transparent solar wa-

ter heater designed to serve as the roof of energy-efficient greenhouses. This innovative semi-

transparent solar water heater operates by splitting incoming light spectra into useful and ineffec-

tive wavebands. The useful portion of the light for most plants is PAR (Photosynthetically Active

Radiation), referring to the portion of the light spectrum that plants use to conduct photosynthesis,

typically between 400 to 700 nanometers. The ineffective segments of light beyond 700nm are

absorbed by the NIR (Near-Infrared) cut-off film and water, which are used for heating water.

The multiple benefits of this solar water heater include:

• Provide even shading with high PAR transmittance and high blocking rate for UV and IR,

including NIR.

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• Provide low-grade heat sources with a relatively high efficiency.

• Reduce the cooling load for the greenhouse.

• Increase the economic viability of the entire system by incorporating the solar water heater

with the greenhouse structure.

An example configuration of this innovative solar water heater is depicted in Figure 6.1. The

rooftop is outfitted with this semi-transparent solar heater that employs NIR cut-off film. The

panel permits most PAR light to transmit into the greenhouse and absorbs most of the NIR to heat

up the water in the panel. Brine/saline water is pumped into the roof panel from the inlet and

heated as it flows through the channel. The heated brine water subsequently enters a heat-driven

desalination system to produce freshwater, such as in the Humidification-Dehumidification and

Membrane Distillation desalination systems that utilize low-grade thermal energy (Chang et al.,

2012).

In the subsequent sections, Section 6.2 will be a critical analysis of the previous literature

and an explanation of the research gap. Then, the structure of the semi-transparent solar panel

is introduced in Section 6.3, followed by the mathematical model used to forecast the optical

and thermal performance metrics of the system outlined in Section 6.4. Next, a comprehensive

description of the experimental setup is presented in Section 6.5, accompanied by the results of

field tests. The numerical results are validated by the experimental measurements in Section 6.6, as

there is a close agreement on the outlet water temperatures and film temperatures. After confirming

the model’s validity through experimental corroboration, the paper further explored the feasibility

analysis of potential applications for this semi-transparent solar panel in Section 6.7. It provides

insights into its suitability, efficiency, and benefits, particularly when used as roofing for energy-

efficient greenhouses. This aligns with the broader aim of developing sustainable and economically

viable solutions to address water and food scarcity challenges in arid regions.

6.2 Literature Review

Previous research has explored various techniques to control solar energy entering the green-

house, focusing on the rooftop. Whitening the roof can be achieved by spraying the exterior cover

103

Figure 6.1 Schematic of an energy-efficient greenhouse with a semi-transparent solar heater rooftop
using NIR cut-off film (Chang et al., 2012).

surface with material like hydrated Calcium oxide (Ca(OH)2) (Baille et al., 2001). It is inexpensive

and can efficiently reduce heat load. However, this method will significantly reduce solar radiation

transmittance, and the paint could be washed away by rain (Mashonjowa et al., 2010). External

shade cloths are usually applied with wet or dry shade cloths on the outer surface of the greenhouse

roof (Ghosal et al., 2003). Although this method can also regulate solar irradiance, it decreases

natural roof ventilation effectiveness and re-emits solar energy to increase the temperature inside

(Willits, 2003). Movable plastic nets, curtains, or refractive screens provide flexible control over

solar energy, but they also reduce natural roof ventilation and re-emit solar radiation inside (Tantau

et al., 2006).

A relatively more sophisticated technique is to utilize radiation filters that can selectively control

solar radiation to optimize the greenhouse environment. Water film was first invented, and it has high

PAR transmittance, but it has poor performance in blocking NIR performance (Abdel-Ghany et al.,

2001b). Later, water solutions, for example, 1.5%CuSO4, were tested instead, and results showed

that the film could remove more than 50% of solar energy and maintain an inside air temperature

of about 5°C below the outside temperature. In addition, Abdel-Ghany et al. (2016) suggested the

heat absorbed by the solution can be stored and used. However, most previous researches were

104

only theoretical simulations (Sadler and Van Bavel, 1984), and the tested outlet temperature of the

heated solution could not reach 40◦C (Abdel-Ghany et al., 2001a). The disadvantages of liquid

film using water solutions include a relatively more complex structure and higher cost (Van Bavel

et al., 1981) compared to other shading techniques, potential hazards due to toxic copper salts, and

lower PAR transmittance (Abdel-Ghany et al., 2016).

In recent years, spectra-shifting films have been invented for photosynthesis and light capture

to increase crop yield. Targeting leafy crops such as lettuces, Shen et al. (2021) fabricated a

type of film that can convert green light (500-600nm) to more photosynthetically active red light

(600-700nm). Results showed some improvements in the lettuce growth, but this type of film did

not affect cooling down the greenhouse.

A significant number of studies were presented focusing on using solar PV as the rooftop of the

greenhouse, including opaque solar PV panels and semi-transparent solar PVs. Opaque solar PV

panels have to partially cover the greenhouse, resulting in permanent and complete shading that is

not evenly distributed in the greenhouse. The shading potentially can lead to a reduction in food

harvest (Moretti and Marucci, 2019), and uneven distribution of the shading can cause differences

in growth and development (Allardyce et al., 2017). Although adjustable solar panel structures have

been proposed and studied (Alinejad et al., 2020), they will significantly increase the complexity

and cost of greenhouses.

Transparent/semi-transparent solar PVs have been developed so that the panels/films can provide

even shading to the inside of the greenhouse. However, these types of PVs must have low

energy conversion efficiency if high transmittance is desired; otherwise, the transparency has to be

significantly compromised if energy efficiency needs to increase, which is not favorable to be used

on the greenhouses. For example, Waller et al. (2022) tested a type of flexible Organic Photovoltaics

(OPVs), but the energy conversion efficiency was only 1.82%. Yano et al. (2014) designed and

tested a type of semi-transparent PV made with Spherical solar microcells. Two prototypes with

different transmittances of 61% and 87% only had energy conversion efficiencies of 4.5% and

1.5%, respectively. Hassanien and Ming (2017) tested their semi-transparent PV, claimed to have

105

8.25% energy conversion efficiency and 47% transmittance according to its manufacturer. Zhao

et al. (2023) proposed and tested a type of OPV with an efficiency as high as 13.5%, but the

transmittance is only 21.5%. Ma et al. (2022) prototyped a novel greenhouse covering using a

compound parabolic structure with PV cells and The spectral splitting film, which can transmit

visible light and convert near-infrared light into electricity. The photovoltaic efficiency was 6.88%,

and the transmittance could be more than 40%. However, the structure was quite complicated, and

it currently has no potential for massive production.

For solar water heaters, there is very little research that considers integrating it into the roof

of greenhouses. Traditional water heaters are opaque and difficult to integrate into the rooftop

of a greenhouse. Ihoume et al. (2023) placed a copper coil between double glass layers on the

greenhouse’s roof to serve as a semi-transparent solar heater. However, no performance data for

the water heater were presented. Water solution film as the greenhouse’s roof could be used as a

water heater, but the outlet water temperature was too low for effective use. Chaibi and Jilar (2004)

coated Glass and Acrylic sheets with semi-transparent absorbing films to build a small solar still

desalination system used as part of the greenhouse roof. However, the water temperature could

only reach 40◦𝐶, and water production was not discussed. The system had a 25% solar spectrum

transmission with 56% absorption, but real optical performance was not measured. Light-selective

(NIR absorbing) films were recommended for future research. Mamouri et al. (2020) proposed

an integrated greenhouse system using a semi-transparent solar water heater with light-splitting

(NIR absorbing) film as the roof to heat up the saline water that could be used in a Humidification-

Dehumidification (HDH) desalination system to produce fresh water. However, the paper was

only a theoretical system analysis and did not offer a specific design for practical application.

Similarly, Mahmood and Al-Ansari (2022) proposed an integrated greenhouse system that used

a semi-transparent solar water heater as the greenhouse roof. This was also only a hypothetical

thermodynamics analysis, and the water simply flowed through a channel formed by two layers of

polycarbonate sheets, which in practice would likely have poor thermal performance due to low

solar radiation absorption and high heat loss.

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Previous semi-transparent solar panels discussed in the literature, have thus suffered either from

low optical performance, low thermal performance, or both. This paper aims to fill this research gap

by proposing, constructing, and examining a semi-transparent solar water heater using NIR cut-off

film. The primary objective is to assess the feasibility and benefits of this novel semi-transparent

solar water heater, focusing on its optical behavior and thermal performance.

6.3 Design of a Semi-Transparent Solar Panel

In order to comprehensively assess the performance of a semi-transparent panel as a solar

water heater, it is crucial to examine the system’s behavior through experimental evaluation and

modeling analysis. While Section 6.4 will focus on the necessary steps for the development of the

mathematical model, in this section, we will describe the concept of a semi-transparent solar water

heater. While conventional solar water heaters are generally comprised of an opaque collector,

which results in a near-complete absorption of incoming solar energy and the light spectrum, the

idea of a semi-transparent panel was introduced (Mamouri et al., 2020) to utilize portion of the

incoming spectrum for heating water, whereas the rest was designated for other purposes (within the

scope of this chapter, this particular purpose is to provide the required energy for the photosynthetic

mechanism within different species of plants).

Figure 6.2 illustrates the configuration of the solar panel used within this chapter. It consists

of four transparent walls. Centrally located is a water channel (Figure 6.3). Above and below the

water channel are two transparent covers that form two air gaps functioning as thermal insulators.

All the transparent walls are made of polycarbonate (PC), and a layer of NIR cut-off film is attached

to the top of the upper wall of the water channel. The top layer of polycarbonate, meanwhile, can

block UV light to protect the NIR cut-off film for extended durability. Section 6.4 will detail the

model used to calculate the optical performance of the solar panel (transmittance, emittance, and

reflectance), which are essential metrics for evaluating the thermal performance of the panel and

for estimating the amount of PAR that will be transmitted into the greenhouse.

Figure 6.3 outlines the structure of a twin-wall PC panel as the water channel in the semi-

transparent solar panel. A semi-transparent NIR cut-off film lies on the upper surface of the

107

Figure 6.2 Configuration of the solar panel. It consists of four transparent walls. Centrally located
is a water channel. Above and below the water channel are two transparent covers that form two air
gaps functioning as thermal insulators. All the transparent walls are made of polycarbonate (PC),
and a layer of NIR cut-off film is attached to the top of the upper wall of the water channel. The top
layer of polycarbonate, meanwhile, can block UV light to protect the NIR cut-off film for extended
durability.

panel. The film alters the incoming solar irradiation by absorbing certain spectrum wavelengths

and allowing the rest to transmit. The absorbed wavelengths provide an energy source to heat water,

whereas transmitted wavelengths are utilized for plant growth.

Figure 6.3 Structure of a twin-wall PC panel used as the water channel in the semi-transparent solar
water heater.

108

6.4 Mathematical Modeling

To accurately predict the solar panel’s performance, the model must account for the sun’s

position relative to the location and time in order to calculate the incident angle of the irradiance.

Simultaneously, the model should also possess the capability to evaluate the optical performance,

including transmittance, reflectance, and absorptance, based on the incident angle. Finally, the

model will determine the outlet water temperatures by taking into account solar irradiance, incident

angle, optical performance, ambient temperature, and wind speed. Subsequent sections will provide

a detailed description of the model.

6.4.1 Sun Position and Incident Angle

Transmittance, reflectance, and absorptance are influenced by changes in the incidence angle.

Consequently, to accurately assess panel performance, it is important that the model incorporates

the sun’s position and incident angle. Figure 6.4 illustrates the spatial relationships between the

sun, the earth, and the solar panel, as well as some definitions of the angles. The angle of incidence

is determined using Equation (6.1) (Duffie and Beckman, 2013).

cos 𝜃 = sin 𝛿 sin 𝜙 cos 𝛽 − sin 𝛿 cos 𝜙 sin 𝛽 cos 𝛾 + cos 𝛿 cos 𝜙 cos 𝛽 cos 𝜔

+ cos 𝛿 sin 𝜙 sin 𝛽 cos 𝛾 cos 𝜔 + cos 𝛿 sin 𝛽 sin 𝛾 sin 𝜔

(6.1)

In Equation (6.1), 𝜃 is the incident angle defined as the angle between the normal vector of the

inclined surface and the solar beam falling on the surface; 𝜙 is the latitude; 𝛽 is the inclination

angle of the surface with respect to the horizontal plane; 𝛾 is the surface azimuth angle defined

as the angle between the projected normal vector of the inclined surface on the horizontal plane

with the south-pointing vector, 𝛿 is the declination angle, and 𝜔 is the hour angle. The following

includes methodology to calculate some of these parameters and, eventually, the incidence angle.

While not all the angles in Figure 6.4 are used in Equation (6.1), the definitions for the other

angles not mentioned are as follows.

Declination (𝛿): The angular position of the sun at solar noon (i.e., when the sun is on the

109

Figure 6.4 Relations among the sun, the earth, and the solar panel surface. (a) Zenith angle (𝜃𝑧): the
angle between the solar beam and the normal to the horizontal earth surface. Solar altitude angle
(𝛼𝑠): the angle between the horizontal and the line to the sun, that is, the complement of the zenith
angle. (b) Solar azimuth angle (𝛾𝑠): the angular displacement from south of the projection of beam
radiation on the horizontal plane. Surface azimuth angle (𝛾): the deviation of the projection on a
horizontal plane of the normal to the surface from the local meridian. (c) The angle of incidence
(𝜃): the angle between the beam radiation on a surface and the normal to that surface. Slope (𝛽):
the angle between the plane of the solar panel surface and the horizontal.

local meridian) with respect to the plane of the equator, north positive, −23.45◦ ≤ 𝛿 ≤ 23.45◦.

𝛿 = 23.45 sin

(cid:18)

360 ×

284 + 𝑑𝑎𝑦𝑛
365

(cid:19)

where 𝑑𝑎𝑦𝑛 is the 𝑛𝑡ℎ day of the year.

Latitude (𝜙): −90◦ ≤ 𝜙 ≤ 90◦.

Hour angle (𝜔): Noon is set to 0◦. Morning has a negative hour angle, while afternoon has

a positive value with ±15◦ variation per hour. 0:00 am to 12:00 pm translates to −180◦ to 180◦.

𝜔 = (𝑆𝑜𝑙𝑎𝑟 𝑡𝑖𝑚𝑒 − 12) × 15◦.

In order to calculate the hour angle, it is necessary to determine the local solar time, which is

different from the standard time displayed in a clock. Equation (6.2) (Tiwari et al., 2016) illustrates

the relation between solar time and standard time.

𝑆𝑜𝑙𝑎𝑟 𝑡𝑖𝑚𝑒 − 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑡𝑖𝑚𝑒 = 4 (𝐿𝑠𝑡 − 𝐿𝑙𝑜𝑐) + 𝐸

(6.2)

110

where 𝐿𝑠𝑡 is the standard meridian longitude, 𝐿𝑙𝑜𝑐 is the longitude of the actual location. The

parameter E is the equation of the time (minute) that can be calculated with Equation (6.3)(Tiwari

et al., 2016).

𝐸 = 229.2(0.000075 + 0.001868𝑐𝑜𝑠𝐵 − 0.032077𝑠𝑖𝑛𝐵 − 0.014615𝑐𝑜𝑠2𝐵 − 0.04089𝑠𝑖𝑛2𝐵) (6.3)

where 𝐵 is calculated by Equation (6.4)

𝐵 = (𝑑𝑎𝑦𝑛 − 1) × 360/365

(6.4)

6.4.2 Model of Optical Performance

6.4.2.1 Optical Performance Modeling

The structure of this novel panel is comprised of multiple layers, and its optical properties

can be derived using light propagation formulas (Duffie and Beckman, 2013; Tiwari et al., 2016;

Brownson, 2013).

When light passes through from one material to another, the angles of incidence (𝜃1) and

refraction (𝜃2) are governed by Equation (6.5), i.e.,

𝑛1 sin (𝜃1) = 𝑛2 sin (𝜃2)

(6.5)

where 𝑛1 is the refractive index of Material 1, and 𝑛2 is the refractive index of Material 2. Given

the two angles, the reflectivity (r) between the two materials can be calculated by Equations (6.6) -

(6.8) (Tiwari et al., 2016).

𝑟⊥ =

sin2(𝜃2 − 𝜃1)
sin2(𝜃2 + 𝜃1)

𝑟 ∥ =

𝑠𝑖𝑛2 (𝜃2 − 𝜃1)
𝑠𝑖𝑛2 (𝜃2 + 𝜃1)

𝑟 =

1
2

(cid:0)𝑟⊥ + 𝑟 ∥

(cid:1) , 𝑟 (0◦) =

(cid:19) 2

(cid:18) 𝑛1 − 𝑛2
𝑛1 + 𝑛2

111

(6.6)

(6.7)

(6.8)

where r is the average of the perpendicular (𝑟⊥) and the parallel (𝑟 ∥) polarized components of the

reflected light, as described in Equation (6.6) and (6.7). The next step is to calculate the transmission

accounting only for absorption, denoted as 𝜏𝛼 using Equation (6.9) (Tiwari et al., 2016), i.e.,

𝜏𝛼 = 𝑒𝑥 𝑝

(cid:18)

−

(cid:19)

𝑘 𝑑
𝑐𝑜𝑠 (𝜃2)

(6.9)

where 𝑘 is the extinction coefficient of Material 2 (measured in 𝑚−1), 𝑑 is the thickness of Material

2, and 𝜃2 is the angle of refraction on the side of Material 2. The extinction coefficient demonstrates

significant variation across different ranges of wavelength for light. For example, water has high

transmissivity for visible light but exhibits very high absorptivity for infrared light. Therefore,

the optical performance is analyzed for every nanometer of wavelength and then is integrated for

different ranges of light. Transmittance (𝜏), reflectance (𝜌), and absorptance (𝛼) can then be

calculated using Equations (6.10) - (6.12) (Tiwari et al., 2016) with reflectivity and transmittance

attributable solely to absorption. Again, these properties are the average of their perpendicular (⊥)

and parallel components (∥) and are obtained through the following equations.

𝜏 =

1
2

(cid:0)𝜏⊥ + 𝜏∥

(cid:1) , 𝜏⊥ =

𝜏𝛼 (1 − 𝑟⊥)2
1 − (𝑟⊥𝜏𝛼)2

, 𝜏∥ =

(cid:1) 2

𝜏𝛼 (cid:0)1 − 𝑟 ∥
1 − (cid:0)𝑟 ∥𝜏𝛼(cid:1) 2

𝜌 =

1
2

(cid:0) 𝜌⊥ + 𝜌∥

(cid:1) , 𝜌⊥ = 𝑟⊥ (1 + 𝜏𝛼𝜏⊥) , 𝜌∥ = 𝑟 ∥

(cid:0)1 + 𝜏𝛼𝜏∥

(cid:1)

(6.10)

(6.11)

𝛼 =

(cid:18) 1 − 𝑟⊥
1 − 𝑟⊥𝜏𝛼
When two layers of different materials stack on one another, the overall transmittance 𝜏12,

(cid:18) 1 − 𝑟 ∥
1 − 𝑟 ∥𝜏𝛼

(cid:1) , 𝛼⊥ = (1 − 𝜏𝛼)

, 𝛼∥ = (1 − 𝜏𝛼)

(cid:0)𝛼⊥ + 𝛼∥

(6.12)

1
2

(cid:19)

(cid:19)

reflectance 𝜌12, and absorptance 𝛼12 can be calculated by Equations (6.13) - (6.15) (Tiwari et al.,

2016), which are given below.

𝜏12 =

1
2

(cid:0)𝜏12,⊥ + 𝜏12,∥

(cid:1) =

(cid:34)(cid:18)

1
2

(cid:19)

𝜏1𝜏2
1 − 𝜌1𝜌2

+

⊥

(cid:18)

𝜏1𝜏2
1 − 𝜌1𝜌2

(cid:35)

(cid:19)

∥

(6.13)

112

𝜌12 =

1
2

(cid:0)𝜌12,⊥ + 𝜌12,∥

(cid:1) =

(cid:34) (cid:18)

1
2

𝜌1 + 𝜏

(cid:19)

𝜌2𝜏1
𝜏2

⊥

(cid:18)

+

𝜌1 + 𝜏

𝜌2𝜏1
𝜏2

(cid:35)

(cid:19)

∥

𝛼12 = 1 − 𝜏12 − 𝜌12

(6.14)

(6.15)

Figure 6.5 Impletemented methodology to estimate the optical performance of the solar panel,
assuming the NIR film placed on top of the water channel.

The optical properties of the solar panel are finally calculated through Equations (6.5) - (6.15)

(Tiwari et al., 2016). The process is outlined in Figure 6.5. Starting from the top layer, we calculate

the combined properties of the first and second layers. Next, by treating the first and second layers

as a single entity, we proceed to combine the first three layers using the previously mentioned

equations. This iterative process continues until the properties for the entire system are obtained.

6.4.2.2 Material Properties

The refractive index and absorptivity of material vary not only among different materials but

also across different wavelengths of light. Therefore, the evaluation of the panel’s performance

spans every nanometer in the range of 300 - 2500nm of light. This section provides a brief overview

of the optical properties of each material incorporated into the mathematical model.

The NIR absorption film was developed in the lab at the University of Colorado. The film,

composed of Epolight™ 1178 and Epolight™ 4019 Near Infrared Dyes, was prepared by dissolving

the dyes in their solvent. Once dried in film molds, the films were ready for use. Figure 6.6 (a)

113

depicts the transmissivity of the NIR absorption film, only considering absorption, across the

wavelengths of 300 - 1200nm. Beyond 1200nm, the film transmissivity rapidly rises to about 95%.

The refractive index of the NIR film was 1.57. Figure 6.6 (b) showcases a sample piece of the

NIR cut-off film, which is displayed atop a white paper labeled "A sample piece of NIR absorption

film". Despite its yellow appearance, the film maintains transparency, allowing the underlying text

to be clearly visible.

The refractive index and light absorptivity of water fluctuate across the wavelength of 300 -

2500nm and were derived by interpolating the data from the reference (Hale and Querry, 1973).

Water exhibits a very low extinction factor for light between 400 - 700 nm but a significantly high

extinction factor for light exceeding 1200 nm. In other words, it allows a very high absorptivity for

infrared light waveband.

Figure 6.6 (a) Transmissivity of the NIR absorption film, (b)A sample piece of NIR absorption film
atop a piece of white paper, (c) ASTM G173-03 Reference Spectra

The refractive index of polycarbonate remains relatively stable, ranging between 1.61 and 1.58

from short to long wavelength of light (Horsthuis et al., 1993). Polycarbonate absorbs nearly 100%

UV light; the extinction coefficient was thus considered to be infinitely large for these wavelengths.

For wavelengths beyond 400nm, the extinction coefficient approaches 0; however, exact numbers

were not able to be found in the literature, so a value of 0.01𝑚−1 was used in the simulations.

Importantly, the first layer of the polycarbonate sheet can almost completely absorb UV light.

Therefore, the radiation in the range of 300-400nm, which constitutes about 3% of the total solar

radiation, is treated as a heat source of the equivalent value in the first layer of the polycarbonate

sheet.

114

In this paper, the overall optical properties of the solar panel are calculated as a function of

wavelength and incidence angle. For every incidence angle, optical properties are computed using

Equations (6.5) through (6.15) for each nanometer of light wavelength. The light spectra use the

reference spectra available from the U.S. National Renewable Energy Laboratory (NREL) website,

as depicted in Figure 6.7(c). For a specific angle, the optical properties across a given range of

discrete wavelengths are determined using a weighted average as specified in Equation (6.16),

which is given below.

𝑊 =

(cid:205)𝑖=𝐿𝑎𝑠𝑡 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛

𝑖=1𝑠𝑡 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝜆𝑖𝐸𝑖 𝑋𝑖
(cid:205)𝑖=𝐿𝑎𝑠𝑡 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛
𝑖=1𝑠𝑡 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝜆𝑖𝐸𝑖

(6.16)

where 𝜆𝑖 is the 𝑖𝑡ℎ wavelength division, 𝑋𝑖 represents properties like calculated transmittance,

reflectance, and absorptance, and 𝐸𝑖 is the spectral irradiance (W/m2 nm). In this research, the

calculations were performed at every nanometer, so the value of 𝜆𝑖 was set to 1nm. The wavelength

ranges of 400 - 700nm (PAR) and 300 - 2500nm were particularly scrutinized for subsequent

research.

Figure 6.7 displays the calculated optical properties utilizing the method outlined previously

in this section. Figure 6.7(a) presents the optical properties for light between 400-700nm (PAR),

and Figure 6.7(b) reveals the properties for light comprehensively across the broader spectrum of

300-2500nm. In both graphs, the optical properties remain relatively constant when the incidence

angle is less than 60◦. Starting around 50◦, the reflectance of the solar panel sharply increases and

reaches 1 when the incidence angle is 90◦. Concurrently, both transmittance and absorptance drop

down to 0. According to Figure 6.7(a), more than 55% of PAR can pass through the panel when

the incidence angle is less than 60◦. However, for the complete spectrum of solar radiation, only

about 30% will pass through the panel, and more than 50% of solar radiation is absorbed by the

solar panel when the incidence angle is lower than 60◦.

6.4.3

1D Model of Thermal Performance and Analysis of the Solar Heater

The thermal performance is evaluated based on a transient one-dimensional (1D) finite differ-

ence analysis, focusing on energy balance in the x direction (along the solar panel). Solar thermal

115

Figure 6.7 Optical properties (a) within the range of 400 – 700nm, (b) spanning 300 – 2500nm. In
both graphs, the optical properties remain relatively constant when the incidence angle is less than
60◦. Starting around 50◦, the reflectance of the solar panel sharply increases and reaches 1 when
the incidence angle is 90◦. Concurrently, both transmittance and absorptance drop down to 0.

resistance circuit analysis is employed to estimate heat losses between the panel and its surrounding

environment.

6.4.3.1

1D Energy Balance in a Finite Length of Water Channel

Figure 6.8 serves as a schematic illustrating how 1D finite difference analysis is implemented.

In the context of the panel, 𝑊 represents the width (m); 𝐿 signifies the length (m); 𝑥 is the axis

along the length of the solar panel, and 𝑑𝑥 is the finite length of the water channel. 𝑇𝑤 is the water

temperature; (cid:164)𝑚𝑤 is the mass flow rate of water; (cid:164)𝑞𝑎𝑏, 𝑓 𝑖𝑙𝑚 is the heat absorbed by the film; (cid:164)𝑞𝑎𝑏,𝑤𝑎𝑡𝑒𝑟

is the heat absorbed by the water; (cid:164)𝑞 𝐿1 and (cid:164)𝑞 𝐿2 are the heat losses to the upper and lower sides of

the solar panel. Water flows from the left along the length of the panel in the 𝑥 direction. The

top portion of Figure 6.8 provides a zoomed-in view of a finite length (𝑑𝑥, m) of the solar panel.

The energy balance is initially expressed by Equation (6.17) and subsequently reformulated into

Equation (6.18).

(cid:164)𝑚𝑤𝐶𝑝 ( 𝑇𝑤 |𝑥+𝑑𝑥 − 𝑇𝑤 |𝑥) + 𝜌𝐶𝑝 (𝐻 × 𝑑𝑥 × 𝑊)

𝜌𝐶𝑝𝐻𝑊

𝑑𝑇
𝑑𝑡

= (cid:164)𝑞𝑢 × 𝑊 − (cid:164)𝑚𝑤𝐶𝑝

𝑑𝑇
𝑑𝑡
𝑑𝑇
𝑑𝑥

= (cid:164)𝑞𝑢 × 𝑑𝑥 × 𝑊

(6.17)

(6.18)

where (cid:164)𝑚𝑤 is the mass flow (kg/s); 𝐶𝑝 is the heat capacity of water (J/(kg.K)); 𝐻 is the height of the

channel (m); 𝜌 is the density of water (kg/m3); (cid:164)𝑞𝑢 means the useful heat transfer rate into the water

116

Figure 6.8 Schematic of one-dimensional energy balance in a finite length of the water channel. 𝑊
is the width of the solar panel; 𝐿 is the length of the solar panel. 𝑥 is the axis along the length of
the solar panel, and 𝑑𝑥 is the finite length of the water channel. 𝑇𝑤 is the water temperature; (cid:164)𝑚𝑤 is
the mass flow rate of water; (cid:164)𝑞𝑎𝑏, 𝑓 𝑖𝑙𝑚 is the heat absorbed by the film; (cid:164)𝑞𝑎𝑏,𝑤𝑎𝑡𝑒𝑟 is the heat absorbed
by the water; (cid:164)𝑞 𝐿1 and (cid:164)𝑞 𝐿2 are the heat losses to the upper and lower sides of the solar panel.

(W/m2). Useful heat flux can be calculated by Equation (6.19).

(cid:164)𝑞𝑢 = ( (cid:164)𝑞𝑎𝑏, 𝑓 𝑖𝑙𝑚 + (cid:164)𝑞𝑎𝑏,𝑤𝑎𝑡𝑒𝑟) − ( (cid:164)𝑞 𝐿1 + (cid:164)𝑞 𝐿2)

(6.19)

(cid:164)𝑞𝑎𝑏, 𝑓 𝑖𝑙𝑚 and (cid:164)𝑞𝑎𝑏,𝑤𝑎𝑡𝑒𝑟 denote the heat absorbed by the film and water. The heat absorbed by

water is treated as heat generation, depicted by the red dots in Figure 6.8.

6.4.3.2 Thermal Resistance Circuit Analysis

Our focus now shifts to calculating the heat loss, which is critical for estimating the useful heat

transfer rate and the water temperature. The subsequent section elaborates on the methodology

used for thermal resistance circuit analysis.

Figure 6.9 serves as an illustrative diagram for the thermal resistance circuit. In order to apply

thermal resistance circuit analysis, it is necessary to make the following assumptions:

1. Heat transfer between the surfaces within the solar panel and between the solar panel and its

surrounding environment is assumed to be perpendicular to the surfaces.

117

Figure 6.9 Thermal resistance circuit for the solar panel analysis. The left side depicts a cross-
sectional view of the solar panel, while the right side presents the corresponding thermal circuit at
location 𝑥 along the length of the solar panel.

2. Though the thermal resistance circuit is generally employed for steady-state scenarios, this

research involves a 1D transient thermal model. Given the slow flow velocity in the water

channel, heat transfer normal to the surface of the panel is assumed to approximate a pseudo-

steady state condition.

Below are the equations used to calculate the thermal resistances between the various nodes, shown

in Figure 6.9.

(1) Between the atmosphere and the top cover

Convective heat transfer and radiation occur between the top side of the panel and the ambient.

The convective heat transfer coefficient is estimated based on wind speed, as shown in Equation

(6.20). Although various correlations are available, Equation (6.20) (Tiwari et al., 2016) was

chosen for its focus solely on convective heat transfer.

ℎ1, 𝑐𝑜𝑛𝑣 =

1
𝑅1, 𝑐𝑜𝑛𝑣

= 2.8 + 3.0𝑉𝑤𝑖𝑛𝑑

𝑓 𝑜𝑟

0 ≤ 𝑉𝑤𝑖𝑛𝑑 ≤ 5 𝑚/𝑠

(6.20)

118

where ℎ1, 𝑐 represents the convective heat transfer coefficient between the top surface and the envi-

ronment (W/(m2.K)), 𝑅1, 𝑐 is its corresponding thermal resistance for convection. 𝑉𝑤𝑖𝑛𝑑 represents

the wind speed over the top surface of the solar panel. Though wind speed wasn’t continuously

monitored, it was measured intermittently using a hotwire anemometer. It was observed that at the

location of the solar panel, the wind speeds above and below the solar panel never exceeded 1 m/s

from all directions. Therefore, during the simulation, the wind speeds were assumed constant at

1 m/s. While multiple correlations are available (Duffie and Beckman, 2013; Tiwari et al., 2016;

Brownson, 2013; Sharples and Charlesworth, 1998; Test et al., 1981) to estimate the convective heat

transfer coefficient over a flat surface, Equation (6.20) (Tiwari et al., 2016) is recommended because

it excludes the effect of radiation that is considered separately with Equation (6.21) (Incropera et al.,

2018).

ℎ1, 𝑟𝑎𝑑 =

1
𝑅1, 𝑟𝑎𝑑

= 𝜀 𝑝𝑐𝜎 (cid:2)𝑇1

2 + 𝑇𝑠𝑘 𝑦

2(cid:3) (cid:0)𝑇1 + 𝑇𝑠𝑘 𝑦(cid:1)

(6.21)

where ℎ1, 𝑟𝑎𝑑 and 𝑅1, 𝑟𝑎𝑑 are the heat transfer coefficient and thermal resistance between the top

surface of the solar panel and the environment due to radiation. 𝜎 = 5.67 × 10−8 𝑊/𝑚2 𝐾 4 is

Stefan-Boltzmann constant; 𝜀 𝑝𝑐 is the emissivity of the polycarbonate sheet, which was 0.9 in the

simulation; 𝑇1 represents the temperature at the top surface of the solar panel (𝐾); 𝑇𝑠𝑘 𝑦 is the sky

temperature, estimated using Equation (6.22) (Tiwari et al., 2016) (𝐾).

𝑇𝑠𝑘 𝑦 = 𝑇𝑎 − 6

(6.22)

where 𝑇𝑎 represents the air temperature above the solar panel (𝐾).

The overall thermal resistance between the top surface of the could be obtained by Equation

(6.23)

𝑅1 =

1
ℎ1, 𝑐𝑜𝑛𝑣 + ℎ1, 𝑟𝑎𝑑

(6.23)

(2) Heat conduction through the first layer of polycarbonate

In a layer of polycarbonate, heat conduction is the only mode of heat transfer considered. It is

calculated using Equation (6.24) (Incropera et al., 2018).

𝑅2 =

1
ℎ2, 𝑐𝑜𝑛𝑑

=

𝑑 𝑝𝑐
𝑘 𝑝𝑐

119

(6.24)

where 𝑘 𝑝𝑐 is the thermal conductivity of the cover material; 𝑑 𝑝𝑐 is the thickness of the cover.

(3) Between the first layer of polycarbonate and the film

The heat transfer between the top layer of the polycarbonate (PC) sheet and the film includes

both convection and radiation. Because the film is so thin that its thickness can be considered

negligible, the temperature at the top surface of the water channel wall - that is, the second layer of

PC sheet - and the film temperature are considered identical. Therefore, the radiative heat transfer

coefficient can be calculated using Equation (6.25).

ℎ3, 𝑟𝑎𝑑 =

1
𝑅3, 𝑟𝑎𝑑

= 𝜎𝜀𝑒 𝑓 𝑓

(cid:16)
𝑓 𝑖𝑙𝑚 + 𝑇 2
𝑇 2
2

(cid:17)

(𝑇 𝑓 𝑖𝑙𝑚 + 𝑇2)

(6.25)

where 𝜀𝑒 𝑓 𝑓 is the effective emissivity calculated using emissivities of both the film (𝜀 𝑓 𝑖𝑙𝑚, 0.9) and

polycarbonate sheet (𝜀 𝑝𝑐) using Equation (6.26).

𝜀𝑒 𝑓 𝑓 = 1/

(cid:18) 1
𝜀 𝑓 𝑖𝑙𝑚

+

1
𝜀 𝑝𝑐

(cid:19)

− 1

(6.26)

In addition to radiative heat transfer, natural convection also occurs between the two surfaces of the

air gap. The convective heat transfer coefficient is determined using the Equations (6.27) - (6.29)

(Incropera et al., 2018).

𝑁𝑢 =






1 + 1.446[1 − 1708

𝑅𝑎·𝑐𝑜𝑠𝛽 ], 1708 < 𝑅𝑎 · 𝑐𝑜𝑠𝛽 < 5900

0.229(𝑅𝑎 · 𝑐𝑜𝑠𝛽)0.252, 5900 < 𝑅𝑎 · 𝑐𝑜𝑠𝛽 < 9.23 × 104

(6.27)

0.157(𝑅𝑎 · 𝑐𝑜𝑠𝛽)0.252, 9.23 × 104 < 𝑅𝑎 · 𝑐𝑜𝑠𝛽 < 106

𝑅𝑎 =

𝑔𝛽′Δ𝑇 𝑑3
𝜈𝛼

(6.28)

1
𝑅3, 𝑐𝑜𝑛𝑣
where 𝛽 is the inclination angle of the panel, ◦; 𝑅𝑎 is Rayleigh number defined by Equation (6.28);

ℎ3, 𝑐𝑜𝑛𝑣 =

(6.29)

=

𝑁𝑢 · 𝑘 𝑎𝑖𝑟
𝑑ℎ,𝑔𝑎 𝑝

𝑁𝑢 is the Nusselt number, used to calculate convective coefficient according to Equation (6.27); 𝑔

is the gravity (𝑚/𝑠2); 𝛽′

is thermal expansion coefficient (for an ideal gas, 𝛽′ = 1/𝑇 (1/𝐾); 𝜈 is

kinematic viscosity (𝑚2/𝑠); 𝛼 is thermal diffusivity (𝑚2/𝑠); Δ𝑇 is temperature difference between

the two walls of the gap (𝐾); 𝑑ℎ,𝑔𝑎 𝑝 is the hydraulic diameter of the gap (m); 𝑘 𝑎𝑖𝑟 is the thermal

120

conductivity of air (𝑊/(𝑚.𝐾)). As a result, the overall thermal resistance between the inner surface

of the cover and the film can be calculated with Equation (6.30).

𝑅3 =

1
ℎ3, 𝑟𝑎𝑑 + ℎ3,𝑐𝑜𝑛𝑣

(6.30)

(4) Heat conduction between the film and the lower surface of the second layer of the PC sheet

Only heat conduction is considered between the film and the lower surface of the second layer

of the PC sheet.

𝑅4 =

𝑑 𝑝𝑐
𝑘 𝑝𝑐

(6.31)

(5) Between the two sides of the water channel

In this section, only convective heat transfer is considered through the two walls of the water

channel. For this prototype, the flow rate of the water was no higher than 10mL/s. Consequently,

the Reynolds number of the flow can be estimated to be around 30, falling within the laminar flow

range. Accordingly, the Nusselt number of the channel is 8.32 (Bejan, 2013), which is appropriate

for a channel where the width is much greater than the height. Additionally, the node for the

water temperature is considered to be located at the center of the water channel. Both the thermal

resistances from the top side of the channel to the node of the water and from the water node to

the bottom surface of the water channel are assumed to be identical. These can be calculated using

Equation (6.32).

ℎ5, 𝑐𝑜𝑛𝑣 =

1
𝑅5

=

𝑁𝑢 · 𝑘 𝑤𝑎𝑡𝑒𝑟
𝑑ℎ

, 𝑁𝑢 = 8.32

(6.32)

where 𝑘 𝑤𝑎𝑡𝑒𝑟 is the thermal conductivity of water, 𝑊/(𝑚.𝐾); 𝑑ℎ is the hydraulic diameter. In the

case of an extended wide channel, 𝑑ℎ is two times the height of the channel, 𝑚.

Furthermore, a heat source resulting from water absorbing infrared light is also considered. The

amount of thermal energy absorbed by the water is estimated by subtracting the heat absorption in

the top layer PC and the NIR-cutoff film from the total absorbed heat by the solar panel.

(6) Heat conduction through the third layer of PC sheet.

The thermal resistance 𝑅6 for the third layer of PC sheet due to conduction can be calculated

using the same fomula as for 𝑅2 and 𝑅4.

121

𝑅6 =

𝑑 𝑝𝑐
𝑘 𝑝𝑐

(6.33)

(7) Between the two sides of the air gap at the bottom.

The thermal resistance 𝑅6 of the air gap at the bottom can be calculated using the same equations

as (6.25) - (6.30), which include radiation and convection. Then,

𝑅7 =

1
ℎ7, 𝑐𝑜𝑛𝑣 + ℎ7, 𝑟𝑎𝑑

(6.34)

(8) Between the two surfaces of the bottom cover.

Between the two surfaces of the bottom cover is the fourth layer of PC sheet, in which only

thermal conduction was considered through the bottom layer. The thermal resistance can be

calculated using the same formula previously introduced for thermal conduction.

𝑅8 =

𝑑 𝑝𝑐
𝑘 𝑝𝑐

(6.35)

(9) Between the bottom surface of the solar panel and air below the panel.

Finally, it is the heat transfer between the underside of the solar panel and the air below the

panel. Convection between the lower side of the solar panel and the air below can be estimated

using Equation (6.20).

ℎ9,𝑐𝑜𝑛𝑣 =

1
𝑅9,𝑐𝑜𝑛𝑣

= 2.8 + 3.0𝑉𝑤𝑖𝑛𝑑

(6.36)

The wind speed is assumed to be 1 m/s in this scenario. In addition, radiative heat transfer between

the bottom surface of the solar panel and the ground can also be calculated using Equation (6.37).

ℎ9,𝑟𝑎𝑑 =

1
𝑅9,𝑟𝑎𝑑

= 𝜀 𝑝𝑐𝜎(𝑇7

2 + 𝑇𝑔𝑟𝑜𝑢𝑛𝑑

2) (𝑇7 + 𝑇𝑔𝑟𝑜𝑢𝑛𝑑)

(6.37)

where 𝑇𝑔𝑟𝑜𝑢𝑛𝑑, 𝐾, represents the temperature of the ground below the solar panel. Based on

measurements, the temperature of ground can be estimated as 𝑇𝑔𝑟𝑜𝑢𝑛𝑑 = 𝑇𝑎 − 2. Therefore, the

thermal resistance would be:

𝑅9 =

1
ℎ9,𝑐𝑜𝑛𝑣 + ℎ9,𝑟𝑎𝑑

122

(6.38)

6.4.3.3 Simulation Flow Chart

A flow chart is presented in Figure 6.10 to outline how the transient simulation was performed.

Based on Equations (6.1) - (6.4), the location of the solar panel and time are first used to calculate

the incidence angle. Subsequently, together with other factors such as solar radiation, inlet water

temperature, flow rate, wind speed, and air temperature, these varying parameters are fed into the

main program at each time step to estimate the outlet water temperature and film temperatures.

Figure 6.10 Simulation flowchart used within this study to estimate the water and film temperatures
at different cross sections of the semi-transparent water panel.

Upon the start of the program, initialization is carried out to store the constant optical and

thermal properties of the material. Additionally, the program includes a function to look up

the optical performance based on the incidence angle and another function to solve the thermal

resistance circuit.

At the beginning of the simulation, film temperatures measured in the experiment are utilized to

calculate the water temperatures and gradients along the length of the solar panel using Equations

(6.39) - (6.41) as the initial boundary conditions. The length of the solar panel is discretized into

201 nodes to ensure sufficient accuracy. Then, thermal resistance circuits for all nodes along the

123

solar panel are solved by iterative calculations starting from the first node.

For a given node 𝑖, an initial guess for the film temperature is made. Subsequently, 𝑇1,𝑖 - 𝑇7,𝑖

are solved using Equation (6.39) and (6.40). Using Equation (6.41), 𝑇3,𝑖 and a new 𝑇 𝑓 𝑖𝑙𝑚,𝑖 can be

obtained with Equation (6.41). This new 𝑇 𝑓 𝑖𝑙𝑚,𝑖 is used to update the previous film temperature,

and this process continues until convergence is achieved. A convergence criterion of a residual of

0.001◦𝐶 is employed.









1
𝑅1

+ 1
𝑅2

1
𝑅2

− 1
𝑅2
+ 1
𝑅3

(cid:16) 1
𝑅2

(cid:17)

−










𝑇1



𝑇2












=









(cid:164)𝑞𝑎𝑏,𝑝𝑐 +

(cid:164)𝑞𝑎𝑏,𝑝𝑐 −

𝑇𝑎, 𝑡𝑜 𝑝
𝑅1
𝑇 𝑓 𝑖𝑙𝑚
𝑅3

1
𝑅5

+ 1
𝑅6

1
𝑅6

0

0















− 1
𝑅6
+ 1
𝑅7

(cid:16) 1
𝑅6

(cid:17)

−

1
𝑅7

0

0

1
𝑅7
+ 1
𝑅8

(cid:17)

−

(cid:16) 1
𝑅7

1
𝑅8

0

0

1
𝑅8
+ 1
𝑅9

(cid:16) 1
𝑅8

(cid:17)

−















𝑇4





𝑇5



𝑇6




𝑇7

























=

𝑇𝑤
𝑅5















(6.39)













(6.40)

+ (cid:164)𝑞𝑎𝑏, 𝑤𝑎𝑡𝑒𝑟2

0

0

𝑇𝑎,𝑏𝑜𝑡
𝑅9

𝑇 𝑓 𝑖𝑙𝑚 − 𝑇3
𝑅4

= (cid:164)𝑞𝑎𝑏, 𝑓 𝑖𝑙𝑚 − (cid:164)𝑞 𝐿1 =

𝑇3 − 𝑇𝑤
𝑅5

+ (cid:164)𝑞𝑎𝑏, 𝑤𝑎𝑡𝑒𝑟1

(6.41)

Upon completing the iteration for all nodes, Equation (6.18) and Equation (6.19) are used to estimate

the water temperatures for the subsequent time step (1s). These estimated temperatures then serve

as known values to calculate the water temperatures in the nex time step, continuing until the end

of the experiments.

6.5 Experimental Setup

6.5.1 Description of the Experimental Setup

To validate the innovation and mathematical modeling of the solar panel, a prototype was

constructed and subjected to tests. Figure 6.11 presents a schematic of the experimental setup.

Pictures of the constructed experimental setup and views of 3D structural design are provided

through Figure 6.12.

In the prototype, the height of the two air gaps was 1cm, while the water channel had a height

of 6mm. The thickness of each of the four polycarbonate sheets was 1mm (Figure 6.13). At both

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Figure 6.11 The prototype solar panel experimental setup, highlighting the placement of thermo-
couples in addition to sensors for measuring solar radiation.

Figure 6.12 Detailed description of the pilot experimental setup and its corresponding 3D model.

ends of the solar panel, inlet and outlet headers were installed, wrapped with foam insulations,

and then inserted with type-T thermocouples. Quantum sensors and pyranometers were employed

to measure the solar radiation in ranges of 400 - 700nm and 385 - 2105nm, respectively. One

set comprised of a quantum sensor and a pyranometer was placed adjacent to the solar panel and

leveled flat to record the solar radiation at one-second intervals. A second set containing a quantum

125

Figure 6.13 3D cross-sectional view of semi-transparent solar water heater, highlighting the thick-
ness of different layers of the pilot experimental setup.

sensor and a pyranometer was fixed to a handle, next to which a circular bubble spirit level was

installed. During the experiment, this handle was manually moved to various positions - below,

above, and along - the solar panel, facing upward and downward. The circular bubble spirit level

aided in ensuring that the sensors were held horizontally.

The solar panel was laid flat on the ground facing south. In this manner, the errors of incidence

angle to the solar panel would be minimized since the inclination and orientation of the solar

panel that were difficult to control and measure did not need to be considered. A tank constantly

replenished with running tap water was placed above the solar panel. This setup ensured a stable

inlet water pressure, allowing for a relatively steady water flow rate through the solar panel. The

prototype panel was 0.69 m wide and 3.54 m long. Besides monitoring the inlet and outlet

water temperatures, temperatures at 9 different positions along the film at approximately 0.36 m

intervals. These were taken using type-T gauge 36 ultra-thin thermocouples, which could have

minimum impact on the thermal performance. These thermocouples were attached to the film

using ultra-clear tape to ensure as accurate measurements as possible.

6.5.2

Instrumentations and Errors

Apogee® quantum sensors and pyranometers were employed to measure the solar radiation

in ranges of 400 - 700nm and 385 - 2105nm, respectively. Type-T thermocouples were used to

measure the water temperatures in the inlet header, outlet header, and film temperatures. Solar

radiation and temperatures were acquired and recorded using the National Instrument(NI) LabView

acquisition system. The flow rate was measured by collecting heated water at the outlet within a

126

period of recorded time. The errors of the measurements were listed in Table 6.1.

Parameters such as transmittance, reflectance, and flow rate are derived from other parameters.

These error propagation can be expressed in Equation 6.42 (Coleman and Steele, 2018).

𝑧 =

𝑥
𝑦

,

𝜎𝑧
𝑧

=

√︄

(cid:16) 𝜎𝑥
𝑥

(cid:17) 2

+

(cid:18) 𝜎𝑦
𝑦

(cid:19) 2

(6.42)

Equation 6.42 is the equation of error propagation for a parameter 𝑧 calculated from dividing 𝑥

with 𝑦. In the equation, 𝜎 is the standard deviation for each variable. For this reason, the error of

the flow rate slightly varies within 1-2% depending on specific water volume and recorded time.

Quantum sensor for solar irradiance
Quantum sensor for transmitted and reflected irradiance

Transmittance and reflectance, 400-700nm

Pyranometer for solar irradiance
Pyranometer sensor for transmitted and reflected irradiance

Transmittance and reflectance, 385-2105nm

Water collection
Time for water collection
Flow rate
Thermocouple
Length measurement

Expression
𝐼𝑄,𝑠𝑜
𝐼𝑄,𝑡𝑟𝑎𝑛𝑠, 𝐼𝑄,𝑟𝑒 𝑓
𝐼𝑄,𝑟𝑒 𝑓
𝐼𝑄,𝑡𝑟𝑎𝑛𝑠
𝐼𝑄,𝑠𝑜
𝐼𝑄,𝑠𝑜

,

𝐼𝑃,𝑠𝑜
𝐼𝑃,𝑡𝑟𝑎𝑛𝑠, 𝐼𝑃,𝑟𝑒 𝑓
𝐼𝑃,𝑟𝑒 𝑓
𝐼𝑃,𝑡𝑟𝑎𝑛𝑠
𝐼𝑃,𝑠𝑜
𝐼𝑃,𝑠𝑜

,

𝑉𝑤
𝑡𝑤
𝑉𝑤/𝑡𝑤
𝑇𝑐
𝑙

Error
±5%
±5%
±7.07%

±3%
±3%
±4.24%
±0.5𝑚𝑙
±0.1𝑠
1 − 2%
±1◦𝐶/±0.75%
±0.4𝑚𝑚

Table 6.1 Errors of measurements for various parameters such as solar radiation, temperature, and
flow rates.

6.6 Results and Analysis

6.6.1 Experimental Results of Optical Performance

In this section, experimental results of transmittance and reflectance in ranges of 400 - 700nm

and 385 - 2105nm are presented and discussed. Figure 6.14 presents the experimental results of

transmittance for PAR light. The red circles represent measured transmittance at various locations

under the solar panel and at different times from 08/30/2021 to 09/17/2022. Although all the

values of measured transmittance closely follow the trends of the theoretical calculation, they are

lower than expected, as represented by the solid line. However, several factors contribute to these

discrepancies:

1. Solar radiation is actually a composite of direct (beam) radiation and diffuse radiation due to

127

the round surface of the earth, air molecules, clouds, dust, etc. In addition, the solar panel

was situated in a narrow courtyard between the greenhouses at MSU, next to a white wall

that can be seen in Figure 6.11. The white wall introduced a significant source of diffuse

radiation during the experiments.

2. The sensor used to measure solar radiation was placed on a stable and flat surface away from

the solar panel. Nevertheless, streaks of shade can be observed in Figure 6.11; therefore,

the measured radiation under the solar panel might have been affected by the shades without

being noticed.

3. The sensors that measured transmitted and reflected radiations were mounted on a handle,

where a circular bubble spirit level was installed adjacent to the sensors. Manual adjustments

to keep the sensors horizontal could have introduced significant angular errors. Moreover,

although the solar panel was placed on seemingly flat ground, the terrain was not perfectly

level. These inconsistencies led to more remarkable errors, especially when the incidence

angle approached 60◦ as depicted in Figure 6.14 where the transmittance suddenly drops as

the incidence angle further increases.

4. Owing to manufacturing defects, the surface of the film was not smooth; in fact, there were

dimples on the film surface. Consequently, light passing through the film was scattered in

all directions. As illustrated in Figure 6.15, the same words in Figure 6.6(b) behind the film

became blurry when the film was raised. This phenomenon was another major factor causing

the measured transmittance to be lower than the theoretical prediction.

Therefore, two additional curves were plotted on the same graph: one assuming that 25% of

light was considered diffuse (blue dash line) and another assuming that 50% of light was diffuse

during the experiments (black dash line). To approximate the effect of diffuse radiation, the sky

is considered isotropic, meaning that the fraction of diffuse radiation emanating from the sky

dome is uniform across the sky. Even though it has been previously mentioned the white walls

around the solar panel could significantly contribute to diffusion, the isotropic diffuse model was

128

Figure 6.14 Transmittance for PAR light, measured at various locations and times (red circles),
compared with calculated results (blue solid line) and predictions for 25% and 50% diffuse radiation
(blue and black dashed lines, respectively). Most measurements fall within the 50% diffuse radiation
range.

still employed for its simplicity. The primary goal of utilizing this model was to validate the

assumptions underlying the mathematical model, as well as to identify potential sources of error.

Figure 6.15 Manufacturing defects (unsmooth surface, visible dimples) in the film cause light
scattering, making clear words (left) appear blurry when the film is raised (right).

The analysis shows that the transmittance decreases if the proportion of diffuse radiation

increases. Conversely, when the incidence angle exceeds 65◦, a higher proportion of diffuse

radiation actually enhances the transmittance. It is observed that although all the measured data

are lower than expected, most still fall within the bounds of the 50% diffuse radiation curve.

Figure 6.16 displays the measured reflectance of the solar panel for PAR, in comparison with

theoretical prediction. Up to an incidence angle of 65◦, a higher proportion of diffuse light will

129

increase the reflectance, thereby decreasing the transmittance. However, as the incidence angle

continues to rise beyond 65◦, the reflectance will decrease with a greater proportion of diffuse

radiation. While most data points align with the 50% diffuse radiation range, some stray outside

of it, particularly when the incidence angle falls between 60◦ and 70◦. This is consistent with the

sources of error previously outlined.

Figure 6.16 Experimental results of reflectance for PAR (red circle), compared with the theoretical
calculations for three scenarios including 0% (solid blue), 25% ( dashed blue), and 50% (solid
black) diffuse light.

Figure 6.17 illustrates the measured transmittance for overall solar radiation in relation to

theoretical predictions, taking into account diffuse radiation. The transmittance is around 0.3,

significantly lower than the transmittance for PAR. Similarly, a higher fraction of diffuse radiation

reduces the transmittance but it improves when the incidence is higher than 65◦. The margin of the

decline is smaller than the decline for PAR transmittance, but all the data points still fall within the

range of 50% of the diffuse radiation curve. Some data points lie outside this range for incidence

angles between 60◦ – 70◦.

Figure 6.18 displays the measurements of solar panel’s reflectance for solar radiation across

385-2105nm wavelength. The values of reflectance for the same incidence angle are slightly lower

than the reflectance for PAR. Most data points are within the bounds of the 50% diffuse radiation

range, although some fall outside this range when the incidence angle approaches the sensitive

region of 60◦ - 70◦.

130

Figure 6.17 Experimental results of transmittance for solar radiation (385 - 2105nm) (red circle)
compared with predictions assuming 0% (blue solid), 25% (blue dashed) and 50% (black dashed)
diffuse light.

Figure 6.18 Experimental results of reflectance for solar radiation (385 - 2105nm) (red circle)
compared with predictions assuming 0% (blue solid), 25% (blue dashed) and 50% (black dashed)
diffuse light.

6.6.2 Experimental Results of Thermal Performance

Figure 6.19 is a map of performance monitored on Sep. 1𝑠𝑡 2021. In Figure 6.19, the green

dashed line, blue dashed line, red dashed line, black solid line, and red solid line represent inlet

water temperature, ambient solar radiation, outlet water temperature, outlet water temperature as

predicted by the 1D mathematical model, and the error between simulation and measurement.

Enclosed by the curves of inlet temperature and outlet temperature is a color map of temperature

difference calculated for every second. Initially, the solar panel was filled with tap water without

131

outflow. Once all other devices were connected and operational, the water in the solar panel became

preheated. The solar water heater outlet was then opened to allow the water to flow. During this

preheating phase, the water in the headers was also slightly heated, but not to the same extent as

the water in the panel. Consequently, in the first few minutes after opening the outlet, the measured

outlet water temperature did not immediately rise as predicted due to the mixing of the cold and

hot water within the outlet header of the solar panel.

As depicted in Figure 6.19, after six minutes from opening the outflow, the simulated and

experimental outlet temperatures began to align closely, within a ±5% error margin. Interestingly,

although the measured outlet temperature followed the simulated trend closely, it consistently

lagged behind, likely due to mixing effects within the headers.

Figure 6.19 Real-time thermal performance of the solar panel. This figure demonstrates the test
results conducted on Sep. 1𝑠𝑡 2021 starting from 13:54. Various lines represent: green for
inlet water temperature (dashed), blue for solar radiation (dashed), red for outlet water temperature
(dashed), and black for outlet water temperature as predicted by the 1D mathematical model (solid),
and an additional red solid line to indicate the error between simulation and measurement. Enclosed
by the curves of inlet temperature and outlet temperature is a color map of temperature difference
calculated for every second. The overall thermal efficiencies of the solar water heater were found
to be 22.35% and 22.52% numerically and experimentally, respectively.

132

In Figure 6.19, three of the major factors influencing the outlet, namely, the inlet water tem-

perature, solar radiation, and flow rate. While inlet and outlet headers were wrapped with black

insulation, solar radiation could still affect the surface temperature of the insulation. Thus, in-

creases in solar radiation led to heated inlet header, and correspondingly increases in the water

temperature in the inlet header. Conversely, when solar radiation levels dropped, so did the inlet

water temperature. However, at the outlet header, the temperature of the insulation should be lower

than the water temperature inside; therefore, it always tends to lose heat from the header to the

environment.

Solar radiation, another significant variable affecting outlet temperature, was notably influenced

by cloud cover. Its fluctuations not only affected the outlet water temperature but also produced

observable differences in temperature between the outlet and inlet. For verification, the temperature

difference between the outlet and inlet was calculated for every second, and a color map of the

temperature difference is presented in Figure 6.19 enclosed by the inlet and outlet temperature

curves for a more straightforward expression. Starting from 10 minutes, the influence of solar

radiation on the temperature difference can be immediately seen from the color map in Figure 6.19.

For example, between 13-16 minutes, after a short drop down of solar radiation, the temperature

difference slightly dropped in the following minutes. From 49 to 62 minutes and 72 to 167

minutes, temperature difference rise or decline can be observed soon after the solar irradiation level

fluctuates. Especially between 93 to 109 minutes, remarkable oscillation of solar radiation also

resulted in a rapid fluctuation of water temperature difference.

Lastly, the water flow rate is a key determinant of the panel’s thermal performance. Based

on the mathematical model, it is evident that a higher water flow rate will reduce the temperature

difference, whereas a lower flow rate will yield a higher temperature increment if all the other

factors remain constant. However, in a real operation, several variables varied simultaneously;

therefore, this relation was only apparent when the flow rate changed from 3.27 to 2.86 mL/s, from

2.72 to 2.51 mL/s, from 2.51 to 5.17 mL/s and from 1.76 to 0.49 mL/s. Overall, the prototype

semi-transparent solar panel tested in Michigan in September demonstrated an ability to achieve a

133

temperature rise of over 30◦𝐶 under adequate solar radiation.

Simultaneously, film temperatures were continuously monitored and recorded every second

throughout the experiments. Figure 6.20 presents five representative time slices from the collected

data. Red circles indicate temperatures measured by gauge 36 thermocouples. The solid blue

lines represent the film temperature curves calculated by the 1D transient mathematical model.

As depicted in Figure 6.20, over 3-hour experiments, most errors between the simulation and

experiments were confined within a ±10% error margin and predominantly hovered around ±5%.

The largest deviations were observed in the 137-minute graph. In summary, the satisfactory level

of accuracy confirms the validity of the mathematical model proposed in this paper, even though it

employs some empirical correlations to estimate thermal resistance.

Figure 6.20 Validating predicted film temperatures with experimental data. Red circles are tem-
perature measurements, and the blue solid lines are the film temperature curves calculated by the
1D transient mathematical model. According to Figure 17, over 3-hour experiments, most errors
between the simulation and experiments were confined within a ±10% error margin and predomi-
nantly hovered around ±5%.

Additionally, the thermal efficiency of the solar water heater was calculated based on Equation

134

(6.43).

𝜂𝑡ℎ =

(cid:205)𝐸𝑛𝑑

𝑆𝑡𝑎𝑟𝑡 Δ𝑡 (cid:164)𝑚𝑤𝐶𝑝 (𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛)
𝑆𝑡𝑎𝑟𝑡 Δ𝑡𝐼 𝐴

(cid:205)𝐸𝑛𝑑

(6.43)

where the Δ𝑡; (𝑠) is the time interval between the two experimental recordings, 𝑑𝑜𝑡𝑚𝑤, 𝑘𝑔/𝑠 is

the mass flow rate of the water heater, 𝐶𝑝, 𝐽/𝑘𝑔◦𝐶 is the heat capacity of water, 𝑇𝑜𝑢𝑡,◦ 𝐶 is the

outlet temperature of the water heat, which can be either numerically calculated or experimentally

measured, 𝐼, 𝑊/𝑚2 is the solar radiation, 𝐴, 𝑚2 is the area of the solar water heater. The numerator

of Equation (6.43) stands for the solar energy transferred to the water, accumulated through the

experiment. The denominator of Equation (6.43) is indeed the accumulated solar irradiance on the

solar panel during the experiment.

The overall thermal efficiency of the solar water heater was found to be 22.35% and 22.52%

numerically and experimentally, respectively, for the experiment tested on Sep. 1𝑠𝑡. However,

the thermal efficiency of the solar water heater is not only affected by its structure and materials

but also by operating conditions such as mass flow rate, solar radiation, ambient temperature,

inlet temperature, etc. Therefore, the thermal performances tested on other days available in

supplemental data varied from 11.5% to 36.8%. Although it is not within the scope of this paper,

an optimization of the design and flow conditions will achieve better performances in arid regions.

6.7 Feasibility of Potential Application as Greenhouse Roof

6.7.1 Shading and Freshwater Production

The first benefit of this semi-transparent solar water heater is that it provides even shading.

Before delving into further details, another term must be introduced. Daily Light Integral, or DLI,

is a related concept that calculates the total amount of PAR light received by a plant throughout the

entire day. It is like tallying up the plant’s daily "dose" of light energy and is typically expressed

in moles of photosynthetic photons per square meter per day (mol/m2/day). DLI is crucial for

understanding plant health and growth. Similarly to humans, plants need the right amount of

energy (in their case, photosynthetic photons) to grow and thrive. Too little or too much light can

be detrimental. Different types of crops have different optimal ranges of DLI for the best growth and

productivity, which is why growers often measure and control DLI in their growing environments.

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Table6.2 lists recommended DLIs for four common crops. In the southwest United States, the DLI

can be more than 50 mol/m2/day in summer. In the spring and fall seasons, the DLI will average

around 40 mol/m2/day. Even in winter, the value of DLI can be more than 20 mol/m2/day(Faust

and Logan, 2018). As a result, when compared to the recommended DLIs in Table 6.2, shading

becomes necessary for most crops during the hot seasons in arid regions.

Lettuce (Matysiak et al., 2022)
Sweet Pepper (Dorais, 2003; Cossu et al., 2020)
Cucumber (Dorais, 2003)
Tomato (Fisher and Runkle, 2004)

Minimum DLI Optimal DLI

12
12
20
20

17
30
30
30

Table 6.2 Recommended DLI (𝑚𝑜𝑙/𝑚2 𝑑𝑎𝑦) for common crops to assess the capability of the
proposed energy-efficient greenhouse for cultivation of various plants.

The second useful purpose of this semi-transparent solar heater is to provide the heat source

for the water purification system mentioned in Section 6.1. As arid regions are facing severe water

scarcity, there happens to be an abundance of produced water sites due to the local oil industries

in these areas. For example, numerous oil and gas wells are densely located in the Southwest

United States, especially Texas and New Mexico(Blondes et al., 2016). Similarly, Middle Eastern

countries that heavily rely on the oil and gas industries are also generating large and ever-increasing

volumes of produced water(Salem and Thiemann, 2022; Eldos et al., 2022).

Conversely, the easier access to saline, brackish, or produced water resources in these regions

presents a promising solution to the ever-increasing challenges of water scarcity (Zhang et al., 2021).

Treating and reusing these water resources offer a sustainable and practical approach to alleviate

water stress and address with the impacts of the prolonged drought (Kesari et al., 2021). Treated

wastewater that meets stringent quality standards can be effectively repurposed for non-potable

applications, including agricultural irrigation, industrial processes, and landscape irrigation. By

utilizing treated water, these regions can reduce their dependence on limited freshwater supplies,

ensuring a more efficient and resilient water management system (Kesari et al., 2021). Moreover,

wastewater reuse also helps in mitigating the environmental impact of untreated effluent discharge,

contributing to the preservation of fragile ecosystems and the overall ecological health of the region

136

(Nkhoma et al., 2021). Embracing wastewater as a valuable resource not only bolsters water

availability but also promotes environmental conservation and sustainable development, making it

an integral part of securing the future water needs of arid regions.

A case study was conducted to examine the feasibility of using the solar panel to be used as a

greenhouse rooftop. For this case, the solar panel is assumed to be 5×5 m2 and installed flatly atop a

greenhouse of identical dimensions situated in Phoenix, AZ. Alongside the mathematical model of

the solar panel outlined in this paper, the models for the HDH system align with our prior research

(Mamouri et al., 2020; Abedi et al., 2021). The HDH system features a humidifier (evaporator) and

dehumidifier (condenser) both constructed from direct-contact packed beds and standing 1 meter

tall. Table 6.3 showcases the performance of the solar panel across several representative days,

with weather data sourced from TMY3 datasets specific to Phoenix.

Typical dates
DLI (𝑚𝑜𝑙/𝑚2 𝑑𝑎𝑦)
Hot brine temp (◦𝐶)
Hot brine collected (𝐿)
Freshwater products (𝐿)

01/08
22.11
53.8
1940
59.66

03/11 05/09
35.05
27.61
54.8
54.7
1892
1550
60.48
49.55

06/06 07/14
35.61
31.85
59.9
58.0
1892
1670
71.56
59.03

08/27 10/01 11/01 12/13
20.54
32.9
53.57
59.5
900
1778
27.68
67.27

30.59
59.16
1584
59.92

24.82
57.0
1226
41.75

Table 6.3 Performance evaluation of the proposed semi-transparent solar water heater with 5 × 5
m2 area on selected days at Phoenix, AZ.

Based on simulation results, the DLI appears to be sufficient for the plants listed in Table 6.3.

Existing literature indicates that hydroponic lettuce, grown in a 5 × 5 𝑚2 area, would require 56.16

L/day of water(Lages Barbosa et al., 2015a). Hence, the water production from the integrated

greenhouse with a semi-transparent solar panel as roof and HDH system should satisfy the water

needs of lettuce. For cucumber, the water requirement is around 1.5 L/day/plant (Hashem et al.,

2011). This water output should be adequate for sustaining up to 36 cucumber plants. However, this

initial design may fall short for crops with higher water demands. For instance, tomatoes require

around 125L/day of water for a 25𝑚2 area. Nevertheless, design optimization should enable the

system to meet a significant portion of the water needs of such crops. Recent advances have led

to the development of NIR cut-off films boasting even greater transmittance, up to 90%, for PAR

(400-700nm) and higher absorptance for NIR (Kim et al., 2022). These could potentially enhance

137

the overall performance of our solar panel. Furthermore, there is considerable scope for tuning

the film’s performance to cater to specific crop types. For example, the transmittance of the NIR

cut-off could be optimized by adjusting the dye material of the film to match the optimal DLI of

lettuce, thereby achieving a higher thermal performance for increased freshwater production.

Based on the material cost of the prototype, the cost of the 5 × 5 𝑚2 solar water heater and HDH

system should be about $2360. If the system would run for 15 years with an average freshwater

production of 60L/day, the rough cost of freshwater should be about 7.2$/𝑚3. This is a very

favorable cost compared with average HDH systems costs (Santosh et al., 2022).

6.7.2 Thermal Cooling Load Reduction

The third outcome of the proposed solar heater is an abatement in the cooling load for the

greenhouse due to the reduced solar radiation entering the greenhouse. A preliminary study using

Sketchup, EnergyPlus, and OpenStudio software assessed the effects of deploying proposed solar

panels on cooling reduction.

Two simple greenhouse models of identical dimensions, as depicted in Figure 6.21, was con-

structed using the software SketchUp. These models were then imported into OpenStudio to

calculate the cooling load of the greenhouses. The size of the greenhouses was 5 × 5 × 2.5 𝑚3, and

they were oriented to normally face south. Windows, made of 3mm clear glass, were installed on

all sidewalls except the north-facing wall. One greenhouse featured a rooftop made of 3mm clear

glass, while the other greenhouse’s rooftop was fitted with a semi-transparent solar water heater.

The material of the solar panel was defined based on optical and thermal properties acquired using

the methodologies outlined in Section 6.4. The weather data were sourced from TMY3 data for

Phoenix, AZ. The design days of July 21𝑠𝑡 and Dec 21𝑠𝑡 were specified based on Design Day files

available from EnergyPlus’s website (Crawley et al., 2001). Regarding the indoor temperature and

coefficient of performance (COP) for the cooling system of the greenhouse, Soussi et al. (2022)

conducted a comprehensive review of the existing literature. For the common crops specified in

Table 6.2, the study suggests a temperature range of 24 to 26◦𝐶, while a typical cooling system has

an overall COP from 2.82 to 3.25. Table 6.4 provides comprehensive information regarding the

138

implemented conditions and EnergyPlus simulation results.

Figure 6.21 A simple greenhouse model in the software SketchUp to estimate the reduction of
cooling load.

Greenhouse with glass roof

Highest indoor temperature, ◦𝐶 (Soussi
et al., 2022)
Air conditioning COP (Soussi et al., 2022)
Annual Electricity for Cooling, 𝑘𝑊 ℎ
Percentage of saving
Annual electricity saving, 𝑘𝑊 ℎ

26

2.92
9097.2
–
–

with

Greenhouse
transparent solar heater
26

semi-

2.92
7513.9
17.4%
1583.3

Table 6.4 Thermal assessment of greenhouse configurations w/o proposed solar panel using Ener-
gyPlus.

The indoor temperature of the two greenhouses was targeted to be lower than 26◦𝐶, and the

effective COP of the air conditioning was 2.92. When comparing the two models, the semi-

transparent solar roof could potentially yield a cooling load reduction of approximately 17.4%

annually. The amount of annual electricity savings would be 1583.3kWh, which would be $205.8

if using Arizona’s electricity price of $0.13/kWh. The above method of simulation was merely an

estimation for the cooling load reduction brought by the solar panel. Nevertheless, the remarkable

results of DLI estimation, freshwater production and cost, and cooling load reduction underscore

the economic feasibility of this semi-transparent solar water heater. This technique is also scalable

for larger applications. However, an accurate and systematic performance analysis program that

simultaneously predicts the thermal performances of the solar panel and the greenhouse, water

139

production, water consumption, and plant growth Abedi et al. (2023b) will be integrated in the near

future, and experiments on a prototype greenhouse will be necessary to validate the concept.

A summarization of the solar water heater performance is presented in Table 6.5, along with

the results of the most recent representative research on semi-transparent solar roof techniques.

Compared with other techniques, this semi-transparent solar water heater can provide a relatively

high PAR transmittance and holds the utmost UV and IR blocking rate. At the same time, the

thermal efficiency of this solar heater is much higher than that of other semi-transparent solar PVs,

with a significant reduction in cooling load.

Reference

Year

Technique

2022

2018

Ma et al. (2022)

Sun et al. (2018)

Semitransparent organic pho-
tovoltaics
PV cells with Parabolic Con-
centrator and spectral splitting
film
Waller
Semitransparent organic pho-
tovoltaics
(2022)
Yuan et al. (2022) 2022 Nano fluid
Meddeb
(2023)
Sajid et al. (2023)

Semitransparent
photovoltaics

2023 Nano fluid

Inorganic

2022

2023

al.

al.

et

et

N/A

78.3%
33%

76 ∼ 83%

Zhao et al. (2023) 2023

Zou et al. (2023)

2023

Semitransparent organic pho-
tovoltaics
Radiative Cooling

21.5%

68.92%

Current study

Semi-transparent solar water
heater with NIR cut-off film

50%

VIS/PAR Trans-
mittance
25%

UV/NIR/IR Blocking
Rate
IR 80%

Photovoltaic/Thermal
Efficiency
6%

44.55%

NIR 78%

6.88%

N/A

NIR 85.4%
N/A

N/A

N/A

1.82%

N/A
3.41%

N/A

13.5%

UV 85.53%,
79.15%

NIR

N/A

UV 100%, IR 94.7%

11.5 ∼ 36.8%

Cooling performance

N/A

N/A

N/A

N/A
N/A

Reduce 21.6%-27.4% cooling
load
N/A

Greenhouse temperature low-
ered by 6◦C and 18.6 ◦C with
or without ventilation
Reduce 17.4% cooling load

Table 6.5 Comparison of solar water heater performance between the proposed configuration in
this chapter with similar setups in most recent literature.

6.8 Summary

This chapter aimed to explore the potential of an integrated greenhouse utilizing a light-splitting

semi-transparent solar water heater. The modeling of optical and one-dimensional transient thermal

performances was initially developed, accompanied by an overview of the solution methodology.

Then, a prototype was successfully designed, constructed, and subjected to testing to evaluate its

optical and thermal performances.

Regarding the optical performance, we found that the measured transmittance aligned closely

with theoretical predictions. All measurements fell within the range predicted by assumptions

involving 100% direct and 50% diffuse radiation. Discrepancies were attributed to factors such as

140

ambient diffuse radiation, shadowing effects, sensor placement errors, and film surface irregulari-

ties. Generally, PAR (400-700nm) transmittance achieved a value of 0.5 for incidence angles less

than 65◦. The overall transmittance for the 300-2500nm spectrum was as low as 0.3, given that

the solar panel can block 100% of UV and 94.7% of IR. Transmittance values began to decline

after an incidence angle of 65◦ due to increased reflectance. Experiments were used to validate the

thermal performance of the water heater. Both experimental and numerical results of outlet water

temperatures aligned within a 5% error margin for most experiments. The system’s efficiency was

influenced by multiple factors, including solar radiation, heat losses, and variations in inlet water

temperatures and flow rates. Film temperatures on the panel were measured and compared to a 1D

transient mathematical model, with most discrepancies between the simulation and experiments

between 5% to 10%, further substantiating the validity of the theoretical model. Experimental

thermal efficiency of the water heaters fluctuates between 11.6% to 36.8%, while numerical simu-

lations suggest 22.4% overall efficiency. Next, a case study for an energy-efficient greenhouse with

a 5×5 m2 semi-transparent was developed and assessed, indicating meeting the DLI requirements

for common crops, decreasing thermal cooling load, and satisfying required water for hydroponic

cultivation.

The feasibility of employing a semi-transparent light-splitting solar water heater appears suitable

as a roofing solution for energy-efficient greenhouses. This design warrants further investigation,

particularly in the context of sustainable and cost-effective agricultural practices in arid regions.

Future work will center on optimizing the solar panel’s structure and films to cater to specific crop

types.

141

CHAPTER 7

ASSESSING THE IMPACT OF INCOMING LIGHT SPECTRUM ON INDOOR
LETTUCE CULTIVATION

This chapter was published in Frontier in Plant Science, Vol 14, by Mahyar Abedi, Xu Tan,

Eric J. Stallknecht, Erik S. Runkle, James F. Klausner, Michael S. Murillo, and André

Bénard, titled as Incorporating the Effect of the Photon Spectrum on Biomass Accumula-

tion of Lettuce Using a Dynamic Growth Model, pages 1525, Copyright Frontiers (2023).

https://doi.org/10.3389/fpls.2023.1106576.

7.1

Introduction

The photon flux density and spectrum can independently and interactively affect crop photo-

synthesis, secondary metabolism, and other physiological processes (Ooms et al., 2016). Paz et al.

(2019) investigated the impact of DLI (i.e., daily light integral), varying from 1.6 to 9.7 mol m−2

day−1 on the growth of indoor-grown red-leaf lettuce and suggested a minimum DLI of 6.5 mol

m−2 day−1. However, the biomass of lettuce continues to increase with DLI until some saturating

value, when the appearance of physiological disorders begin to appear (e.g., around 17 mol m−2

day−1 (Both et al., 1994; Kelly et al., 2020). While it is common for crops to have species- and

cultivar-specific DLI recommendations for maximized growth rate, the spectral distribution at a

constant DLI has additional impacts on biomass accumulation and morphology. For example,

decreasing the red to far-red ratio (R:FR) typically increases extension growth (e.g., greater leaf

area or elongated stems) that often increases per-plant biomass as a result of increased photon

interception (Park and Runkle, 2018a,b, 2019; He et al., 2021). Similarly, increasing the fraction

of blue (B) light a plant receives inhibits extension growth and light interception and can decrease

the per-plant biomass of lettuce (Park and Runkle, 2019; Kong and Nemali, 2021; Meng et al.,

2019). Increasing the fraction of B and UV light can also increase the biosynthesis of secondary

metabolites like anthocyanins which act as photo-protectants and can influence the photosynthetic

rate (Meng and Runkle, 2019; He et al., 2021). As an additional consideration to the effect of light

intensity and spectral distribution, PAR does not have a constant quantum yield of photosynthesis

142

(mol CO2 assimilated per mol photon absorbed) on a per-nanometer basis; red light typically has

a greater quantum yield than blue or green light (Hogewoning et al., 2012). Meng et al. (2020)

analyzed the interaction of blue and green light on hydroponic lettuce growth, and replacing green

with red light increased the quantum yield of photosynthesis.

Innovations have been made with respect to spectral-shifting materials for agricultural use that

attempt to leverage our understanding of how light intensity and spectrum influence crops. For

example, Shen et al. (2021) developed a spectral-shifting film that primarily absorbs blue and green

light and fluoresces red and far-red light to theoretically increase lettuce biomass accumulation

through increased quantum efficiency and light interception. Hebert et al. (2022) constructed

luminescent quantum dot films that decrease overall DLI by 14%, but the modified spectrum

enhances the tomato biomass yield and vegetative growth by 6% and 10%, respectively. Despite the

wealth of knowledge on how light intensity and distribution affect crop growth, models predicting

crop growth have not developed at a similar rate.

A plant growth model is a valuable tool to predict yield and provide an approximation for

the impact of factors (e.g., water use or CO2 concentration). In addition, plant growth modeling

allows researchers to perform virtual studies to test a hypothesis without investing the required

time to perform costly experiments. Van Henten and Van Straten (1994) developed a dynamic

model to predict lettuce dry mass as a state variable in time using environmental inputs such

as CO2 concentration, spectral irradiance for photosynthetically active radiation, and ambient

temperature. Jones et al. (1991) proposed a model for tomato growth that responds to constantly

varying environmental parameters, and the plant state was presented through seven variables that

included dry mass for different components, leaf number, and leaf area. These are two of several

computational models that consider environmental parameters to increase crop yield. While these

models consider the impacts of spectral distribution through the overall spectral irradiance (overall

energy of the incoming spectrum), the impacts of spectral distribution on a photometric basis are

often disregarded. There are few models in the literature that incorporate the impact of the photon

spectrum of incoming light on plant growth. Dieleman et al. (2019) aimed to investigate the impact

143

of light quality on tomato physiological and morphological responses. Young tomato plants were

cultivated under 7 different light treatments, and various parameters were measured, including leaf

light reflection and transmission, accumulated biomass, photosynthesis rate, and concentration of

light-capturing pigments. Based on these measurements and the 3D model developed in GroIMP,

and when extrapolated to a mature (fruit-bearing crop), it was suggested that dynamic light spectra

might stimulate growth and production for an indoor crop production system.

The aim of this chapter is to modify an existing calibrated dynamic growth model of lettuce

to accommodate the impact of spectral distribution. Several regression scenarios are investigated

to find a modified model that estimates the impact of spectral distribution and intensity on plant

growth. A new modified light-use efficiency coefficient that quantifies the impact of spectral

distribution is also presented below.

7.2 Plant Growth Computational Modeling

7.2.1 Plant Growth Model for Lettuce

The dynamic growth model of lettuce proposed by Van Henten (1994) is modified in this study

to numerically investigate the impact of spectral distribution and intensity on lettuce dry mass and

yield. Using dry mass as the primary output for the model, this variable is further subdivided

into structural dry mass and nonstructural dry mass, which accounts for starch, glucose, and other

similar elements. The model assumes that the two categories of dry mass fully define the state of the

plant and describe lettuce growth by calculating these sub-variables using the following ordinary

differential equations (ODE),

𝑑𝑋𝑛𝑠𝑑𝑚
𝑑𝑡

= 𝑐𝛼 𝑓𝑝ℎ𝑜𝑡 − 𝑟𝑔𝑟 𝑋𝑠𝑑𝑚 − 𝑓𝑟𝑒𝑠𝑝 −

1 − 𝑐 𝛽
𝑐 𝛽

𝑟𝑔𝑟 𝑋𝑠𝑑𝑚

𝑑𝑋𝑠𝑑𝑚
𝑑𝑡

= 𝑟𝑔𝑟 𝑋𝑠𝑑𝑚

(7.1)

(7.2)

Equations (7.1) and (7.2) represent the transient behavior in the structural and non-structural
dry mass per unit of area (cid:0)𝑔 𝑚−2(cid:1) in response to photosynthesis. In the above equations, 𝑓𝑝ℎ𝑜𝑡 =
𝑓𝑝ℎ𝑜𝑡 (cid:0)𝐶𝐶𝑂2
is the maintenance respiration (cid:0)𝑔 𝑚−2 𝑠−1(cid:1), and 𝑟𝑔𝑟 = 𝑟𝑔𝑟 (𝑇, 𝑋𝑛𝑠𝑑𝑚, 𝑋𝑠𝑑𝑚) is the growth rate of

, 𝐼, 𝑇, 𝑋𝑠𝑑𝑚(cid:1) is the gross canopy photosynthesis (cid:0)𝑔 𝑚−2 𝑠−1(cid:1), 𝑓𝑟𝑒𝑠𝑝 = 𝑓𝑟𝑒𝑠𝑝 (𝑇, 𝑋𝑛𝑠𝑑𝑚, 𝑋𝑠𝑑𝑚)

144

structural material (cid:0)𝑔 𝑚−2 𝑠−1(cid:1), while 𝑐𝛼 and 𝑐 𝛽 describe the conversion rate of CO2 to sugar

(CH2O) and yield factor which is a measure of non-structural dry mass losses due to respiration

and photosynthetic activities, respectively. The value for 𝑐𝛼 is the molecular weight ratio of CO2

to CH2O and is set to 0.68. According to Sweeney (1981), 𝑐 𝛽 for lettuce is approximately 0.8. The
growth rate (cid:0)𝑟𝑔𝑟 (cid:1) refers to the rate at which non-structural materials are transformed into structural

materials, i.e.,

𝑟𝑔𝑟 = 𝑐𝑔𝑟,𝑚𝑎𝑥

𝑋𝑛𝑠𝑑𝑚
𝑐𝛾 𝑋𝑠𝑑𝑚 + 𝑋𝑛𝑠𝑑𝑚

𝑐

(𝑇−20)/10

𝑄10,𝑔𝑟

(7.3)

In Equation (7.3), 𝑇 is the canopy temperature (◦𝐶), 𝑐𝑔𝑟,𝑚𝑎𝑥 is the saturation growth rate at

20 ◦𝐶, 𝑐𝛾 is the growth rate coefficient, and 𝑐𝑄10,𝑔𝑟 is the measure of growth rate sensitivity to the

canopy temperature. Van Holsteijn (1981) approximated the saturation growth rate coefficient to

5 × 10−6 𝑠−1; Sweeney (1981) estimated the growth rate constant for lettuce to 1.0. The growth

rate sensitivity constant is set to 1.6, which means that for every 10 ◦𝐶 increase in the canopy

temperature, the growth rate increases by a factor of 1.6. The maintenance respiration rate is

predicted through the following equation,

𝑓𝑟𝑒𝑠𝑝 = (cid:0)𝑐𝑟𝑒𝑠𝑝,𝑠ℎ𝑡 (1 − 𝑐𝜏) 𝑋𝑠𝑑𝑚 + 𝑐𝑟𝑒𝑠𝑝,𝑟𝑡𝑐𝜏 𝑋𝑠𝑑𝑚(cid:1) 𝑐

(𝑇−25)/10

𝑄10,𝑟𝑒𝑠𝑝

(7.4)

In Equation (7.4), 𝑐𝑟𝑒𝑠𝑝,𝑠ℎ𝑡 and 𝑐𝑟𝑒𝑠𝑝,𝑟𝑡 represent shoot and root maintenance respiration coefficients

at 25 ◦𝐶 and indicate the amount of glucose consumption per structural dry material. Van Henten

(1994) estimated shoot and root respiration coefficients as 3.47 × 10−7 𝑠−1 and 1.16 × 10−7 𝑠−1,

respectively. 𝑐𝑄10,𝑟𝑒𝑠𝑝 is the sensitivity of maintenance respiration to canopy temperature and
Van Henten (1994) assigned a value of 2.0 for this coefficient. 𝑐𝜏 is the ratio of root dry mass to

the overall dry mass of the plant, which can depend on the type of cultivation. Lorenz and Wiebe

(1980) reported an average value of 0.15 for lettuce cultivated in soil, while Sakamoto et al. (2015)

measured an average value of 0.14 for hydroponic lettuce cultivation. Goudriaan and Monteith

(1990) formulated an empirical correlation to estimate gross canopy photosynthesis,

𝑓𝑝ℎ𝑜𝑡 = (1 − exp(−𝑐𝐾 𝑐𝑙𝑎𝑟 (1 − 𝑐𝜏) 𝑋𝑠𝑑𝑚)) 𝑓𝑝ℎ𝑜𝑡,𝑚𝑎𝑥

(7.5)

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In Equation (7.5), 𝑐𝐾 is the extinction coefficient, and for lettuce with planophile characteristics, it

is set to 0.9; 𝑐𝑙𝑎𝑟 is the structural leaf area ratio, and Lorenz and Wiebe (1980) approximated it to

75×10−3 𝑚2 𝑔−1; and 𝑓𝑝ℎ𝑜𝑡,𝑚𝑎𝑥 is the gross CO2 assimilation rate for a canopy with 1 square meter of

effective surface area. Acock et al. (1978) presented an equation to calculate 𝑓𝑝ℎ𝑜𝑡,𝑚𝑎𝑥 considering

the effect of CO2 concentration and spectral irradiance integrated over wavebands within PAR as

well as canopy temperature and photorespiration.

𝑓𝑝ℎ𝑜𝑡,𝑚𝑎𝑥 =

𝜀𝐼𝑔𝐶𝑂2
𝜀𝐼 + 𝑔𝐶𝑂2

𝑐𝜔 (cid:0)𝐶𝐶𝑂2 − Γ(cid:1)
𝑐𝜔 (cid:0)𝐶𝐶𝑂2 − Γ(cid:1)

(7.6)

In Equation (7.6), 𝜀 is the light-use efficiency, 𝐼 is the spectral irradiance integrated over the

wavebands within PAR that regulate plant growth, 𝑔𝐶𝑂2 is the conductance of canopy for the
diffusion of CO2, 𝑐𝜔 is the density of CO2 that has a value of 1.83 × 10−3 𝑔 𝑚−3, 𝐶𝐶𝑂2 is the

concentration of CO2 in the greenhouse, and Γ is the CO2 compensation point, accounting for

the impact of the temperature on photosynthesis rate (Van Henten, 1994). CO2 compensation is

determined based on canopy temperature using the following correlation,

Γ = 𝑐Γ𝑐

(𝑇−20)/10

𝑄10,Γ

(7.7)

In Equation (7.7), 𝑐Γ is the CO2 compensation point at 20 ◦𝐶 which is 40 𝑚𝐿 𝐿−1, and 𝑐𝑄10,Γ

is the sensitivity of CO2 compensation with canopy temperature, which Goudriaan et al. (1985)

approximated it as 2.0. Light-use efficiency is computed considering light level impact on CO2

compensation and photorespiration Goudriaan et al. (1985),

𝜀 = 𝑐𝜀

𝐶𝐶𝑂2 − Γ
𝐶𝐶𝑂2 + 2Γ

(7.8)

In Equation (7.8), 𝑐𝜀 is the quantum use efficiency which is the energy required for a reduction of

one mole CO2, and Goudriaan et al. (1985) approximated its value to be about 17.0 × 10−6 𝑔 𝐽−1. In

this study, there is an assumption that this parameter is affected by the photon spectral distribution;

therefore, its value varies depending on the lighting conditions utilized for lettuce growth. Goudri-

aan et al. (1985) developed a mathematical correlation for the canopy conductance for CO2 diffusion,

146

which is derived considering the boundary layer, stomatal, and carboxylation conductance,

1
𝑔𝐶𝑂2

=

1
𝑔𝑏𝑛𝑑

+

1
𝑔𝑠𝑡𝑚

+

1
𝑔𝑐𝑎𝑟

(7.9)

In Equation (7.9), 𝑔𝑏𝑛𝑑, 𝑔𝑠𝑡𝑚, and 𝑔𝑐𝑎𝑟 represent the boundary layer, stomatal, and carboxyla-

tion conductance, respectively. Stanghellini (1987) estimated the boundary layer conductance to

0.007 𝑚 𝑠−1 at a 5 ◦𝐶 temperature gradient, 0.1 𝑚 𝑠−1 wind speed, and leaf with a characteristic

length of 0.075 𝑚. For a plant that grows in an environment without stress, Stanghellini (1987)

approximated stomatal conductance to 0.005 𝑚 𝑠−1. Carboxylation conductance is a function of

canopy temperature, and its value (from 5 to 40 ◦𝐶) is determined using the following empirical

correlation,

𝑔𝑐𝑎𝑟 = −1.32 × 10−5𝑇 2 + 5.94 × 10−4𝑇 − 2.64 × 10−3

(7.10)

Table 7.1 provides a summary of the definition of different coefficients and their numerical values

within the plant growth model.

7.2.2 Plant Growth ODE Solver

A MATLAB code was developed to find a solution for the ODE Equations (7.1), and (7.2). The

code utilized experimental temperature, spectral irradiance integrated over wavebands from 400 to

750 𝑛𝑚, and CO2 concentration as inputs to compute the two sub-variable dry masses as outputs.

Input and output data were extracted from experiments that investigated the impact of the photon

spectrum on the production of lettuce ’Rouxai’ growth by Meng and Runkle (2019), Meng et al.

(2019), and Meng et al. (2020). Meng and Runkle (2019) carried out three replications with a

PPFD of 100 and 180 𝜇𝑚𝑜𝑙 𝑚−2 𝑠−1 during 0-2 and 2-3 days, respectively. After that, the seedlings

were grown under various LED treatments with a 24-hour photoperiod, and the temperature was set

to 23 ◦C. Fresh and dry mass data were obtained using destructive tests for plants harvested on day

10. Similarly, Meng et al. (2019) performed experiments three times at a total photon flux density

of 180 𝜇𝑚𝑜𝑙 𝑚−2 𝑠−1. The seedlings were transplanted into a hydroponic system with a 20-hour

photoperiod, an average air temperature of 21.1 ◦C, average CO2 concentration of 402 𝑚𝐿 𝐿−1, and

relative humidity ranging from 41% to 70%. Meng et al. (2020) conducted two replications at a

147

Parameter
𝑐 𝛼
𝑐𝛽
𝑐𝑔𝑟 ,𝑚𝑎𝑥
𝑐𝛾

𝑐𝑄10,𝑔𝑟

𝑐𝑟 𝑒𝑠 𝑝,𝑠ℎ𝑡

𝑐𝑟 𝑒𝑠 𝑝,𝑟𝑡

𝑐𝑄10,𝑟 𝑒𝑠 𝑝

𝑐 𝜏

𝑐𝐾
𝑐𝑙𝑎𝑟
𝑐 𝜔
𝑐Γ
𝑐𝑄10,Γ

𝑐 𝜀

𝑔𝑏𝑛𝑑
𝑔𝑠𝑡 𝑚

Definition
Conversion rate of CO2 to CH2O
Yield factor
Saturation growth rate at 20 ◦𝐶
Growth rate coefficient
Growth rate sensitivity to
the canopy temperature
Shoot maintenance respiration
coefficient at 25 ◦𝐶
Root maintenance respiration
coefficient at 25 ◦𝐶
Sensitivity of maintenance respiration
to the canopy temperature
Ratio of root dry mass
to total plant dry mass (soil)
Ratio of root dry mass to
total plant dry mass (hydroponic)
Extinction coefficient
Structural leaf area ratio
Density of CO2
CO2 compensation point at 20 ◦𝐶
Sensitivity of CO2 compensation
with canopy temperature
Quantum use efficiency as energy required
for a reduction of one molecule of CO2
Boundary layer conductance
Stomatal conductance

Value
0.68
0.8
5 × 10−6 𝑠−1
1.0

1.6

3.47 × 10−7 𝑠−1

Reference
Van Henten (1994)
Sweeney (1981)
Van Holsteijn (1981)
Sweeney (1981)

Sweeney (1981)

Van Henten (1994)

1.16 × 10−7 𝑠−1

Van Henten (1994)

2.0

0.15

0.14

Van Henten (1994)

Lorenz and Wiebe (1980)

Sakamoto et al. (2015)

0.9
75 × 10−3 𝑚2 𝑔−1
1.83 × 10−3 𝑔 𝑚−3
40 𝑚𝐿 𝐿 −1

Goudriaan and Monteith (1990)
Lorenz and Wiebe (1980)
Van Henten (1994)
Goudriaan et al. (1985)

2.0

Goudriaan et al. (1985)

17.0 × 10−6 𝑔 𝐽 −1

Goudriaan et al. (1985)

0.007 𝑚 𝑠−1
0.005 𝑚 𝑠−1

Stanghellini (1987)
Stanghellini (1987)

Table 7.1 Summary of coefficients needed in Equations (7.1)-(7.9) for lettuce cultivation modeling.

temperature of 20 ◦C, a total photon flux density of 50 𝜇𝑚𝑜𝑙 𝑚−2 𝑠−1, and 24-hour photoperiod. The

next day, the temperature, the photoperiod, and total photon flux density were set to 22 ◦C, 20 hours,

and 180 𝜇𝑚𝑜𝑙 𝑚−2 𝑠−1, respectively. On the fourth day, the seedlings were exposed to nine different

light-quality treatments under the same controlled conditions. For the first replication, the average

temperature, relative humidity, and CO2 concentration was 22.4 ◦C, 410 𝑚𝐿 𝐿−1, and 34%, and in

the second replication, these parameters were 22.5 ◦C, 398 𝑚𝐿 𝐿−1, and 35%, respectively. Table

7.2 represents the experimental data for red-leaf lettuce ’Rouxai’ under different light treatment

conditions, while Figure 7.1 illustrates the variation of incoming light spectra.

Using integrated spectral irradiance, CO2 concentration, and temperature, the Van Henten

(1994) growth model is used with the parameters in Table 7.1 to predict dry mass for different light

treatment experiments. Figure 7.2 represents the necessity of considering the impact of spectral

148

Figure 7.1 Spectral distribution for different case studies of lighting treatment for lettuce reported
in the literature to study the effect of spectral distribution on lettuce growth. The label at the top of
each graph represents a light treatment experiment according to Table 7.2.

149

Treatment
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Literature

Meng et al. (2020)
Meng et al. (2020)
Meng et al. (2020)
Meng et al. (2020)
Meng et al. (2020)
Meng et al. (2020)
Meng et al. (2020)
Meng and Runkle (2019)
Meng and Runkle (2019)
Meng and Runkle (2019)
Meng et al. (2019)
Meng et al. (2019)
Meng et al. (2019)
Meng et al. (2019)
Meng et al. (2019)
Meng et al. (2019)
Meng et al. (2019)
Meng et al. (2019)
Meng et al. (2019)
Meng et al. (2019)

Treatment
Type
R180
G60R120
B20R160
B20G60R100
B60R120(1)
B60G60R60
WW180(1)
B30R150
B30R150FR30
R180FR30
B60R120(2)
B40G20R120
B20G40R120
G60R120
B40R120FR20
B20R120FR40
R120FR60
B20G20R120FR20
WW180(2)
EQW180

Dry Mass
(𝑔)
2.931
2.745
2.258
2.449
2.051
1.527
2.470
0.046
0.052
0.045
1.014
1.187
1.348
1.587
1.232
1.438
1.622
1.417
1.394
1.087

PFD
(cid:0)𝜇𝑚𝑜𝑙 𝑚−2𝑠−1(cid:1)
180.2
184.3
179.6
180.2
183.0
178.7
184.8
183.7
216.5
214.2
178.1
182.5
181.7
184.3
180.8
183.6
174.2
182.4
188.1
181.7

I𝑃 𝐴𝑅+𝐹 𝑅
(cid:0)𝑊𝑚−2(cid:1)
32.8
36.3
34.4
37.2
38.5
40.3
36.5
36.2
41.7
38.4
37.3
37.3
36.4
36.3
36.1
34.4
30.1
35.4
37.0
38.4

Table 7.2 Experimental data for different spectral treatments obtained from Meng and Runkle
(2019) and Meng et al. (2019, 2020). Abbreviation 𝐵, 𝐺, 𝑅, 𝐹 𝑅, 𝑊𝑊, and 𝐸𝑄𝑊 refers to blue
(400 − 500 𝑛𝑚), green (500 − 600 𝑛𝑚), red (600 − 700 𝑛𝑚), far-red (700 − 750 𝑛𝑚), warm-white,
and equalized white light-emitting diodes, respectively according to Meng et al. (2020). 𝑃𝐹 𝐷,
and 𝐼𝑃 𝐴𝑅+𝐹 𝑅 represent photon flux density and spectral irradiance integrated over PAR and far-red
wavebands.

distribution on lettuce growth by showing the difference between the experimental data and the

plant growth model. For example, the growth model predicted only 6 of the 20 lighting treatments

to be within 25% of the actual dry mass values.

Numerical error is the measure of a difference between the experimental dry mass of lettuce

and the model prediction using the suggested value for 𝑐𝜀, which was 17.0 × 10−6 𝑔 𝐽−1. With the

assumption of unvarying 𝑐𝜀 for different experiments, the dynamic growth model does not accurately

predict for various light treatment experiments other than typical greenhouse light conditions.

150

Figure 7.2 Numerical error for the lettuce growth model using the 𝑐𝜀 value by Van Henten (1994).
𝐷 𝑀𝑠𝑖𝑚, and 𝐷 𝑀𝑒𝑥 𝑝 are lettuce dry mass for numerical simulation and experimental study in 𝑔,
respectively. The considerable differences, some with more than 75 % error, indicate the necessity
of considering the impact of spectral irradiance and flux density on the 𝑐𝜀 value for an accurate
prediction of lettuce growth yield.

7.2.3 Validation of ODEs Solver Through Altering Light-Use Efficiency for Different Ex-

periments

As mentioned earlier, using a constant 𝑐𝜀 led to a considerable error in lettuce dry mass

prediction; however, as we will show, a varying 𝑐𝜀 depending on spectral distribution allows

prediction in good accordance with experimental data. Knowing the dry mass of lettuce for

different experiments, the solver tries to find a value for 𝑐𝜀 that allows a prediction of a state

variable in good accordance with experimental data. These values will be used in the next section

to develop a model that predicts the impact of the photon spectrum on 𝑐𝜀, and eventually on plant

growth.

Figure 7.3 compares the lettuce dry mass predicted by the model with the experimental dry

mass for the investigated light treatments. It is inferred from Figure 7.3 that for the specific quantum

use efficiency for different light treatment experiments, the solver is capable of accurate prediction

of the lettuce state variable (dry mass) on the day of harvest.

151

Figure 7.3 Comparison of lettuce dry mass for a dynamic growth model with experimental data
under different spectral distributions and intensities. The label at the top of each graph represents
a light treatment experiment according to Table 7.2.

152

7.3

Implementation of Regression Methodology to Account for the Impact of Spectral Dis-
tribution and Intensity on Lettuce Growth

This section provides insight into our linear regression model. The general form of the model is

presented in the next subsection, which is followed by a discussion on the input features of the model.

Exploratory data analysis is performed on the input dataset in subsection 7.3.3. The generic form

of the empirical models is investigated in subsection 7.3.4, and the performance of different models

is evaluated using various metrics such as R2, mean absolute percentage error (MAPE), Akaike

information criterion (AIC), and Bayesian information criterion (BIC), in the next subsection. The

effects of combining the suggested empirical model with the dynamic growth model for lettuce are

studied in subsection 7.3.6. In the last subsection, the precision of the proposed combined dynamic

growth model is evaluated using data from another study conducted under completely different

experimental conditions.

7.3.1 Light-Use Efficiency Prediction Based on Incoming Spectrum

The aim of this study is to develop a model that predicts the quantum use efficiency (𝑐𝜀) as

a function of spectral photon flux density or integrated spectral irradiance within the PAR+FR

waveband (i.e., 400-750 𝑛𝑚). A linear regression approach proves to be an invaluable tool for

generating a basic model for obtaining weights for different features and establishing a simple

mathematical model in the form of ¯𝑐𝜀 = (cid:205)4

𝑖=1 (𝜔𝑖𝐹𝑖) where 𝜔𝑖 and 𝐹𝑖 correspond to the weight
(coefficient) and the value for the ith input feature, respectively. Since the incoming spectrum is

a continuous function (Figure 7.1), an idea was devised to generate discrete features based on the

continuous distribution of the spectrum for the linear regression model. This idea involves dividing

the incoming spectrum into four segments, which in the context of this study, correspond to four

distinctive wavebands in PAR+FR: blue (400-500 nm), green (500-600 nm), red (600-700 nm),

and far-red (700-750 nm). A discrete value is assigned for each segment based on the integral of

spectral distribution. Subsection 7.3.2 provides a detailed description of how these discrete values

are obtained for each spectrum.

In addition, it is possible to investigate the interaction between

different light wavebands on quantum use efficiency through the regression model in the form

153

Figure 7.4 The path to developing empirical correlation for light-use efficiency based on spectral
photon flux density distribution, which is shown on the left. In this figure, 𝜆 is the wavelength
(nm), SPFD is spectral photon flux density (𝜇mol m−2 s−1 nm−1), 𝑐𝜀 is the light-use efficiency in
the dynamic growth model of lettuce, and F𝑖 and 𝜔𝑖 are the discrete input features based on the
incoming spectrum and the corresponding weights, respectively. Terms with prime correspond to
the interaction between different wavebands. Panels 1, 2, and 3 are representations of Figures 7.1,
7.3, and 7.5, respectively. . The same logic is also applicable to the spectral irradiance distribution.

of ¯𝑐𝜀 = (cid:205)4

𝑖=1 (𝜔𝑖𝐹𝑖) + (cid:205) 𝑗

(cid:16)

𝜔′

𝑗 𝐹 ′
𝑗

(cid:17)

where 𝐹 ′

𝑗 can be defined as the multiplication of two fraction

ratios, e.g., the blue and green wavebands. Figure 7.4 provides an overview of the development of

empirical correlation for light-use efficiency based on the continuous spectrum distribution.

7.3.2 Definition of the Fraction Ratio

As previously stated, the dynamic growth model’s efficiency can be improved by developing a

model for 𝑐𝜀 that takes into account the impact of spectral distribution. This can be accomplished

by creating a function for 𝑐𝜀 that is dependent on the photon flux density or integrated spectral

irradiance ratio for 100-nm wavebands in PAR and 50-nm FR waveband. Calculation of these ratios

based on spectral photon flux distribution is more convenient since Meng et al. (2020) assigned

a label based on photon flux density treatments with different wavebands. Considering lighting

154

treatment 18, or "B20G20R120FR20" as an example, the photon flux density for blue and green

light is 20 𝜇𝑚𝑜𝑙 𝑚−2 𝑠−1, red light is 120 𝜇𝑚𝑜𝑙 𝑚−2 𝑠−1, and far-red light is 20 𝜇𝑚𝑜𝑙 𝑚−2 𝑠−1.

The photon flux density for different wavebands represents the areas under the curve in Figure

7.5. Therefore, photon flux density ratios for the blue, green, and far-red wavebands are 20
180,

while for the red waveband is equal to 120

180. Computation of the ratios for integrated spectral

irradiation of the PAR+FR wavebands is different, since spectral irradiance is a measure of the

energy carried by a photon. Therefore, integrated spectral irradiance (I) for a specific spectrum

of PAR+FR is determined by calculating the energy for each wavelength through multiplication

of wavelength energy and its number of photons and integrating those over the specific waveband.

For "B20G20R120FR20" as an example, the integrated spectral irradiance for blue, green, red

and far-red wavebands are 5.57 𝑊 𝑚−2, 4.57 𝑊 𝑚−2, 21.74 𝑊 𝑚−2, and 3.51 𝑊 𝑚−2, respectively.

Based on the integrated spectral irradiance values computed for different wavebands, the integrated
35.38 , and 3.50
spectral irradiance intensity ratios for blue, green, red, and far-red are 5.57
35.38,

35.38 , 21.74

35.38, 4.57

or 15.7 : 12.9 : 61.4 : 9.9 respectively.

Figure 7.5 Dividing the photon spectrum for experimental
treatment number 18, or
"B20G20R20FR120", to calculate the intensity ratio that corresponds with the integrated spec-
tral irradiance, or PFD distribution. B, G, R, FR corresponds to blue (400 − 500 𝑛𝑚), green
(500 − 600 𝑛𝑚), red (600 − 700 𝑛𝑚), and far-red (700 − 750 𝑛𝑚) wavebands.

155

7.3.3 Exploratory Data Analysis

With the calculation of 𝑐𝜀 from the experimental data, the next step is to create regression models

to fit polynomial functions over a set of discrete variables and predict the light-use efficiency. As

the aim of this study is to establish a framework that can estimate light-use efficiency as a function

of incoming spectra, the input features include discrete parameters associated with either PFD or

spectral irradiance distribution. The first set of input variables consists of photon flux density ratios

for blue, green, red, and far-red wavebands, which are calculated by integrating the photon flux

density distribution shown in Figure 7.1. On the other hand, the second set of input parameters

includes spectral irradiance ratios for the same wavebands, obtained by integrating over spectral

irradiance distribution for various lighting distributions. Before investigating various regression

models, the properties of the data used for regression are explored. Table 7.3 represents the

mean, standard deviation (std), minimum (min), maximum (max), and percentile values for the

investigated features (25% or first quartile, 50% or second quartile or median, 75% or third quartile),

the input (F is the fraction ratio which is either based on photon flux density (PFD) or spectral

irradiance integrated over wavelengths (I) whereas B, G, R, and FR represent blue, green, red, and

far-red wavebands) and the output (c𝜀 is the light-use efficiency) of the model.

Variable Mean
0.127
𝐹𝐵,𝑃𝐹 𝐷
0.147
𝐹𝐺,𝑃𝐹 𝐷
0.660
𝐹𝑅,𝑃𝐹 𝐷
0.066
𝐹𝐹 𝑅,𝑃𝐹 𝐷
0.168
𝐹𝐵,𝐼
0.158
𝐹𝐺,𝐼
0.614
𝐹𝑅,𝐼
0.060
𝐹𝐹 𝑅,𝐼
1.30
𝑐𝜀 × 105

Std
0.112
0.178
0.167
0.093
0.142
0.187
0.174
0.088
0.142

Min
0
0
0.284
0
0
0
0.254
0
0.110

25% 50% 75% Max
0.333
0.049
0.588
0
0.639
1
0.333
0
0.421
0.065
0.605
0
0.562
1
0.321
0
1.61
1.21

0.111
0.056
0.667
0
0.155
0.063
0.612
0
1.26

0.181
0.309
0.679
0.111
0.250
0.322
0.665
0.097
1.40

Table 7.3 Statistical information for ratios based on integrated spectral and photon flux density
distributions, and 𝑐𝜀. Mean, std, min, and max represent the average, standard variation, minimum,
and maximum values in the dataset. 25%, 50%, and 75% represent numerical values for the first
quartile, median, and third quartile (based on the assumption that data is sorted in ascending order).
F is the fraction ratio which is either based on photon flux density (PFD) or spectral irradiance
integrated over wavelengths (I) whereas B, G, R, and FR represent blue, green, red, and far-red
wavebands, and c𝜀 is the light-use efficiency.

156

7.3.4 Predictive Model Including Polynomial Features for the Quantum Use Efficiency Co-

efficient

Different polynomial models examined within the aim of this study have a form similar to the

following equation,

¯𝑐𝜀 = 𝑎0 +

(cid:32)

4
∑︁

𝑖=1

𝑎𝑖𝐹𝑖 + 𝑏𝑖𝐹2

𝑖 + 𝑐𝑖𝐹3

𝑖 + 𝑑𝑖𝐹4

𝑖 +

(cid:33)

(cid:0)𝑒𝑖 𝑗 𝐹𝑖𝐹𝑗 (cid:1)

4
∑︁

𝑗=𝑖

(7.11)

Not all of the models have every term presented in Equation (7.11), e.g., the regression model

based on the first-order term is defined as ¯𝑐𝜀 = 𝑎0 + (cid:205)4

𝑖=1 (𝑎𝑖𝐹𝑖). Regression models are defined in

a way that includes up to 16 weight coefficients. Within the scope of this study, 22 distinctive terms

are investigated, that are provided in Equation (7.11), and includes ratios (F𝑖, 4 terms representing

each waveband), the square of ratios (F2

𝑖 , 4 terms), the cubic of ratios (F3

𝑖 , 4 terms), the quartic of

ratios (F4

𝑖 , 4 terms), and interaction ratios (F𝑖F 𝑗 , 6 terms). Therefore, studied regression models

within the scope of this study are comprised of linear models with 4 (includes F𝑖 terms), 8, 12, 14,

and 16 (includes F𝑖, F2

𝑖 , F3

𝑖 , F4

𝑖 terms) weight coefficients.

Since the dataset is comprised of 20 observations of 𝑐𝜀 for different spectral distributions and

intensities (7.1), increasing the number of coefficients beyond the suggested limit would result in

an overfitted model. In other words, this would lead to a model capable of accurate prediction

for the studied data; however, evaluating the performance of the model against new data would

decrease the fidelity of the model. The term "nonlinear" in this section refers to polynomial models

based on Equation (7.11) in which 𝑒𝑖 𝑗 ≠ 0 for every i and j value. The regression models which

estimate the impact of incoming light spectrum on the light-use efficiency are classified into the

following categories: 1) models based on PFD ratios, which disregard the impact of overall photon

flux density; 2) models based on integrated spectral irradiance ratios which disregard the impact of

overall value; 3) models based on PFD ratios, which considered the impact of overall photon flux

density; 4) models based on integrated spectral irradiance ratios which considered the impact of

overall value. Figures 7.7a, 7.7b, 7.7c, and 7.7d represent the accuracy of categories 1, 2, 3, and 4

using R2 metric.

157

To prevent overfitting and ensure the model’s applicability to new data, a validation study is

conducted on the dataset. This involves reserving a portion of the data for testing, which is not

used during the model training phase. The testing data is used to evaluate the model’s performance

on new and unseen data. The goal is to find a model that performs well on both training data and

testing data, thereby preventing underfitting or overfitting issues. For instance, for a regression

model with 16 weight coefficients, 3 samples are randomly chosen for testing purposes. The

remaining 17 samples are used to train the regression model, and then its accuracy is evaluated on

the 3 unseen samples. The selected regression model (and the corresponding weights for different

terms) is the one that performs well on both training data (17 samples) and testing data (3 samples).

This approach ensures that the model is not overfitting and can predict well on new data, making it

useful for practical applications. In addition to using unseen data for the validation of the regression

model, a regularization penalty (L1 or L2 norm) is introduced into the regression model to decrease

the variation caused by the complexity of the model.

7.3.5 Development and Performance Comparison of Regression Models

In this study, the Scikit-learn built-in function LinearRegression developed by Pedregosa
et al. (2011) is used to build a model that minimizes the residual sum of squares (cid:0)𝑅2(cid:1) as the criteria
(cid:205)𝑛
𝑖=1 (𝑦𝑖− ˆ𝑦𝑖)2
𝑖=1 (𝑦𝑖− ¯𝑦)2 ,
(cid:205)𝑛
in which 𝑦𝑖 and ˆ𝑦𝑖 represented the true and predicted value for the i𝑡ℎ sample and ¯𝑦 is the average

for the closest linear function to the actual data. The R2 score is calculated using 𝑅2 = 1−

of the actual values. In addition to 𝑅2 criteria, the mean absolute percentage error (MAPE) is also

calculated for different models and is defined as MAPE=

1
𝑛𝑠𝑎𝑚 𝑝𝑙𝑒𝑠

(cid:205)𝑛𝑠𝑎𝑚 𝑝𝑙𝑒𝑠
𝑖=1

|𝑦𝑖− ˆ𝑦𝑖 |
max(𝜖,|𝑦𝑖 |) , where 𝜖 is an

arbitrary non-zero small positive number to ensure that MAPE is defined.

Figure 7.6 demonstrates the prediction accuracy of polynomial models compared with the value

used within the solver through the identity (dashed) line. The identity line describes the behavior

of a model that predicts with 100% accuracy. It is surmised the accuracy increased with a higher

number of features; Figure 7.6-b shows that the addition of 6 more features in the model that

corresponds to the term in Equation (7.11) in the form of 𝑒𝑖 𝑗 𝑋𝑖 𝑋 𝑗 elicits more compact scatter

distribution across the identity line compared to Figure 7.6a.

158

(a) Models based on 𝑒𝑖 𝑗 = 0

(b) Models based on 𝑒𝑖 𝑗 ≠ 0

Figure 7.6 Accuracy of first-order regression models with the assumption of a) Neglecting nonlin-
earity (cid:0)𝑒𝑖 𝑗 = 0(cid:1), and b) Considering nonlinearity (cid:0)𝑒𝑖 𝑗 ≠ 0(cid:1). I𝑃 𝐴𝑅+𝐹 𝑅 refers to a regression model
based on the integrated spectral irradiance ratio, while PFD represent a model based on photon flux
density ratio.

Although Figures 7.6 provides insight on the regression models’ accuracy, it is difficult to utilize

them to compare all of the investigated models. Therefore, R2 and MAPE accuracy criteria are

employed for the purpose of comparison, which is presented in Figures 7.7 and 7.8.

According to Figures 7.7 and 7.8, in spite of simplicity for the first-order and the combination of

first and second-order models, these models have poor accuracy in predicting the 𝑐𝜀 as a function of

spectral distribution with R2 score less than 0.75. However, the addition of third and fourth-order

terms creates a 16-feature regression model that has an average error of 2 percent (Figure 7.7d).

Furthermore, normalizing 𝑐𝜀 to accommodate the impact of overall integrated spectral irradiance

or photon flux density increases the fidelity of the regression model.

In addition to R2 and MAPE metrics, the Akaike information criterion (AIC) and the Bayesian

information criterion (BIC) are also computed for the studied models, which are the measures of the

model’s complexity. The value of AIC and BIC for models with a constant parameter is obtained

using the following correlations (Seabold and Perktold, 2010): AIC = −2 × 𝐿𝐿 + log(𝑁) × (𝑘 + 1),

and BIC = −2× 𝐿𝐿 +2× (𝑘 +1), whereas LL is the log of the likelihood function (how likely it is that

the model predicted the actual values), N is the size of training data, and k is the number of features,

159

(a) Disregarding the impact of photon flux den-
sity value

(b) Disregarding the impact of integrated spectral ir-
radiance value

(c) Accounting for the impact of photon flux density
value

(d) Accounting for the impact of integrated spectral
irradiance value

Figure 7.7 Comparison of different models based on R2 score criteria. Abbreviations within these
figures are NL: nonlinear (includes 6 interaction terms between wavebands), Fi: first-order terms,
third-order terms, Fo: fourth-order terms. R2 score closer to 1
Se: second-order terms, Th:
indicates a more accurate model.

respectively. It is worth mentioning that a lower value of AIC or BIC indicates that the fitted model

is a better fit for the data, as it balances the goodness of fit and the complexity of the model (Baguley,

2018). Figures 7.9 and 7.10 provide visual representations of the impact of the model’s complexity

on AIC and BIC value. For the studied dataset, by increasing the accuracy of the model through

the addition of new terms, the likelihood function also improves, which ultimately outweighs the

negative penalty associated with the higher number of features (k); therefore, for the investigated

models, the introduction of new features into the regression model would generally decrease AIC

value. Figure 7.10 demonstrates that the BIC shows a different pattern, where regression models

160

(a) Disregarding the impact of photon flux density
value

(b) Disregarding the impact of integrated spectral ir-
radiance value

(c) Accounting for the impact of photon flux density
value

(d) Accounting for the impact of integrated spectral
irradiance value

Figure 7.8 Comparison of different models based on the mean absolute percentage error (MAPE)
score criteria. Abbreviations within these figures are NL: nonlinear (includes 6 interaction terms
third-order terms, Fo:
between wavebands), Fi: first-order terms, Se: second-order terms, Th:
fourth-order terms. The lower value for MAPE score indicates a more accurate model.

including nonlinear terms and only one of the first-, second-, or third-order terms are better fitted

than those consisting of nonlinear terms and two of the first-, second-, or third-order terms.

It is important to note that while a lower AIC or BIC value suggests a better model, it does

not necessarily mean that the model is the best possible fit for the data. In order to determine the

best-fitted model, a comprehensive analysis of the performance of the studied models is conducted

based on AIC, BIC, MAPE, and R2 metrics. Based on this comparison, it is evident that the

model, which incorporates first-, second-, third-, and fourth-order terms based on the integrated

spectral irradiance ratio considering the impact of overall integrated spectral irradiance of light-use

161

(a) Disregarding the impact of photon flux den-
sity value

(b) Disregarding the impact of integrated spectral ir-
radiance value

(c) Accounting for the impact of photon flux density
value

(d) Accounting for the impact of integrated spectral
irradiance value

Figure 7.9 Comparison of different models based on AIC criteria. Abbreviations within these
figures are NL: nonlinear (includes 6 interaction terms between wavebands), Fi: first-order terms,
Se: second-order terms, Th: third-order terms, Fo: fourth-order terms. The lower the value for
AIC, the better the fit of the model (Baguley, 2018).

efficiency, performs better than the other models with higher accuracy, and relatively lower AIC

and BIC values.

Equation (7.12) demonstrates the high fidelity regression model based on spectral irradiance

distribution normalized with integrated spectral irradiance for R180 light treatment based on Table

7.2. As shown in Figure 7.11, predictions of the suggested model are in a good accordance with

numerical data; however, additional data could prove useful in developing a more comprehensive

model.

162

(a) Disregarding the impact of photon flux den-
sity value

(b) Disregarding the impact of integrated spectral ir-
radiance value

(c) Accounting for the impact of photon flux density
value

(d) Accounting for the impact of integrated spectral
irradiance value

Figure 7.10 Comparison of different models based on BIC criteria. Abbreviations within these
figures are NL: nonlinear (includes 6 interaction terms between wavebands), Fi: first-order terms,
Se: second-order terms, Th: third-order terms, Fo: fourth-order terms. The lower the value for
BIC, the better the fit of the model (Baguley, 2018).

¯𝑐𝜀/𝑅𝐼 = −1.40 × 10−4 + 1.82 × 10−4𝐹𝐵,𝐼 + 2.06 × 10−4𝐹2

𝐵,𝐼 − 7.71 × 10−4𝐹3

𝐵,𝐼 + 8.38 × 10−4𝐹4
𝐵,𝐼

+ 2.32 × 10−4𝐹𝐺,𝐼 − 4.20 × 10−4𝐹2

𝐺,𝐼 + 1.53 × 10−3𝐹3

𝐺,𝐼 − 1.56 × 10−3𝐹4

𝐺,𝐼 − 1.90 × 10−4𝐹𝑅,𝐼

+ 1.03 × 10−3𝐹2

𝑅,𝐼 − 1.10 × 10−3𝐹3

𝑅,𝐼 + 4.13 × 10−4𝐹4

𝑅,𝐼 + 4.68 × 10−4𝐹𝐹 𝑅,𝐼 − 5.25 × 10−3𝐹2

𝐹 𝑅,𝐼

+ 2.92 × 10−2𝐹3

𝐹 𝑅,𝐼 − 4.77 × 10−2𝐹4

𝐹 𝑅,𝐼

Equation (7.12) is constrained by the following condition,

𝐹𝐵,𝐼 + 𝐹𝐺,𝐼 + 𝐹𝑅,𝐼 + 𝐹𝐹 𝑅,𝐼 = 1

163

(7.12)

(7.13)

Figure 7.11 Comparison of 𝑐𝜀 for the suggested model with numerical simulation for different light
treatments.

7.3.6 Coupling the Regression Model with Van Henten Dynamic Growth Model for Lettuce

Using Equation (7.12) and integrated spectral irradiance fraction ratio for the investigated

wavebands of the different light treatment cases, the Van Henten (1994) dynamic growth model is

utilized to compare the accuracy of the modified growth model that accounts for spectral distribution

and intensity. Figure 7.12 compares the difference between experimental dry mass for lettuce with

dry mass prediction of the modified growth model.

Comparing the numerical error presented in Figure 7.12 with Figure 7.2, it is inferred that the

suggested regression model of the 𝑐𝜀 improves the accuracy of Van Henten (1994) growth model

and adequately considers the impact of spectral distribution on plant growth.

7.3.7 Cross-Validation of the Proposed Light-Use Efficiency Model with Novel Data

In the previous section, the performance of the proposed mathematical model is investigated

through integration with the Van Henten (1994) dynamic growth model. To further investigate

164

Figure 7.12 Computed numerical error is significantly reduced based on 𝑐𝜀 value using Equation
(7.12) (regression label, black bar) compared with error using the suggested constant value for 𝑣𝜀
by Van Henten (1994) (constant label, light gray bar). 𝐷 𝑀𝑠𝑖𝑚, and 𝐷 𝑀𝑒𝑥 𝑝 are lettuce dry mass for
numerical simulation and experimental study in 𝑔, respectively. As shown in the figure, coupling
the regression model with the dynamic growth model improved the accuracy of prediction for
lettuce cultivated under different spectral distributions.

the accuracy of the light-use efficiency model based on the spectral irradiance ratios of various

wavebands, data from Both et al. (1994) on lettuce cultivated in a controlled greenhouse environment

is utilized. From October 1992 to March 1993, six controlled light treatments (without the use

of supplemental lighting) were conducted for lettuce grown hydroponically. For these treatments,

during the first 11 days, the temperature and CO2 concentration were maintained at 25 ◦𝐶 and 350

𝑚𝐿/𝐿, respectively. After day 11, the temperature was set to 24 ◦𝐶 between 7 am and 5 pm and

18.8 ◦𝐶 for the rest of the day, while CO2 was enriched to 1000 𝑚𝐿/𝐿. Table 7.4 represents data

used for cross-validation of the suggested regression-based light-use efficiency model. Spectral

irradiance intensity and distribution ratios are approximated using reported daily light integral for

the different treatments and predicted solar irradiation by Tobiska et al. (2000).

According to Figure 7.13, using the proposed regression-based light-use efficiency model,

lettuce dry mass predictions were in close agreement (mostly within 2-3 percent error) with the

experimental data.

165

Experimental period

November 1992
January 1993
February 1993

(cid:16)

Daily light integral
𝑚𝑜𝑙 𝑚−2 𝑑−1(cid:17)
6.2
4.7
10.5

Dry Mass

Day 14

Day 18

Day 21

Day 25

Day 28

Day 32

Day 35

0.064
0.063
0.085

0.153
0.141
0.288

0.3
0.2
0.53

0.76
0.44
1.21

1.01
0.84
1.98

1.735
1.2
3.15

2.46
1.87
4.81

Table 7.4 Experimental dry mass data for greenhouse cultivated hydroponic lettuce grown under
controlled light treatments obtained by Both et al. (1994).

Figure 7.13 Comparison of dynamic growth model accuracy using the suggested value for c𝜀 by
Van Henten (1994), and obtained value using the proposed regression-based light-use efficiency
model with experimental data from Both et al. (1994) for periods of November 1992, and January
and February of 1993. The regression-based model is capable of approximating dry mass for
greenhouse cultivated lettuce.

7.4 Summary and Remark

The aim of this chapter is to predict the impact of incoming light spectral distribution and its

intensity on lettuce growth. For this purpose, a dynamic model of plant growth for lettuce provided

by Van Henten (1994) is modified. An ODE solver is developed to simulate the dynamic behavior of

lettuce from the seedling stage to maturity. It is assumed that the spectral distribution of light and its

intensity affect the model through a coefficient 𝑐𝜀, which accounts for energy provided by photons

for a reduction of one molecule of CO2. Using data for lettuce cultivated under 20 different indoor

lighting treatments, the ODE solver calculated 𝑐𝜀 for different cases. Several models are fitted using

spectral distribution ratios for 4 light wavebands: blue (400 − 500 𝑛𝑚), green (500 − 600 𝑛𝑚), red

(600 − 700 𝑛𝑚), and far-red (700 − 750 𝑛𝑚) as input data and the obtained 𝑐𝜀 as the sole output.

To determine the algebraic structure of the model with the highest accuracy, a variety of regression

models with varying numbers of features, from 4 (ratios for the blue, green, red, and far-red

166

wavebands) to 16 (first, second, third, and fourth-order values for these ratios) are investigated. The

combination of first to fourth-order terms that had the highest accuracy (98%) was a regression

model based on integrated spectral irradiance distribution (in which the predicted 𝑐𝜀 was based

on normalized overall spectral irradiance).

In order to obtain coefficients for different terms in

the regression model, 17 of the 20 experimental data were utilized, while the rest prevented the

overfitting of the regression model. To further evaluate the accuracy of the regression model, 21

experimental data for three replications of indoor-cultivated lettuce were used (Both et al., 1994)

and are presented in Figure 7.13.

The impact of incoming spectral distribution on lettuce plant growth is investigated. By

considering two constrained scenarios, it is possible to visualize the impact of varying spectral

distribution on light-use efficiency.

In these scenarios, the spectral irradiance integrated over

wavelengths (𝐼𝑃 𝐴𝑅+𝐹 𝑅) remains unchanged while one of the wavebands is eliminated from the

spectra.

In the first scenario, it is assumed that the far-red waveband is missing from the light

spectra and only contains the traditionally defined PAR waveband. Contrary to the first scenario,

in the second one, the green waveband is replaced with far-red; thus, the incoming spectrum is

composed of blue, red, and far-red wavebands. Figures 7.14a and 7.14b demonstrate how light-use

efficiency varies in scenarios one and two, respectively. Based on these figures, the red waveband

promotes, and the blue waveband inhibits biomass accumulation in lettuce by increasing and

decreasing light-use efficiency, respectively. The impact of the blue waveband on plant growth

is enhanced by the presence of the green waveband. On the other hand, the addition of the far-

red waveband to the light spectrum mitigates the impact of the blue/green waveband. Therefore,

maximum lettuce biomass accumulation can be achieved using the outcomes of these scenarios by

emphasizing the red and far-red wavebands and avoiding a high spectral irradiance ratio of the blue

and green bands. However, this model ignores important quality considerations such as leaf color,

texture, nutritional content, and post-harvest longevity.

The model presented in Equation (7.12) provides a simplified framework to evaluate the impact

of spectral distribution on lettuce plant growth. This contrasts with a model for tomato growth

167

(a) Variation of predicted light-use efficiency in the
absence of far-red light (cid:0)𝐹𝐹 𝑅,𝐼 = 0(cid:1).

(b) Variation of predicted light-use efficiency in the
absence of green light (cid:0)𝐹𝐺,𝐼 = 0(cid:1).

Figure 7.14 Impact of the incoming light spectral distribution on the light-use efficiency coefficient
(𝑐𝜀) considering the same spectral irradiance integrated over wavelength (𝐼𝑃 𝐴𝑅+𝐹 𝑅 remains un-
changed). Abbreviations B and R refer to blue and red. The constraint of Equation (7.13) enforces
a linear relationship between 𝐹𝐵,𝐼 and 𝐹𝑅,𝐼 within each scenario, and ensures a clear visualization
of the effect of the spectral distribution on 𝑐𝜀.

(Dieleman et al., 2019), in which the 3D model needs to be solved in order to investigate the effect

of light quality. Moreover, the application of this model to the cultivation of lettuce can increase

biomass accumulation during the plant growth cycle. This model can also be used to optimize light

conditions, allowing for more efficient use of energy and resources.

Although the regression model predictions are in good accordance with the solver predictions,

additional experimental data with a focus on the impact of light spectrum on lettuce plant morphol-

ogy will likely create a more comprehensive model with higher fidelity. In addition, interactions

likely exist between light intensity and the photon spectrum, and additional data are needed to

test and improve the model’s performance. Specifically, morphological acclimation, such as total

leaf area, canopy area, number of leaves, leaf pigmentation, and chlorophyll concentration, can

affect the photosynthetic rate and light interception and would ideally be parameterized in future

growth models. Finally, this technique has the potential to be applied to other horticultural crops,

particularly leafy vegetable crops, to incorporate the impact of spectral distribution on biomass

accumulation and crop yield.

168

CHAPTER 8

THE INTEGRATION OF GREENHOUSE AND WATER DESALINATION SYSTEM
FOR SUSTAINABLE FOOD AND WATER PRODUCTION

The content of this chapter was published in the following conference:

Integrated Greenhouse for Food and Water Production, by Mahyar Abedi, Xu Tan, James

F. Klausner, and André Bénard, ASME 2023 Heat Transfer Summer Conference SHTC2023,

July. 10-12, 2023, https://doi.org/10.1115/HT2023-106914.

8.1

Introduction

As far as our daily lives are concerned, water has always played an integral role. Numerous

applications of it are found in various sectors, from the domestic to the commercial to the industrial,

which includes agriculture (Mancosu et al., 2015). As a result, water scarcity would create a cause-

and-effect cycle that would ultimately lead to food shortages.

Even though the public perceives water to be readily available, only three percent of surface

water resources are freshwater. The remainder is saline water that requires different treatments

before it can be used, depending on the salinity level.

In the past few decades, the impacts of

global warming, population growth, and economic advancements have intensified the challenges

of accessing freshwater resources worldwide (Unesco, 2019). This is especially true in the Middle

East, Africa, and some regions of America.

In order to meet the escalating food demand, modern farming increasingly relies on large green-

houses that occupy vast areas. In most instances, a conventional greenhouse requires a considerable

amount of energy to maintain a favorable environment for plant cultivation, which is commonly

obtained from non-renewable sources. Using renewable energy sources to satisfy the thermal needs

of a greenhouse was studied by Jahangiri Mamouri et al. (2018); Mamouri et al. (2020). The con-

cept revolves around using spectrum-shifting materials that absorb parts of the incoming spectral

irradiance that take no part in the photosynthesis of a plant, in addition to a desalination unit. De-

salination technologies integrated with the greenhouse allow the treatment of contaminated or brine

waters (Mancosu et al., 2015; Unesco, 2019). Some of these technologies include reverse osmosis

169

(Goh et al., 2018), solar ponds (El-Sebaii et al., 2011), and the humidification-dehumidification

(HDH) procedure (Goosen et al., 2003). Humidification-dehumidification technologies have some

advantages over other processes, such as lower capital costs, the capability to treat nearly all salinity

levels, and integration with low-grade energy resources (Abedi et al., 2021). Furthermore, the

addition of a packed-bed medium to the process improves the efficiency of desalination (Klausner

et al., 2004) The proposed system can also be placed under a solar desalination chimney investigated

by Abedi et al. (2023a), whereas the desalination system could be operated autonomously using the

power generated by the solar chimney.

In this chapter, a thermal model of a greenhouse (Sethi, 2009), direct-contact packed-bed

desalination (Alnaimat et al., 2011), and a dynamic plant growth model for lettuce (Van Henten,

1994), are all coupled together, and mathematically solved using instantaneous environmental data

for Phoenix, Arizona. Performance analyses are carried out to estimate the desalination potential,

the cultivation yield, and the amount of energy saved. Coupling all three models allows considering

the transient behavior of a plant during its growth cycle as it accumulates biomass and increases

plant leaf area. Previously, Sethi (2009) considered a constant value for mass and the area of the

plant, while Jahangiri Mamouri et al. (2018); Mamouri et al. (2020) assumes the quasi-steady-

state for thermal modeling of the greenhouse, neither accounting for the transient behavior of the

greenhouse and plants. Accounting for the overall transient behavior of the greenhouse and plants

is needed for an accurate assessment of a greenhouse’s performance.

8.2 Proposed Integrated Greenhouse

The integrated greenhouse concept has reduced reliance on external sources such as water or

energy (for heating/cooling purposes). As mentioned above, the studied design is comprised of a

desalination system and a transparent solar water heater in addition to a conventional greenhouse.

The transparent solar water heater provides shading, which in turn decreases the ventilation load

and produces hot saline water that passes through the desalination system. Moreover, the spectrum-

shifting material placed on the solar water heater allows the transmission of sufficient daily light

integral (DLI) for plant growth. Figure 8.1 shows a schematic of the proposed integrated greenhouse.

170

In the following, the modeling methodology is presented, starting with solar irradiation calculations,

followed by thermal modeling of the greenhouse, which includes differential equations for plant,

air, and greenhouse floor temperatures, and the transient model of the HDH desalination system.

Figure 8.1 Schematic of an integrated greenhouse with a transparent solar water heater, and a
direct-contact packed-bed desalination system.

8.3 Methodology for Modeling the Integrated Greenhouse

The mathematical model of the integrated greenhouse comprises of optical model for the

greenhouse cover, a thermal model of the greenhouse, a mathematical model for the direct-contact

packed-bed humidification-dehumidification desalination system, and a dynamic growth model for

the plant cultivated in the greenhouse. The first step for the thermal modeling of the greenhouse is

to estimate transmittance, reflectance, and absorptance for each surface of the greenhouse covers,

which varies with the incident angle of the incoming solar beam. The incident angle (𝜃𝑖), defined

as the angle between the normal vector of the inclined surface and the solar beam falling on the

surface, for each surface is calculated based on the sun’s position and geographical coordination of

the investigated location (Tiwari et al., 2016),

cos 𝜃𝑖 = (cos 𝜙 cos 𝛽 + sin 𝜙 sin 𝛽 cos 𝛾) cos 𝛿 cos 𝜔 + sin 𝛿 (sin 𝜙 cos 𝛽 − cos 𝜙 sin 𝛽 cos 𝛾)

(8.1)

+ cos 𝛿 sin 𝜔 sin 𝛽 sin 𝛾

171

In Equation (8.1), 𝜙 is latitude, 𝛽 is the inclination angle of the surface with respect to the osculating

plane, 𝛾 is the surface azimuth angle which is the angle between the projected normal vector of the

inclined surface on the osculating plane with the south-pointing vector, 𝛿 is the declination angle,

and 𝜔 is the hour angle. The declination angle (𝛿) defined as the angle between the earth’s and the

sun’s center is determined using the following correlation (Cooper’s equation),

𝛿 = 23.45 sin

(cid:20) 360
365

(cid:21)

(284 + 𝑛)

(8.2)

whereas 𝑛 is the day number in a year.

In addition, hour angle (𝜔) is computed through this

expression,

𝜔 = (𝑆𝑇 − 12) × 15◦

(8.3)

which 𝑆𝑇 is the solar time, refers to the time based on the motion of the sun, with solar noon being

the time the sun crosses the local meridian at the investigated location,

𝑆𝑇 = 𝐿𝑇 + 4 (𝐿𝑆𝑇 − 𝐿 𝐿𝑇 ) + 𝐸

(8.4)

In Equation (8.4), 𝐿𝑇 is the local time, 𝐿𝑆𝑇 is the longitude for the local meridian at the investigated

location, 𝐿 𝐿𝑇 is the investigated location longitude, and 𝐸 is the equation of time which is obtained

using the following,

𝐸 = 229.2(0.000075+0.001868 cos 𝐵−0.032077 sin 𝐵−0.014615 cos 2𝐵−0.04089 sin 2𝐵) (8.5)

whereas 𝐵 is the parameter based on the day’s number in the year (𝑛), and its value is given by

(𝑛 − 1) 360

365. Table 8.1 summarizes details for the area, inclination angle, and azimuth angle of

various greenhouse cover sections. After calculating the incident angle for every surface in Figure

8.2, overall solar irradiance is computed through the following Duffie and Beckman (2013),

𝐼𝑡 = 𝐼𝐷𝑁 𝐼 × cos (𝜃𝑖) + 𝐼𝐺𝐻𝐼

𝑎 (1 − cos 𝛽)
2

+ 𝐼𝐷𝐻𝐼

(1 − cos 𝛽)
2

(8.6)

In the Equation (8.6), 𝑎 is the albedo, 𝐼𝐷𝑁 𝐼 is the direct normal irradiance, 𝐼𝐷𝐻𝐼 is the diffuse

horizontal irradiance, and 𝐼𝐺𝐻𝐼 is the global horizontal irradiance at the studied location (see

172

Figure 8.2 Schematic of studied greenhouse geometry for investigation of the potential of integrated
configuration.

Section Area (cid:0)𝑚2(cid:1)

Inclination angle (𝛽) Surface azimuth angle (𝛾)

SW
SR
NW
NR
EW
WW

48
51.26
48
51.26
38
38

90◦
20.56◦
90◦
159.44◦
90◦
90◦

0◦
0◦
180◦
180◦
-90◦
90◦

Table 8.1 Geometric layout of the investigated greenhouse. SW, SR, NW, NR, EW, and WW refer
to the south wall, south roof, north wall, north roof, east wall, and west wall, respectively.

Section 8.4.1). The total irradiance (𝑆𝑡) for the greenhouse is the sum of overall irradiance falling

on each surface of the greenhouse cover by the area of the investigated surface. Table 8.1 provides

details for each section of the greenhouse cover regarding inclination and surface azimuth angles

to calculate the incident angle of the incoming radiation at a given time.

Transmittance, reflectance, and absorptance for different sections of the cover are next approx-

173

Figure 8.3 Schematic diagram for transmittance, reflectance, and absorptance computation for
different walls of the proposed greenhouse.

imated. For a beam falling on a surface between two materials with refractive index 𝑛1 and 𝑛2,
(cid:1), where 𝑟⊥ and 𝑟 ∥ are perpendicular and parallel

the reflectivity is computed using 𝑟 = 1
2

(cid:0)𝑟⊥ + 𝑟 ∥

polarized components of the reflected light, respectively. The perpendicular component is obtained
through sin2 (𝜃2−𝜃1)
sin2 (𝜃2+𝜃1)
while the parallel component is estimated using tan2 (𝜃2−𝜃1)

whereas 𝜃1 and 𝜃2 are incident angle and refractive angle (𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2),

tan2 (𝜃2+𝜃1) . Using reflectivity value, the reflectance
(𝜌), the absorptance (𝛼), and the transmittance (𝜏) are approximated through following correlations

Tiwari et al. (2016),

𝜏 =

1
2

(cid:0)𝜏⊥ + 𝜏∥

(cid:1) , 𝜏⊥ =

𝜏𝛼 (1 − 𝑟⊥)2
1 − (𝑟⊥𝜏𝛼)2

, 𝜏∥ =

(cid:1) 2

𝜏𝛼 (cid:0)1 − 𝑟 ∥
1 − (cid:0)𝑟 ∥𝜏𝛼(cid:1) 2

𝜌 =

1
2

(cid:0)𝜌⊥ + 𝜌∥

(cid:1) , 𝜌⊥ = 𝑟⊥ (1 + 𝜏𝛼𝜏⊥) , 𝜌∥ = 𝑟 ∥
(cid:18) 1 − 𝑟⊥
1 − 𝑟⊥𝜏𝛼

(cid:19)

(cid:1) , 𝛼⊥ = (1 − 𝜏𝛼)

, 𝛼∥ = (1 − 𝜏𝛼)

(cid:0)1 + 𝜏𝛼𝜏∥

(cid:1)

(cid:19)

(cid:18) 1 − 𝑟 ∥
1 − 𝑟 ∥𝜏𝛼

𝛼 =

1
2

(cid:0)𝛼⊥ + 𝛼∥

(8.7)

(8.8)

(8.9)

In Equations (8.7)-(8.9), 𝜏⊥, 𝜌⊥, and 𝛼⊥ are perpendicular components of transmittance, reflectance,

and absorptance, while 𝜏∥, 𝜌∥, and 𝛼∥ are parallel components, respectively. Moreover, 𝜏𝛼 is the
(cid:17)

transmittance value when absorptance is only considered and estimated through 𝜏𝛼 = exp

(cid:16)

,

− 𝑘 𝑑
cos 𝜃2

174

whereas 𝑘 is the extinction coefficient, and 𝑑 is the thickness of the medium. The value for these

components are estimated using these equations,

𝜏⊥ =

𝜏𝛼 (1 − 𝑟⊥)2
1 − (𝑟⊥𝜏𝛼)2

, 𝜏∥ =

(cid:1) 2

𝜏𝛼 (cid:0)1 − 𝑟 ∥
1 − (cid:0)𝑟 ∥𝜏𝛼(cid:1) 2
(cid:0)1 + 𝜏𝛼𝜏∥

(cid:1)

, 𝜌∥ = 𝑟 ∥

𝜌⊥ = 𝑟⊥ (1 + 𝜏𝛼𝜏⊥)
(cid:19)

(cid:18) 1 − 𝑟⊥
1 − 𝑟⊥𝜏𝛼

𝛼⊥ = (1 − 𝜏𝛼)

, 𝛼∥ = (1 − 𝜏𝛼)

(cid:19)

(cid:18) 1 − 𝑟 ∥
1 − 𝑟 ∥𝜏𝛼

(8.10)

(8.11)

(8.12)

In Equations (8.7)-(8.9), 𝜏𝛼 is the transmittance value when absorptance is only considered and

estimated through 𝜏𝛼 = exp

(cid:17)

(cid:16)

− 𝑘 𝑑
cos 𝜃2

of the medium.

, whereas 𝑘 is the extinction coefficient, and 𝑑 is the thickness

The thermal model for the greenhouse is similar to the model developed by Sethi (2009), and

it includes energy balances for the plant (Equation (8.13)), the greenhouse floor (Equation (8.14)),

and the air (Equation (8.15)),

𝛼𝑝 (1 − 𝜌) 𝜏𝑆𝑡 = 𝑀𝑝𝐶𝑝,𝑝

𝑑𝑇𝑝
𝑑𝑡

+ ℎ 𝑝𝑟 (𝑇𝑃 − 𝑇𝑅) + ℎ𝑟 𝐴𝑝 (𝑇𝑃 − 𝑇𝑅)

𝛼𝑔 (cid:0)1 − 𝛼𝑝(cid:1) (1 − 𝜌) 𝜏𝑆𝑡 = ℎ𝑏 𝐴𝑔 (cid:0)𝑇 𝑓 − 𝑇𝑔(cid:1) + ℎ𝑎 𝐴𝑔 (cid:0)𝑇 𝑓 − 𝑇𝑅(cid:1)

(8.13)

(8.14)

ℎ 𝑝𝑟 𝐴𝑝 (cid:0)𝑇𝑝 − 𝑇𝑅(cid:1) + ℎ𝑟 𝐴𝑝 (cid:0)𝑇𝑝 − 𝑇𝑅(cid:1) + ℎ𝑎 𝐴𝑔 (cid:0)𝑇 𝑓 − 𝑇𝑅(cid:1)

+ (cid:0)1 − 𝛼𝑔(cid:1) (cid:0)1 − 𝛼𝑝(cid:1) (1 − 𝜌) 𝜏𝑆𝑡 =

𝑀𝑎𝐶𝑝,𝑎

𝑑𝑇𝑅
𝑑𝑡

+𝑈𝑡 𝐴𝑐 (𝑇𝑅 − 𝑇𝑎𝑚𝑏) + ℎ𝑑 𝐴𝑑 (𝑇𝑅 − 𝑇𝑎𝑚𝑏) + 𝐸𝜈

(8.15)

In Equations (8.13)-(8.15), 𝛼𝑔 and 𝛼𝑝 are absorption coefficients for greenhouse ground and plant;

𝜏 is the transmittance of the greenhouse cover; 𝜌 is the reflectance of the greenhouse cover; 𝑆𝑡

is the total irradiance (𝑊); 𝑀𝑃 and 𝑀𝑎 are masses of the plant and air in the greenhouse (𝑘𝑔);
𝐶𝑝,𝑎 and 𝐶𝑝,𝑝 are specific heat coefficients for air and plant in the greenhouse (cid:0)𝐽 𝑘𝑔−1𝐾 −1(cid:1); 𝐴𝑐,
𝐴𝑑, 𝐴𝑔 and 𝐴𝑝 are the area of the greenhouse cover, door, ground and plant (cid:0)𝑚2(cid:1); ℎ𝑎, ℎ𝑏, ℎ 𝑝𝑟,

and ℎ𝑟 are convective heat transfer between greenhouse floor and air, heat transfer coefficient

between greenhouse floor and ground beneath it, total convective and evaporative heat transfer

175

coefficient between plant and greenhouse air, and radiation heat transfer coefficient between plant
and greenhouse air (cid:0)𝑊𝑚−2𝐾 −1(cid:1); 𝑇𝑎𝑚𝑏, 𝑇 𝑓 , 𝑇𝑔, 𝑇𝑃, and 𝑇𝑅 are ambient, floor, ground beneath the

floor, plant, and greenhouse air temperature (𝐾); 𝐸𝑣 is the energy required for the greenhouse

ventilation (𝑊); and 𝑈𝑡 is the overall heat transfer coefficient of the greenhouse to the ambient
air(cid:0)𝑊𝑚−2𝐾 −1(cid:1). Tiwari (2003) developed expressions to estimate the value of ℎ 𝑝𝑟 and ℎ𝑟,

ℎ 𝑝𝑟 = ℎ 𝑝 +

0.016 × ℎ 𝑝 (cid:2)𝑃𝑠𝑎𝑡 (𝑇𝑝) − 𝛾𝑟 𝑃𝑠𝑎𝑡 (𝑇𝑅)(cid:3)
𝑇𝑃 − 𝑇𝑅

ℎ𝑟 = 𝐹𝑃𝑅𝜀𝜎 (𝑇𝑃 + 𝑇𝑅)

(cid:16)
𝑃 + 𝑇 2
𝑇 2
𝑅

(cid:17)

(8.16)

(8.17)

In Equation (8.16)-(8.17), ℎ 𝑝 is the convective heat transfer in the greenhouse which is the function

of air velocity within the greenhouse, 𝑃𝑠𝑎𝑡 is the saturation pressure at a given temperature, 𝛾𝑅 is

the relative humidity for the greenhouse air, 𝐹𝑃𝑅 is the shape factor between plant and greenhouse

which its suggested value is 1.0, 𝜀 is the emissivity of the plant and assumed to be 0.7, and 𝜎 is

the Stefan–Boltzmann constant with the value of 5.67 × 10−8 𝑊𝑚−2𝐾 −4. Mamouri et al. (2020)

studied the concept of a greenhouse with a transparent solar heater as a roof, and developed a model

to predict the behavior of the system,

𝑆𝑡 − (cid:164)𝑄𝑙𝑜𝑠𝑠 − (cid:164)𝑄𝑡 = (cid:164)𝑚𝐶𝑝,𝑊 (𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛)

(8.18)

In Equation (8.18), (cid:164)𝑄𝑙𝑜𝑠𝑠 is the solar water heat loss to the ambient, (cid:164)𝑄𝑡 is the transmitted heat to the

greenhouse, (cid:164)𝑚 is the mass flow of water, 𝐶𝑝,𝑊 is the specific heat transfer coefficient of water, 𝑇𝑖𝑛

and 𝑇𝑜𝑢𝑡 are the inlet and outlet temperature for the water within the transparent solar water heater.

Alnaimat et al. (2011) proposed and validated one-dimensional transient models to predict the

behavior of a condenser and an evaporator within a direct-contact packed-bed desalination system.

These models considered energy balance to predict the evolution of liquid temperature (𝑇𝐿), air
temperature (𝑇𝑎), and packed-bed temperature (cid:0)𝑇𝑝𝑎𝑐𝑘 (cid:1),

𝜕𝑇𝐿
𝜕𝑡

=

𝐿
𝜌𝐿𝛼𝐿

𝜕𝑇𝐿
𝜕𝑧

−

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 − ℎ𝐿(cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝,𝐿

−

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝐿 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌𝐿𝛼𝐿𝐶𝑝,𝐿

−

=

𝜕𝑇𝑎
−𝐺
𝜕𝑇𝑎
𝜕𝑧
𝜌𝑎𝛼𝑎
𝜕𝑡
𝑈𝑎𝑤 (𝑇𝐿 − 𝑇𝑎)
𝜌𝑎𝛼𝑎 (1 + 𝜔) 𝐶𝑝𝐺

𝜕𝜔
𝜕𝑧

𝐺 (cid:0)ℎ 𝑓 𝑔 (𝑇𝐿) − ℎ𝑣 (𝑇𝑎)(cid:1)
𝜌𝑎𝛼𝑎 (1 + 𝜔)𝐶𝑝,𝐺

+

176

−

𝑈𝑎𝑤 (𝑇𝐿 − 𝑇𝑎)
𝜌𝐿𝛼𝐿𝐶𝑝,𝐿
𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝑎(cid:1)
𝜌𝑎𝛼𝑎 (1 + 𝜔) 𝐶𝑝,𝐺

+

(8.19)

(8.20)

𝜕𝑇𝑝𝑎𝑐𝑘
𝜕𝑡

𝑈𝐿𝑎𝑤 (cid:0)𝑇𝐿 − 𝑇𝑝𝑎𝑐𝑘 (cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝,𝑝𝑎𝑐𝑘

𝑈𝐺 (cid:0)𝑎 𝑝 − 𝑎𝑤(cid:1) (cid:0)𝑇𝑝𝑎𝑐𝑘 − 𝑇𝑎(cid:1)
𝜌 𝑝𝑎𝑐𝑘 𝛼𝑝𝑎𝑐𝑘𝐶𝑝,𝑝𝑎𝑐𝑘

−

=

(8.21)

In Equation (8.20), ℎ 𝑓 𝑔 (𝑇𝐿) and ℎ𝑣 (𝑇𝑎) refer to the latent heat of vaporization at the temperature

of the liquid, and vapor enthalpy at the temperature of the air, respectively. Through considering

liquid mass balance, evolution of humidity ratio (𝜔) is obtained for a condenser (Equation (8.22)),

and an evaporator (Equation (8.23)),

𝜕𝜔
𝜕𝑧

=

𝜕𝑇𝑎
𝜕𝑧

𝑃
𝑃 − 𝑃𝑠𝑎𝑡 (𝑇𝑎)

(cid:16)

𝜔

𝑏 − 2𝑐𝑇𝑎 + 3𝑑𝑇 2
𝑎

(cid:17)

𝜕𝜔
𝜕𝑧

=

𝑘𝐺 𝑎𝑤
𝐺

𝑀𝑣
𝑅

(cid:18) 𝑃𝑠𝑎𝑡 (𝑇𝑖)
𝑇𝑖

−

(cid:19)

𝜔
𝜔 + 0.622

𝑃
𝑇𝑎

(8.22)

(8.23)

In Equations (8.19)-(8.23), the value for most of the parameters can be obtained from the ther-

modynamic table, while empirical correlations are used to obtain the rest. Abedi et al. (2021)

carried out an extensive investigation on various empirical correlations for the mass transfer

coefficient of liquid or air, and the interfacial area, and suggested that Onda’s empirical corre-

lations for interfacial area

𝑎𝑤 = 𝑎 𝑝

1 − exp

(cid:18)

(cid:18)

(cid:20)

−1.45

(cid:17) 0.75

(cid:16) 𝜎𝑐
𝜎𝐿

𝑅𝑒0.1

𝐿 𝐹𝑟 −0.05

𝐿 𝑊 𝑒0.2
𝐿

(cid:21) (cid:19)(cid:19)

, liquid mass

(cid:18)

transfer coefficient
(cid:18)

𝑘𝐺 = 𝑐𝐺

(cid:16) 𝐷𝐺
𝑎 𝑝 𝑑2
𝑝

(cid:17) (cid:16) 𝜌𝐺𝑢𝐺
𝑎 𝑝 𝜇𝐺

𝑘 𝐿 = 0.0051
(𝑎 𝑝 𝑑 𝑝) −0.4
(cid:19)
𝑆𝑐1/3
𝐺

(cid:17) 0.7

(cid:16) 𝜇𝐿𝑔
𝜌𝐿

(cid:17) 1/3 (cid:16) 𝜌𝐿𝑢𝐿
𝑎𝑤 𝜇𝐿

(cid:17) 2/3

𝑆𝑐−0.5
𝐿

(cid:19)

, and gas mass transfer coefficient

allow predicting the behavior of a direct-contact packed-bed

desalination system in good accordance with the experimental data.

The final model utilized within this study is a dynamic plant growth model for lettuce proposed

by Van Henten (1994) accounting for the transient behavior of the plant at different stages. In the

model, lettuce dry mass is estimated for two sub-variables of non-structural (𝑋𝑛𝑠𝑑𝑤) and structural

(𝑋𝑠𝑑𝑤) dry mass through the following expressions,

𝑑𝑋𝑛𝑠𝑑𝑚
𝑑𝑡

= 𝑐𝛼 𝑓𝑝ℎ𝑜𝑡 − 𝑟𝑔𝑟 𝑋𝑠𝑑𝑚 − 𝑓𝑟𝑒𝑠𝑝 −

1 − 𝑐 𝛽
𝑐 𝛽

𝑟𝑔𝑟 𝑋𝑠𝑑𝑚

𝑑𝑋𝑠𝑑𝑚
𝑑𝑡

= 𝑟𝑔𝑟 𝑋𝑠𝑑𝑚

(8.24)

(8.25)

In Equations (8.24)-(8.25),

𝑓𝑝ℎ𝑜𝑡 is the gross canopy photosynthesis,

𝑓𝑟𝑒𝑠𝑝 is the maintenance

respiration, and 𝑟𝑔𝑟 is the growth rate of structural material, while 𝑐𝛼 and 𝑐 𝛽 describe the conversion

rate of carbon dioxide to sugar and the yield factor which is a measure of non-structural dry mass

177

losses due to respiration and photosynthesis, respectively. Using the values of the two sub-variables
for lettuce dry mass, the lettuce leaf area is calculated using 𝐴𝐿𝑒𝑎 𝑓 = (1−𝑐 𝜏)𝑐𝑙𝑎𝑟 𝑋𝑠𝑑𝑤

, whereas 𝑐𝜏

𝑁 𝑝𝑙𝑎𝑛𝑡

is the ratio of root dry mass to plant dry mass, 𝑐𝑙𝑎𝑟 is structural leaf area ratio, and 𝑁 𝑝𝑙𝑎𝑛𝑡 is the

density of plant per square meter.

8.4 Results and Discussion

Using the coupled mathematical models for different components of the integrated greenhouse,

and the environmental data, these models are discretized and solved numerically to obtain the states

of the system at a given time. First, a description of the boundary conditions for these models is

provided. Next, the impact of using a transparent solar water heater on the energy efficiency of

the greenhouse is examined. Following that, the estimated yield of the greenhouse for the lettuce

cultivar is obtained. Finally, the desalination potential of the system is studied to see whether the

integrated greenhouse can sustain the potable water needs for lettuce cultivation.

8.4.1 Boundary Conditions

As mentioned earlier, the theoretical performance investigation of the integrated greenhouse is

carried out for Phoenix, Arizona. The environmental data for the studied location are provided by

National Renewable Energy Laboratory (NREL) (Sengupta et al., 2018) which includes ambient

temperature, relative humidity, and pressure, solar irradiation which breaks down into direct normal

irradiance (DNI), global horizontal irradiance (GHI), and diffuse horizontal irradiance (DHI).

Figures 8.4 and 8.5 describe the hourly average variation in the environmental data across a year,

including various components of solar irradiation, temperature, and relative humidity.

The environmental data are utilized in the thermal modeling of the greenhouse through Equa-

tions (8.13)-(8.15). Furthermore, data for ambient temperature and relative humidity are used for

the inlet boundary conditions of air coming into the evaporator and the desalination unit. The inlet

temperature of the water going into the transparent solar water heater and the condenser are also

set to the ambient temperature. Mass flows for air passing through the desalination unit and water

coming into the evaporator, and the condenser is set to 0.1 kg, while the cross-sectional area and the

packed-bed height for the evaporator and the condenser are fixed to 0.2 𝑚2, and 1 𝑚, respectively.

178

Figure 8.4 Annual average solar irradiation data for direct normal (DNI), global horizontal (GHI),
and diffuse horizontal irradiance (DHI) for Phoenix, Arizona Sengupta et al. (2018).

Figure 8.5 Annual average data for ambient temperature and relative humidity for Phoenix, Arizona
(Sengupta et al., 2018).

8.4.2 Energy Efficiency of Integrated Greenhouse

As mentioned earlier, a conventional greenhouse requires a considerable amount of energy to

maintain temperature and humidity across a year. The term 𝐸𝜈 in Equation (8.15) approximates

the required energy for heating/cooling load and ventilation. As a first step towards calculating the

ventilation load of the greenhouse, Equations (8.13)-(8.15) are solved for this variable in addition
to temperatures of the greenhouse floor (cid:0)𝑇 𝑓 (cid:1), and plant (cid:0)𝑇𝑝(cid:1). Several other assumptions are taken

into consideration, including temperatures of the greenhouse room and the ground beneath the

greenhouse set to 24 ◦𝐶, and 17 ◦𝐶, respectively. Moreover, it was also suggested that greenhouse

ground and plant absorptance coefficients be set to 0.3 and 0.4 (Sethi, 2009). Furthermore,

the greenhouse relative humidity is set to 85 percent during the day and 70 percent during the

night for the cultivation of the lettuce. Using these assumptions, the greenhouse thermal model

is mathematically solved to obtain the ventilation load and the plant temperature, which will

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be utilized for the lettuce plant growth model. Figure 8.6 compares the ventilation load for a

traditional greenhouse without a transparent solar water heater with the proposed configuration for

the integrated greenhouse.

Figure 8.6 Comparison in the heating/cooling load for a traditional greenhouse without a transparent
solar water heater with the proposed integrated greenhouse.

As illustrated in Figure 8.6, installing a transparent solar water heater as the roof of the integrated

greenhouse decreases the amount of heating/cooling for the greenhouse by an average of 30 percent.

Therefore, the proposed integrated greenhouse is more energy efficient compared to a traditional

one.

8.4.3 Potential of Desalination System

Next, the desalination potential of the integrated greenhouse with the HDH system is examined.

Second order finite difference scheme is utilized to discretize Equations (8.19) - (8.22). Solver

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experimental validity and independency from grid resolution for both the evaporator and the

condenser were previously investigated by Abedi et al. (2023a). Since the mass flow rate of the

water for the solar water heater was set to 0.1 kg, considering a cross-sectional area of 0.2 m2, the

inlet mass flux of water and air for both evaporator and the condenser was set to 0.5 kg m−2 s−1.

The air inlet temperature and relative humidity for the evaporator were assumed to be the same

as the ambient conditions at the studied location (Figure 8.5), while the water inlet temperature

for the evaporator was obtained based on the thermal performance of the transparent solar water

heater. Given that the air coming into the condenser comes from the evaporator, the inlet boundary

conditions of the air coming into the condenser are assumed to be equal to the outlet boundary

conditions of the air leaving the evaporator. Moreover, the water inlet temperature is also set to the

ambient temperature for the condenser.

The amount of freshwater produced by the HDH desalination system is determined by obtaining

humidity ratio distribution in the condenser. Figure 8.7 represents the daily produced freshwater

by the proposed greenhouse integrated with an HDH system.

Figure 8.7 Changes in the daily freshwater production for the HDH system integrated with the
greenhouse during a year. The color of each bar illustrates the temperature of the water leaving the
transparent solar water heater.

It can be inferred from Figure 8.7 that the system is capable of producing freshwater for an

average of 40 kg each day. Lages Barbosa et al. (2015b) suggested that hydroponic lettuce required

about 3 kg of water to produce 1 kg of lettuce each month, considering the average fresh lettuce

yield to be about 250 kg each month (Figure 8.10), each cultivation required about 750 kg of water

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which compared to daily freshwater production, the proposed integrated greenhouse can satisfy the

water need for lettuce production.

8.4.4 Lettuce Cultivation Yield

The main purpose of a greenhouse is to provide a controlled environment in the absence of

extreme conditions for enhanced cultivation of plants. To investigate yield in the proposed integrated

greenhouse, lettuce is chosen as the cultivated plant. While the Van-Henten plant growth model

(Van Henten, 1994) estimates the dynamic behavior of lettuce at different stages of its life cycle,

the model predicts the overall dry mass of the lettuce1. To estimate the fresh mass of the lettuce,

experimental data for indoor-cultivated lettuce from two studies (Meng and Runkle, 2019; Meng

et al., 2020) were utilized to obtain the ratio of fresh mass to dry mass. According to these studies,

the fresh mass to the dry mass ratio in the seedling stage is around 13, while in the maturity stage,

its ratio increases up to 23. Figure 8.8 represents the variation in the ratio of fresh mass to dry mass

for indoor-cultivated lettuce.

In this study, an average value of 18 for the fresh mass to dry mass ratio is used to obtain

the fresh mass of lettuce harvested each month using the predicted dry mass through the dynamic

growth model. Using plant temperature obtained by solving Equation (8.13), overall irradiance for

the greenhouse cover and CO2 concentration in the range of 350∼380 mL L−1, lettuce dry mass

is obtained for 12 cultivations, assuming each cultivation begins at the first of each month, and

harvest happens at the end of that month. Figure 8.9 illustrates the evolution of lettuce dry mass

for each cultivation across the year.

Based on the harvested dry mass at the end of each month, and assuming 50 ∼ 60 for plant

density per unit of surface area, lettuce fresh yield is estimated. As shown in Figure 8.10, the

greenhouse is capable of producing up to 300 kg of fresh lettuce in a year.

While the lettuce yield may seem a bit low, it is worth mentioning that these values are obtained

for one row of lettuce cultivation. For hydroponic cultivation, there are usually several rows of the

cultivar, which increases the overall yield. Therefore, the approximate fresh yield for the integrated

1The validation of the plant growth model is carried out in a separate study by Abedi et al. (2023b).

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Figure 8.8 Variation of the probability density of the fresh mass to dry mass ratio for indoor-
cultivated lettuce harvested on various days. The ratio is used to calculate the fresh mass for each
cultivation.

greenhouse and lettuce cultivar could reach up to 900 to 1200 kg.

8.5 Summary

The focus of this chapter is to mathematically model an integrated greenhouse with a transpar-

ent solar water heater as a roof and a direct-contact packed-bed humidification-dehumidification

desalination system. To predict the potential of such a greenhouse with respect to desalination

potential, thermal efficiency, and productivity yield, a thermal model for the greenhouse, an optical

and thermal model of the solar water heater, a mathematical model for a transient HDH desali-

nation, and a dynamic plant growth model for lettuce are coupled and solved for environmental

conditions of Phoenix, Arizona. The result suggested that implementing a transparent solar water

heater as the roof of the proposed integrated greenhouse would decrease thermal load to main-

tain controlled-environment conditions inside a greenhouse by around 30 percent. Furthermore,

simulations indicated that the desalination component is capable of treating an average of 30 kg

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Figure 8.9 Evolution of lettuce dry mass for different cultivations in different months predicted by
lettuce dynamic growth model.

of contaminated or brine water. In addition, the result of the plant growth model suggested that

for a single row of lettuce with a density of 60 plants per unit of surface area, the fresh yield is

around 250∼ 300 kg. It is also suggested that considering a 3 kg potable water requirement for 1

kg of lettuce, the desalination unit is capable of providing the required water for each cultivation.

Consideration of a complex thermal model for the transparent solar water heater and the analysis of

the performance of an energy-efficient greenhouse at numerous locations worldwide may provide

a deeper understanding of the proposed integrated greenhouse’s potential.

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Figure 8.10 Lettuce yield for different cultivations, and plant density of 60 plant m−2, for the
investigated greenhouse represented in Figure 8.2. The color of each bar illustrates the average
ambient temperature during the cultivation.

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CHAPTER 9

CONCLUSION

9.1 Summary

In this dissertation, experimental and computational studies are performed on different systems

to evaluate the feasibility of integrating HDH desalination technology into buildings. In the first

step, a mathematical model of the HDH water treatment system has been meticulously validated

with experimental data. Then, a data-driven surrogate model of the same system is developed, and

its prediction accuracy is compared with that of the mathematical model. Within the scope of this

study, three structures have been examined thoroughly in thermal and desalination performance.

Solar chimneys, which are conventionally deployed as green power plants, are first examined.

Due to the original functionality of these systems as power units, the integrated desalination

configuration has the potential of autonomous desalination capability. Moreover, the additional

function of the system as a greenhouse, the empty space in the chimney which is ideal for hosting

a water treatment system, and the system’s scalability are additional merits of integrated solar

desalination chimneys.

Solar air heaters, which are commonly implemented as ventilation systems, are assessed next.

Contrary to solar chimneys, these systems can operate under natural or forced convection, with

efficient thermal performance in forced mode. Furthermore, they can be easily deployed as part of

residential or industrial buildings, which mitigates the overall capital cost of the system.

The third investigated structure is a greenhouse, in which the integrated system is particularly

more economically appealing due to the functionality of producing its potable water from contam-

inated, saline, or used resources. In addition, the proposed design of the integrated greenhouse is

an energy-efficient building, which implies less dependency on external energy resources.

9.2 Remark

The mathematical modeling of the water treatment unit suggests that the models’ prediction is

within 5 to 10 percent error when the boundary conditions are in the validity range of the empirical

correlations; outside of the aforementioned range, the uncertainty reaches 40 to 60 percent for

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the prediction of air or water temperature. While the developed surrogate model is much more

accurate, the sensitivity analysis results and the chaotic uncertainty in prediction imply that more

comprehensive data is required to present a high-fidelity surrogate model.

Based on the solar desalination chimneys, it is suggested that a large-scale similar to the

geometry of Manzanares solar chimney (Haaf et al., 1983) capable of autonomous desalination of

contaminated or saline water, can satisfy the freshwater needs of 800 to 1000 households which

makes it ideal for geographically distributed water treatment system. On the other hand, a small-

scale configuration based on the geometry of Florida’s solar chimney (Pasumarthi and Sherif,

1998) is suitable for satisfying one household water need, and it can be placed next to a house. On

the other hand, the system, which is based on an integrated solar air heater desalination system,

had higher thermal efficiency compared to the solar chimney, and it resulted in a more efficient

desalination process. Furthermore, the addition of the water flow, which results in a dual solar

air-water heater, creates a system with higher thermal efficiency and a more considerable reduction

in CO2 emission.

The modeling of a greenhouse coupled with a desalination system and a NIR cut-off film attached

to a transparent solar water heater suggested that deploying a transparent solar water heater resulted

in a 30% reduction in the ventilation load to maintain the greenhouse’s indoor temperature at a

favorable condition. Moreover, for the case study based in Phoenix, AZ, the desalination system

can treat and produce an average of 30 kg of potable water daily, which according to Barbosa et al.

(2019), could satisfy the water requirement of 250 kg of fresh lettuce in a monthly cultivation

period.

9.3 Future Works

In future work, a 3D computational model of solar desalination chimneys can provide further

information on prominent cofactors that has a considerable impact on their importance. These fac-

tors include the geometry of the solar chimney, ambient conditions (temperature, wind velocity, and

relative humidity), packed-bed properties, flow characteristics, and turbine geometry. Moreover,

while computational modeling is helpful in optimizing the behavior of a system, performing an

187

experimental study is a necessary step for reliable prediction. Building experimental pilots of the

proposed integrated desalination systems are critical to validating the computational models and

ensuring the feasibility of the proposed systems. The pilots can also provide insights into potential

design improvements and operational challenges, whereas the computational model can not. In

addition, the experiments can help to identify any discrepancies or limitations of the models that

need to be addressed. Therefore, future work should focus on constructing experimental pilots of

the proposed integrated desalination systems to validate and optimize the computational models.

As another suggestion for future work, the machine learning techniques that were partially

implemented within the scope of this study could be further implemented to replace the spectrum-

incorporated dynamic growth model of lettuce with a surrogate model. This data-driven model is

more comprehensive than the proposed model because it creates its own intermediate parameters.

This approach can be utilized to model the growth of different types of plants and their response to

different environmental conditions. It is suggested that the surrogate model be trained with a diverse

dataset, considering different growing conditions and plant species, to improve its accuracy and

applicability. These models can be coupled with the greenhouse model to assess the performance

of the greenhouse for plant cultivation other than lettuce.

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BIBLIOGRAPHY

Abdel-Ghany, A. M., Al-Helal, I. M., Alsadon, A. A., Ibrahim, A. A., and Shady, M. R. (2016).
Closed solar house with radiation filtering roof for transplant production in arid regions: Energy
consumption. Energies, 9(3):136.

Abdel-Ghany, A. M., Al-Helal, I. M., Alzahrani, S. M., Alsadon, A. A., Ali, I. M., Elleithy,
R. M., et al. (2012). Covering materials incorporating radiation-preventing techniques to meet
greenhouse cooling challenges in arid regions: a review. The Scientific World Journal, 2012.

Abdel-Ghany, A. M., Kozai, T., Abdel-Shafi, N. Y., Taha, I. S., and Huzayyin, A. S. (2001a).
Dynamic simulation modeling of heat and water vapor transfer in a fluid-roof greenhouse.
Journal of Agricultural Meteorology, 57(4):169–182.

Abdel-Ghany, A. M., Kozai, T., Kubota, C., and Taha, I. S. (2001b). Investigation of the spectral
optical properties of the liquid radiation filters for using in the greenhouse applications. Journal
of Agricultural Meteorology, 57(1):11–19.

Abdel-Salam, M., Hilal, M., El-Dib, A., and Abdel Monem, M. (1993). Experimental study of

humidification-dehumidification desalination system. Energy sources, 15(3):475–490.

Abdullah, A., El-Samadony, Y., and Omara, Z. (2017). Performance evaluation of plastic solar air
heater with different cross sectional configuration. Applied Thermal Engineering, 121:218–223.

Abedi, M., Saha, P., Tan, X., Klausner, J. F., and Benard, A. (2021). Evaluation of mass transfer
and interfacial area correlations in direct contact packed-bed: Comparison of correlations. In
2nd International Conference on Fluid Flow and Thermal Science (ICFFTS’21).

Abedi, M., Tan, X., Klausner, J. F., and Bénard, A. (2023a). Solar desalination chimneys: Inves-
tigation on the feasibility of integrating solar chimneys with humidification–dehumidification
systems. Renewable Energy, 202:88–102.

Abedi, M., Tan, X., Stallknecht, E. J., Runkle, E. S., Klausner, J. F., Murillo, M. S., and Bénard,
A. (2023b). Incorporating the effect of the photon spectrum on biomass accumulation of lettuce
using a dynamic growth model. Frontiers in Plant Science, 14:1106576.

Abo-Elfadl, S., Yousef, M. S., El-Dosoky, M., and Hassan, H. (2021). Energy, exergy, and economic
analysis of tubular solar air heater with porous material: an experimental study. Applied Thermal
Engineering, 196:117294.

Abuşka, M., Şevik, S., and Kayapunar, A. (2019). A comparative investigation of the effect
of honeycomb core on the latent heat storage with pcm in solar air heater. Applied Thermal
Engineering, 148:684–693.

Ackermann, A. S. E. (1915). The utilisation of solar energy. Journal of the Royal Society of Arts,

189

63(3258):538–565.

Acock, B., Charles-Edwards, D., Fitter, D., Hand, D., Ludwig, L., Warren Wilson, J., and Withers,
A. (1978). The contribution of leaves from different levels within a tomato crop to canopy net
photosynthesis: an experimental examination of two canopy models. Journal of Experimental
Botany, 29(4):815–827.

Agrawal, Y., Bhagoria, J., Gautam, A., Chaurasiya, P. K., Dhanraj, J. A., Solomon, J. M., and
Salyan, S. (2022). Experimental evaluation of hydrothermal performance of solar air heater with
discrete roughened plate. Applied Thermal Engineering, 211:118379.

Akhbari, M., Rahimi, A., and Hatamipour, M. S. (2020). Modeling and experimental study of a

triangular channel solar air heater. Applied Thermal Engineering, 170:114902.

Al-Hallaj, S., Farid, M. M., and Tamimi, A. R. (1998). Solar desalination with a humidification-

dehumidification cycle: performance of the unit. Desalination, 120(3):273–280.

Al-Sulaiman, F. A., Zubair, M. I., Atif, M., Gandhidasan, P., Al-Dini, S. A., and Antar, M. A.
(2015). Humidification dehumidification desalination system using parabolic trough solar air
collector. Applied Thermal Engineering, 75:809–816.

Alam, T. and Kim, M.-H. (2017). Heat transfer enhancement in solar air heater duct with conical

protrusion roughness ribs. Applied Thermal Engineering, 126:458–469.

Alinejad, T., Yaghoubi, M., and Vadiee, A. (2020). Thermo-environomic assessment of an in-
tegrated greenhouse with an adjustable solar photovoltaic blind system. Renewable energy,
156:1–13.

Allardyce, C. S., Fankhauser, C., Zakeeruddin, S. M., Grätzel, M., and Dyson, P. J. (2017). The
influence of greenhouse-integrated photovoltaics on crop production. Solar Energy, 155:517–
522.

Alnaimat, F. and Klausner, J. F. (2012). Solar diffusion driven desalination for decentralized water

production. Desalination, 289:35–44.

Alnaimat, F. and Klausner, J. F. (2013). Enhanced performance of solar diffusion driven desalina-

tion. Journal of Thermal Science and Engineering Applications, 5(4):041001.

Alnaimat, F., Klausner, J. F., and Mei, R. (2011). Transient analysis of direct contact evaporation
and condensation within packed beds. International journal of heat and mass transfer, 54(15-
16):3381–3393.

Alnaimat, F., Klausner, J. F., and Mei, R. (2013). Transient dynamic response of solar diffusion

driven desalination. Applied thermal engineering, 51(1-2):520–528.

190

Alnaimat, F., Ziauddin, M., and Mathew, B. (2021). A review of recent advances in humidification
and dehumidification desalination technologies using solar energy. Desalination, 499:114860.

Amer, E., Kotb, H., Mostafa, G., and El-Ghalban, A. (2009). Theoretical and experimental
investigation of humidification–dehumidification desalination unit. Desalination, 249(3):949–
959.

Ansari, M. and Bazargan, M. (2018). Optimization of flat plate solar air heaters with ribbed

surfaces. Applied Thermal Engineering, 136:356–363.

Arabi, M. K. A. and Reddy, K. V. (2003). Performance evaluation of desalination processes
based on the humidification/dehumidification cycle with different carrier gases. Desalination,
156(1-3):281–293.

Asayesh, M., Kasaeian, A., and Ataei, A. (2017). Optimization of a combined solar chimney for

desalination and power generation. Energy Conversion and Management, 150:72–80.

Assari, M., Tabrizi, H. B., and Jafari, I. (2011). Experimental and theoretical investigation of dual

purpose solar collector. Solar Energy, 85(3):601–608.

Baguley, T. (2018). Serious Stat: A guide to advanced statistics for the behavioral sciences.

Bloomsbury Publishing.

Bahadori, A. and Vuthaluru, H. B. (2010). A simple method for the estimation of thermal insulation

thickness. Applied Energy, 87(2):613–619.

Baille, A., Kittas, C., and Katsoulas, N. (2001). Influence of whitening on greenhouse microclimate

and crop energy partitioning. Agricultural and Forest Meteorology, 107(4):293–306.

Barbosa, E. G., de Araujo, M. E. V., de Moraes, M. J., Martins, M. A., Alves, B. G. X., and Barbosa,
E. G. (2019). Influence of the absorber tubes configuration on the performance of low cost solar
water heating systems. Journal of Cleaner Production, 222:22–28.

Bejan, A. (2013). Convection heat transfer. John wiley & sons.

Ben-Amara, M., Houcine, I., Guizani, A.-A., and Maalej, M. (2005). Efficiency investigation of
a new-design air solar plate collector used in a humidification–dehumidification desalination
process. Renewable Energy, 30(9):1309–1327.

Billet, R. and Schultes, M. (1993). Predicting mass transfer in packed columns. Chemical Engineer-
ing & Technology: Industrial Chemistry-Plant Equipment-Process Engineering-Biotechnology,
16(1):1–9.

Blondes, M. S., Gans, K. D., Thordsen, J., Reidy, M., Thomas, B., Engle, M. A., Kharaka, Y. K.,
and Rowan, E. L. (2016). Us geological survey national produced waters geochemical database

191

v2. 3 (provisional). United States Geological Survey.

Bodell, B. R. (Aug. 9, 1966). Distillation of saline water using silicone rubber membrane.

Both, A., Albright, L., Langhans, R., Reiser, R., and Vinzant, B. (1994). Hydroponic lettuce pro-
duction influenced by integrated supplemental light levels in a controlled environment agriculture
facility: Experimental results. In Acta Horticulturae, pages 45–52.

Bourouni, K., Chaibi, M., and Tadrist, L. (2001). Water desalination by humidification and

dehumidification of air: state of the art. Desalination, 137(1-3):167–176.

Bravo, J. L. and Fair, J. R. (1982). Generalized correlation for mass transfer in packed distillation
columns. Industrial & Engineering Chemistry Process Design and Development, 21(1):162–170.

Brownson, J. R. (2013). Solar energy conversion systems. Academic Press.

Cabanyes, I. (1903). Las chimeneas solares (solar chimneys). La ernergia eléctrica.

Calvert, J. G. (1990). Glossary of atmospheric chemistry terms (recommendations 1990). Pure

and applied chemistry, 62(11):2167–2219.

Cengel, Y. A. and Ghajar, A. J. (2020). Heat and mass transfer: Fundamentals and applications.

McGraw-Hill Inc, New York, NY, 6th edition edition.

Chaibi, M. and Jilar, T. (2004). System design, operation and performance of roof-integrated

desalination in greenhouses. Solar energy, 76(5):545–561.

Chang, H., Lyu, S.-G., Tsai, C.-M., Chen, Y.-H., Cheng, T.-W., and Chou, Y.-H. (2012). Experi-
mental and simulation study of a solar thermal driven membrane distillation desalination process.
Desalination, 286:400–411.

Chaube, A., Sahoo, P., and Solanki, S. (2006). Analysis of heat transfer augmentation and flow
characteristics due to rib roughness over absorber plate of a solar air heater. Renewable Energy,
31(3):317–331.

Chian, E. S., Chen, J. P., Sheng, P.-X., Ting, Y.-P., and Wang, L. K. (2007). Reverse osmosis
technology for desalination. In Advanced physicochemical treatment technologies, pages 329–
366. Springer.

Chitsomboon, T. (2000). Potential and efficiency of solar chimney in the production of electrical
energy. Research and Development Journal of the Engineering Institute of Thailand, 11(3):38–
44.

Chitsomboon, T. (2001). A validated analytical model for flow in solar chimney. International

Journal of Renewable Energy Engineering, 3(2):339–346.

192

Cloete, R. (2008). Solar tower sheds light on little-used technology. Engineering News Online

http://wwwengineeringnews co za/article php.

Coleman, H. W. and Steele, W. G. (2018). Experimentation, validation, and uncertainty analysis

for engineers. John Wiley & Sons.

Cossu, M., Yano, A., Solinas, S., Deligios, P. A., Tiloca, M. T., Cossu, A., and Ledda, L. (2020).
Agricultural sustainability estimation of the european photovoltaic greenhouses. European
Journal of Agronomy, 118:126074.

Crawley, D. B., Lawrie, L. K., Winkelmann, F. C., Buhl, W. F., Huang, Y. J., Pedersen, C. O.,
Strand, R. K., Liesen, R. J., Fisher, D. E., Witte, M. J., et al. (2001). Energyplus: creating a
new-generation building energy simulation program. Energy and buildings, 33(4):319–331.

Dai, Y., Huang, H., and Wang, R. (2003). Case study of solar chimney power plants in northwestern

regions of china. Renewable Energy, 28(8):1295–1304.

Deubener, J., Helsch, G., Moiseev, A., and Bornhöft, H. (2009). Glasses for solar energy conversion

systems. Journal of the European Ceramic Society, 29(7):1203–1210.

Dieleman, J. A., De Visser, P. H., Meinen, E., Grit, J. G., and Dueck, T. A. (2019). Integrating
morphological and physiological responses of tomato plants to light quality to the crop level by
3d modeling. Frontiers in Plant Science, 10:839.

Dorais, M. (2003). The use of supplemental lighting for vegetable crop production: light inten-
sity, crop response, nutrition, crop management, cultural practices. In Canadian Greenhouse
Conference, volume 9, pages 1–8.

dos Santos Bernardes, M. A., Valle, R. M., and Cortez, M. F.-B. (1999). Numerical analysis of
natural laminar convection in a radial solar heater. International journal of thermal sciences,
38(1):42–50.

Duffie, J. A. and Beckman, W. A. (2013). Solar engineering of thermal processes. John Wiley &

Sons.

El-Agouz, S. and Abugderah, M. (2008). Experimental analysis of humidification process by air

passing through seawater. Energy Conversion and Management, 49(12):3698–3703.

El-Dessouky, H. T. (1989). Humidification-dehumidification desalination process using waste heat

from a gas turbine. Desalination, 71(1):19–33.

El-Sebaii, A., Ramadan, M., Aboul-Enein, S., and Khallaf, A. (2011). History of the solar ponds:

a review study. Renewable and Sustainable Energy Reviews, 15(6):3319–3325.

Eldos, H. I., Khan, M., Zouari, N., Saeed, S., and Al-Ghouti, M. A. (2022). Characterization and

193

assessment of process water from oil and gas production: A case study of process wastewater in
qatar. Case Studies in Chemical and Environmental Engineering, 6:100210.

Faegh, M., Behnam, P., and Shafii, M. B. (2019). A review on recent advances in humidification-
dehumidification (hdh) desalination systems integrated with refrigeration, power and desalination
technologies. Energy Conversion and Management, 196:1002–1036.

Faust, J. E. and Logan, J. (2018). Daily light integral: A research review and high-resolution maps

of the united states. HortScience, 53(9):1250–1257.

Fisher, P. and Runkle, E. (2004). Lighting up profits. Understanding greenhouse lighting Meister

Media Willoughby, OH.

Gannon, A. J. and von Backstro¨ m, T. W. (2000). Solar chimney cycle analysis with system loss

and solar collector performance. J. Sol. Energy Eng., 122(3):133–137.

Gholamalizadeh, E. and Kim, M.-H. (2016). Cfd (computational fluid dynamics) analysis of a

solar-chimney power plant with inclined collector roof. Energy, 107:661–667.

Gholamalizadeh, E. and Mansouri, S. (2013). A comprehensive approach to design and improve a
solar chimney power plant: A special case–kerman project. Applied Energy, 102:975–982.

Ghosal, M. K., Tiwari, G., and Srivastava, N. (2003). Modeling and experimental validation of a
greenhouse with evaporative cooling by moving water film over external shade cloth. Energy
and Buildings, 35(8):843–850.

Gill, R. S., Hans, V. S., and Singh, R. P. (2021). Optimization of artificial roughness parameters in
a solar air heater duct roughened with hybrid ribs. Applied Thermal Engineering, 191:116871.

Goh, P., Lau, W., Othman, M., and Ismail, A. (2018). Membrane fouling in desalination and its

mitigation strategies. Desalination, 425:130–155.

Goosen, M., Sablani, S., Paton, C., Perret, J., Al-Nuaimi, A., Haffar, I., Al-Hinai, H., and Shayya,
W. (2003). Solar energy desalination for arid coastal regions: development of a humidification–
dehumidification seawater greenhouse. Solar energy, 75(5):413–419.

Goudriaan, J. and Monteith, J. (1990). A mathematical function for crop growth based on light

interception and leaf area expansion. Annals of Botany, 66(6):695–701.

Goudriaan, J., Van Laar, H., Keulen, H. v., and Louwerse, W. (1985). Photosynthesis, co2 and plant

production. In Wheat growth and modelling, pages 107–122. Springer.

Haaf, W., Friedrich, K., Mayr, G., and Schlaich, J. (1983). Solar chimneys part i: principle and
construction of the pilot plant in manzanares. International Journal of Solar Energy, 2(1):3–20.

194

Habte, A., Sengupta, M., and Lopez, A. (2017). Evaluation of the national solar radiation database
(nsrdb): 1998-2015. Technical report, National Renewable Energy Lab.(NREL), Golden, CO
(United States).

Hale, G. M. and Querry, M. R. (1973). Optical constants of water in the 200-nm to 200-𝜇m

wavelength region. Applied optics, 12(3):555–563.

Hashem, F. A., Medany, M. A., Abd El-Moniem, E. M., and Abdallah, M. M. F. (2011). Influence
of green-house cover on potential evapotranspiration and cucumber water requirements. Annals
of Agricultural Sciences, 56(1):49–55.

Hassanien, R. H. E. and Ming, L. (2017). Influences of greenhouse-integrated semi-transparent
photovoltaics on microclimate and lettuce growth. International Journal of Agricultural and
Biological Engineering, 10(6):11–22.

He, R., Zhang, Y., Song, S., Su, W., Hao, Y., and Liu, H. (2021). Uv-a and fr irradiation improves
growth and nutritional properties of lettuce grown in an artificial light plant factory. Food
Chemistry, 345:128727.

Hebert, D., Boonekamp, J., Parrish, C. H., Ramasamy, K., Makarov, N. S., Castañeda, C., Schud-
debeurs, L., McDaniel, H., and Bergren, M. R. (2022). Luminescent quantum dot films improve
light use efficiency and crop quality in greenhouse horticulture. Frontiers in Chemistry, page
1345.

Hogewoning, S. W., Wientjes, E., Douwstra, P., Trouwborst, G., Van Ieperen, W., Croce, R., and
Harbinson, J. (2012). Photosynthetic quantum yield dynamics: from photosystems to leaves.
The Plant Cell, 24(5):1921–1935.

Horsthuis, W. H., Koerkamp, M. M. K., Heideman, J.-L. P., Mertens, H. W., and Hams, B. H.
(1993). Polymer-based integrated optic devices. In Nonlinear Optical Properties of Organic
Materials VI, volume 2025, pages 516–523. SPIE.

Hou, S., Ye, S., and Zhang, H. (2005). Performance optimization of solar humidification–
dehumidification desalination process using pinch technology. Desalination, 183(1-3):143–149.

Houcine, I., BenAmara, M., Guizani, A., and Maâlej, M. (2006). Pilot plant testing of a new solar
desalination process by a multiple-effect-humidification technique. Desalination, 196(1-3):105–
124.

Hurtado, F., Kaiser, A., and Zamora, B. (2012). Evaluation of the influence of soil thermal inertia

on the performance of a solar chimney power plant. Energy, 47(1):213–224.

Ihoume, I., Tadili, R., Arbaoui, N., and Krabch, H. (2023). Design of a low-cost active and
sustainable autonomous system for heating agricultural greenhouses: A case study on strawberry
(fragaria vulgaris) growth. Heliyon, 9(3).

195

Incropera, F. P., DeWitt, D. P., Bergman, T. L., and Lavine, A. S. (2018). Fundamentals of Heat

and Mass Transfer. John Wiley Inc., New York, NY, 8th edition edition.

Issacci, F., Zvirin, Y., and Grossman, G. (1988). Heat transfer analysis of a finned solar air heater.

Journal of Solar Energy Engineering, 110(2):145–155.

Jahangiri Mamouri, S., Roy, C., Klausner, J., Yin, X., Yang, R., Runkle, E., and Bénard, A. (2018).
A novel approach for an advanced sustainable greenhouse using spectral-splitting material and a
solar desalination unit. In AGU Fall Meeting Abstracts, volume 2018, pages GC53F–1008.

Jia, B., Liu, F., and Wang, D. (2019). Experimental study on the performance of spiral solar air

heater. Solar Energy, 182:16–21.

Jones, J. W., Dayan, E., Allen, L., Van Keulen, H., and Challa, H. (1991). A dynamic tomato

growth and yield model (tomgro). Transactions of the ASABE, 34(2):663–0672.

Kakac, S., Liu, H., and Pramuanjaroenkij, A. (2002). Heat exchangers: selection, rating, and

thermal design. CRC press.

Kasaeian, A., Heidari, E., and Vatan, S. N. (2011). Experimental investigation of climatic effects on
the efficiency of a solar chimney pilot power plant. Renewable and Sustainable energy reviews,
15(9):5202–5206.

Kasaeian, A., Molana, S., Rahmani, K., and Wen, D. (2017). A review on solar chimney systems.

Renewable and sustainable energy reviews, 67:954–987.

Kasperski, J. and Nemś, M. (2013). Investigation of thermo-hydraulic performance of concentrated
solar air-heater with internal multiple-fin array. Applied Thermal Engineering, 58(1-2):411–419.

Kelly, N., Choe, D., Meng, Q., and Runkle, E. S. (2020). Promotion of lettuce growth under an
increasing daily light integral depends on the combination of the photosynthetic photon flux
density and photoperiod. Scientia Horticulturae, 272:109565.

Kesari, K. K., Soni, R., Jamal, Q. M. S., Tripathi, P., Lal, J. A., Jha, N. K., Siddiqui, M. H., Kumar,
P., Tripathi, V., and Ruokolainen, J. (2021). Wastewater treatment and reuse: a review of its
applications and health implications. Water, Air, & Soil Pollution, 232:1–28.

Khalil, M. H., Khan, M. A., Ramzan, M., Rahman, M. U., Amin, M. K. M., and Ali, A. (2012).
Drying of apricots using a proficient dish type solar air heater. World applied sciences journal,
18(8):1102–1106.

Kim, H. M., Lee, H. K., Kim, S., and Kim, J. P. (2022). Near-infrared (nir) absorbing films based
on diimmonium dye and cyanine dye for high-performance nir cut-off filter. Dyes and Pigments,
207:110702.

196

Klausner, J. F., Li, Y., Darwish, M., and Mei, R. (2004). Innovative diffusion driven desalination

process. J. Energy Resour. Technol., 126(3):219–225.

Klausner, J. F., Li, Y., and Mei, R. (2006). Evaporative heat and mass transfer for the diffusion

driven desalination process. Heat and mass transfer, 42(6):528–536.

Kolev, N. (1976). Operational parameters of randomly packed-columns. Chemie Ingenieur Technik,

48(12):1105–1112.

Kong, Y. and Nemali, K. (2021). Blue and far-red light affect area and number of individual leaves
to influence vegetative growth and pigment synthesis in lettuce. Frontiers in Plant Science,
12:667407.

Koonsrisuk, A. (2012). Mathematical modeling of sloped solar chimney power plants. Energy,

47(1):582–589.

Kreetz, H. (1997). Theoretical investigations and design of a temporary "a ren water storage for ü
r the updraft power plant. Diploma, Energy Process Engineering and Conversion Technologies
of Renewable Energies-EVUR, Technical University Berlin, Berlin, Germany.

Kreith, F. and Bohem, R. (1988). Direct-contact heat transfer, hemisphere pub. Corp., Washington.

Krisst, R. (1983). Energy-transfer systems. Alternative sources of energy, 63:8–8.

Lages Barbosa, G., Almeida Gadelha, F. D., Kublik, N., Proctor, A., Reichelm, L., Weissinger, E.,
Wohlleb, G. M., and Halden, R. U. (2015a). Comparison of land, water, and energy requirements
of lettuce grown using hydroponic vs. conventional agricultural methods. International journal
of environmental research and public health, 12(6):6879–6891.

Lages Barbosa, G., Almeida Gadelha, F. D., Kublik, N., Proctor, A., Reichelm, L., Weissinger, E.,
Wohlleb, G. M., and Halden, R. U. (2015b). Comparison of land, water, and energy requirements
of lettuce grown using hydroponic vs. conventional agricultural methods. International journal
of environmental research and public health, 12(6):6879–6891.

Langtry, R. B. and Menter, F. R. (2009). Correlation-based transition modeling for unstructured

parallelized computational fluid dynamics codes. AIAA journal, 47(12):2894–2906.

Li, X., Yuan, G., Wang, Z., Li, H., and Xu, Z. (2014). Experimental study on a humidification
and dehumidification desalination system of solar air heater with evacuated tubes. Desalination,
351:1–8.

Li, Y., Klausner, J. F., Mei, R., and Knight, J. (2006). Direct contact condensation in packed beds.

International Journal of Heat and Mass Transfer, 49(25-26):4751–4761.

Lodhi, M. (1999). Application of helio-aero-gravity concept in producing energy and suppressing

197

pollution. Energy conversion and management, 40(4):407–421.

Lorenz, H. and Wiebe, H. (1980). Effect of temperature on photosynthesis of lettuce adapted to

different light and temperature conditions. Scientia Horticulturae, 13(2):115–123.

Ludwig, H. (2010). Energy consumption of reverse osmosis seawater desalination-possibilities
for its optimisation in design and operation of swro plants. Desalination and Water Treatment,
13(1-3):13–25.

Ma, Q., Zhang, Y., Wu, G., Yang, Q., Yuan, Y., Cheng, R., Tong, Y., and Fang, H. (2022).
Photovoltaic/spectrum performance analysis of a multifunctional solid spectral splitting covering
for passive solar greenhouse roof. Energy Conversion and Management, 251:114955.

Mahmood, F. and Al-Ansari, T. (2022). Design and analysis of a renewable energy driven green-
house integrated with a solar still for arid climates. Energy Conversion and Management,
258:115512.

Maia, C. B., Ferreira, A. G., Valle, R. M., and Cortez, M. F. (2009). Theoretical evaluation of
the influence of geometric parameters and materials on the behavior of the airflow in a solar
chimney. Computers & Fluids, 38(3):625–636.

Maia, C. B., Silva, F. V., Oliveira, V. L., and Kazmerski, L. L. (2019). An overview of the use of

solar chimneys for desalination. Solar Energy, 183:83–95.

Mammadov, F. (2012). Study of selective surface of solar heat receiver. International Journal of

Energy Engineering, 2(4):138–144.

Mamouri, S. J., Tan, X., Klausner, J. F., Yang, R., and Bénard, A. (2020). Performance of
an integrated greenhouse equipped with light-splitting material and an hdh desalination unit.
Energy Conversion and Management: X, 7:100045.

Mancosu, N., Snyder, R. L., Kyriakakis, G., and Spano, D. (2015). Water scarcity and future

challenges for food production. Water, 7(3):975–992.

Mashonjowa, E., Ronsse, F., Mhizha, T., Milford, J., Lemeur, R., and Pieters, J. (2010). The effects
of whitening and dust accumulation on the microclimate and canopy behaviour of rose plants
(rosa hybrida) in a greenhouse in zimbabwe. Solar Energy, 84(1):10–23.

Matysiak, B., Ropelewska, E., Wrzodak, A., Kowalski, A., and Kaniszewski, S. (2022). Yield and
quality of romaine lettuce at different daily light integral in an indoor controlled environment.
Agronomy, 12(5):1026.

Mazria, E. (1979). Passive solar energy book.

Meddeb, H., Götz-Köhler, M., Flathmann, C., Seibt, M., Gehrke, K., and Vehse, M. (2023).

198

Novel semi-transparent solar cell based on ultrathin multiple si/ge quantum wells. Progress in
Photovoltaics: Research and Applications, 31(12):1396–1408.

Meng, Q., Boldt, J., and Runkle, E. S. (2020). Blue radiation interacts with green radiation
to influence growth and predominantly controls quality attributes of lettuce. Journal of the
American Society for Horticultural Science, 145(2):75–87.

Meng, Q., Kelly, N., and Runkle, E. S. (2019). Substituting green or far-red radiation for blue
radiation induces shade avoidance and promotes growth in lettuce and kale. Environmental and
Experimental Botany, 162:383–391.

Meng, Q. and Runkle, E. S. (2019). Far-red radiation interacts with relative and absolute blue and
red photon flux densities to regulate growth, morphology, and pigmentation of lettuce and basil
seedlings. Scientia Horticulturae, 255:269–280.

Menni, Y., Chamkha, A. J., Lorenzini, G., Kaid, N., Ameur, H., and Bensafi, M. (2019). Advances
of nanofluids in solar collectors—a review of numerical studies. Math Model Eng Probl,
6(3):415–27.

Mohamed, A., Ahmed, M. S., Maghrabie, H. M., and Shahdy, A. G. (2021). Desalination process
using humidification–dehumidification technique: A detailed review. International Journal of
Energy Research, 45(3):3698–3749.

Moretti, S. and Marucci, A. (2019). A photovoltaic greenhouse with variable shading for the

optimization of agricultural and energy production. Energies, 12(13):2589.

Morse, E. (1882). Utilizing the sun’s rays in warming houses. Scientific American.

Müller-Holst, H., Engelhardt, M., Herve, M., and Schölkopf, W. (1998). Solarthermal seawater

desalination systems for decentralised use. Renewable Energy, 14(1-4):311–318.

Müller-Holst, H., Engelhardt, M., and Schölkopf, W. (1999). Small-scale thermal seawater desali-

nation simulation and optimization of system design. Desalination, 122(2-3):255–262.

Mullett, L. (1987). The solar chimney—overall efficiency, design and performance. International

journal of ambient energy, 8(1):35–40.

Muthusamy, C. and Srithar, K. (2015). Energy and exergy analysis for a humidification–
dehumidification desalination system integrated with multiple inserts. Desalination, 367:49–59.

Najmi, M., Nazari, A., Mansouri, H., and Zahedi, G. (2012). Feasibility study on optimization of

a typical solar chimney power plant. Heat and Mass Transfer, 48(3):475–485.

Narayan, G. P., McGovern, R. K., Thiel, G. P., Miller, J. A., Lienhard, V., Sharqawy, M., et al. (2011).
In World Congress/Perth

Status of humidification dehumidification desalination technology.

199

Convention and Exhibition Centre, Perth, Australia.

Narayan, G. P., Sharqawy, M. H., Summers, E. K., Lienhard, J. H., Zubair, S. M., and Antar, M. A.
(2010). The potential of solar-driven humidification–dehumidification desalination for small-
scale decentralized water production. Renewable and sustainable energy reviews, 14(4):1187–
1201.

Nawayseh, N. K., Farid, M. M., Al-Hallaj, S., and Al-Timimi, A. R. (1999). Solar desalination
based on humidification process—i. evaluating the heat and mass transfer coefficients. Energy
conversion and management, 40(13):1423–1439.

Niroomand, N., Zamen, M., and Amidpour, M. (2015). Theoretical investigation of using a direct
contact dehumidifier in humidification–dehumidification desalination unit based on an open air
cycle. Desalination and Water Treatment, 54(2):305–315.

Nizetic, S., Ninic, N., and Klarin, B. (2008). Analysis and feasibility of implementing solar chimney

power plants in the mediterranean region. Energy, 33(11):1680–1690.

Nkhoma, P. R., Alsharif, K., Ananga, E., Eduful, M., and Acheampong, M. (2021). Recycled water
reuse: what factors affect public acceptance? Environmental Conservation, 48(4):278–286.

None, N. (2013). Life cycle greenhouse gas emissions from electricity generation. Technical report,

National Renewable Energy Lab.(NREL), Golden, CO (United States).

Onda, K., Takeuchi, H., and Okumoto, Y. (1968). Mass transfer coefficients between gas and liquid

phases in packed columns. Journal of chemical engineering of Japan, 1(1):56–62.

Ooms, M. D., Dinh, C. T., Sargent, E. H., and Sinton, D. (2016). Photon management for augmented

photosynthesis. Nature Communications, 7(1):1–13.

Padki, M. and Sherif, S. (1999). On a simple analytical model for solar chimneys. International

journal of energy research, 23(4):345–349.

Park, Y. and Runkle, E. S. (2018a). Far-red radiation and photosynthetic photon flux density
independently regulate seedling growth but interactively regulate flowering. Environmental and
Experimental Botany, 155:206–216.

Park, Y. and Runkle, E. S. (2018b). Spectral effects of light-emitting diodes on plant growth, visual
color quality, and photosynthetic photon efficacy: White versus blue plus red radiation. PLoS
One, 13(8):e0202386.

Park, Y. and Runkle, E. S. (2019). Blue radiation attenuates the effects of the red to far-red ratio on
extension growth but not on flowering. Environmental and Experimental Botany, 168:103871.

Pastohr, H., Kornadt, O., and Gürlebeck, K. (2004). Numerical and analytical calculations of the

200

temperature and flow field in the upwind power plant. International Journal of Energy Research,
28(6):495–510.

Pasumarthi, N. and Sherif, S. (1998). Experimental and theoretical performance of a demonstration
solar chimney model—part ii: experimental and theoretical results and economic analysis.
International Journal of Energy Research, 22(5):443–461.

Paz, M., Fisher, P. R., and Gómez, C. (2019). Minimum light requirements for indoor gardening of

lettuce. Urban Agriculture & Regional Food Systems, 4(1):1–10.

Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M.,
Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher,
M., Perrot, M., and Duchesnay, E. (2011). Scikit-learn: Machine learning in Python. Journal of
Machine Learning Research, 12:2825–2830.

Platzer, W. J. (1987). Solar transmission of transparent insulation material. Solar Energy Materials,

16(1-3):275–287.

Prasad, B. and Sah, G. (2014). Plate temperature and heat transfer characteristics of artificially

roughened solar air heater. Energy procedia, 62:256–269.

Puranik, S. and Vogelpohl, A. (1974). Effective interfacial area in irrigated packed columns.

Chemical Engineering Science, 29(2):501–507.

Qiblawey, H. M. and Banat, F. (2008). Solar thermal desalination technologies. Desalination,

220(1-3):633–644.

Rahimi-Ahar, Z., Hatamipour, M. S., and Ghalavand, Y. (2018). Solar assisted modified variable
pressure humidification-dehumidification desalination system. Energy Conversion and Manage-
ment, 162:321–330.

Rajaseenivasan, T. and Srithar, K. (2017). Potential of a dual purpose solar collector on humidifi-

cation dehumidification desalination system. Desalination, 404:35–40.

Ravi, R. K. and Saini, R. (2018). Nusselt number and friction factor correlations for forced
convective type counter flow solar air heater having discrete multi v shaped and staggered rib
roughness on both sides of the absorber plate. Applied Thermal Engineering, 129:735–746.

Rhee, S. and Edwards, D. (1981). Laminar entrance flow in a flat plate duct with asymmetric

suction and heating. Numerical heat transfer, 4(1):85–100.

Roy, C., Klausner, J. F., and Bénard, A. (2021). Numerical study on the impact of fluid distribution
on a counter-current direct contact evaporator. International Journal of Heat and Mass Transfer,
166:120561.

201

Sadler, E. and Van Bavel, C. (1984). Simulation and measurement of energy partition in a fluid-roof

greenhouse. Agricultural and forest meteorology, 33(1):1–13.

Sajid, M. U., Saghir, M. Z., Dincer, I., and Bicer, Y. (2023). Spectrum splitting through cus–
zno/water hybrid nanofluid for agricultural greenhouse cooling applications: an experimental
study. Journal of Thermal Analysis and Calorimetry, pages 1–15.

Sakamoto, M., Suzuki, T., et al. (2015). Effect of root-zone temperature on growth and quality of
hydroponically grown red leaf lettuce (lactuca sativa l. cv. red wave). American Journal of Plant
Sciences, 6(14):2350.

Salem, F. and Thiemann, T. (2022). Produced water from oil and gas exploration—problems,

solutions and opportunities. Journal of Water Resource and Protection, 14(2):142–185.

Santosh, R., Lee, H.-S., and Kim, Y.-D. (2022). A comprehensive review on humidifiers and
dehumidifiers in solar and low-grade waste heat powered humidification-dehumidification de-
salination systems. Journal of Cleaner Production, 347:131300.

Saxena, A., Verma, P., Srivastava, G., and Kishore, N. (2020). Design and thermal performance
evaluation of an air heater with low cost thermal energy storage. Applied Thermal Engineering,
167:114768.

Schulz, E., Speekenbrink, M., and Krause, A. (2018). A tutorial on gaussian process regression:
Modelling, exploring, and exploiting functions. Journal of Mathematical Psychology, 85:1–16.

Seabold, S. and Perktold, J. (2010). Statsmodels: Econometric and statistical modeling with python.
In Proceedings of the 9th Python in Science Conference, volume 57, pages 10–25080. Austin,
TX.

Sengupta, M., Xie, Y., Lopez, A., Habte, A., Maclaurin, G., and Shelby, J. (2018). The national

solar radiation data base (nsrdb). Renewable and sustainable energy reviews, 89:51–60.

Sethi, V. P. (2009). On the selection of shape and orientation of a greenhouse: Thermal modeling

and experimental validation. Solar Energy, 83(1):21–38.

Sharon, H. and Reddy, K. (2015). A review of solar energy driven desalination technologies.

Renewable and Sustainable Energy Reviews, 41:1080–1118.

Sharples, S. and Charlesworth, P. (1998). Full-scale measurements of wind-induced convective

heat transfer from a roof-mounted flat plate solar collector. Solar Energy, 62(2):69–77.

Sharqawy, M. H. and Liu, H. (2015). The effect of pressure on the performance of bubble column

dehumidifier. International Journal of Heat and Mass Transfer, 87:212–221.

Shatat, M., Worall, M., and Riffat, S. (2013). Opportunities for solar water desalination worldwide.

202

sustain cities soc 9: 67–80.

Shen, L., Lou, R., Park, Y., Guo, Y., Stallknecht, E. J., Xiao, Y., Rieder, D., Yang, R., Runkle, E. S.,
and Yin, X. (2021). Increasing greenhouse production by spectral-shifting and unidirectional
light-extracting photonics. Nature Food, 2(6):434–441.

Shi, M. G. and Mersmann, A. (2011). Effective interfacial area in packed columns. International

journal of heat and mass transfer, 54(15-16):3381–3393.

Siddiqui, F. R., Elminshawy, N. A., and Addas, M. F. (2016). Design and performance improvement
of a solar desalination system by using solar air heater: Experimental and theoretical approach.
Desalination, 399:78–87.

Simpson, G. B. and Jewitt, G. P. (2019). The development of the water-energy-food nexus as a
framework for achieving resource security: a review. Frontiers in Environmental Science, 7:8.

Somwanshi, A. and Sarkar, N. (2020). Thermal performance of a dual-purpose collector-cum-

storage type air-water heater. Applied Thermal Engineering, 171:115094.

Soomro, S. H., Santosh, R., Bak, C.-U., Kim, W.-S., and Kim, Y.-D. (2021). Humidification-
dehumidification desalination system powered by simultaneous air-water solar heater. Sustain-
ability, 13(23):13491.

Soussi, M., Chaibi, M. T., Buchholz, M., and Saghrouni, Z. (2022). Comprehensive review on
climate control and cooling systems in greenhouses under hot and arid conditions. Agronomy,
12(3):626.

Stanghellini, C. (1987). Transpiration of greenhouse crops: an aid to climate management.

Wageningen University and Research.

Summers, E. K., Antar, M. A., et al. (2012). Design and optimization of an air heating solar collector
with integrated phase change material energy storage for use in humidification–dehumidification
desalination. Solar Energy, 86(11):3417–3429.

Sun, C., Xia, R., Shi, H., Yao, H., Liu, X., Hou, J., Huang, F., Yip, H.-L., and Cao, Y. (2018).
Heat-insulating multifunctional semitransparent polymer solar cells. Joule, 2(9):1816–1826.

Sweeney, D. (1981). Modelling the growth of winter lettuce. Mathematics and Plant Physiology,

pages 217–229.

Tantau, H., Salokhe, V., et al. (2006). Microclimate and air exchange rates in greenhouses covered

with different nets in the humid tropics. Biosystems Engineering, 94(2):239–253.

Test, F., Lessmann, R., and Johary, A. (1981). Heat transfer during wind flow over rectangular

bodies in the natural environment. Journal of Heat Transfer, pages 262–267.

203

Tiwari, G. (2003). Greenhouse technology for controlled environment. Alpha Science Int’l Ltd.

Tiwari, G., Tiwari, A., et al. (2016). Handbook of solar energy, volume 498. Springer.

Tobiska, W. K., Woods, T., Eparvier, F., Viereck, R., Floyd, L., Bouwer, D., Rottman, G., and
White, O. (2000). The solar2000 empirical solar irradiance model and forecast tool. Journal of
Atmospheric and Solar-Terrestrial Physics, 62(14):1233–1250.

Togrul, I. T., Pehl𝜄van, D., and Akosman, C. (2004). Development and testing of a solar air-heater

with conical concentrator. Renewable Energy, 29(2):263–275.

Tyagi, R., Ranjan, R., and Kishore, K. (2014). Performance studies on flat plate solar air heater

subjected to various flow patterns. Applied Solar Energy, 50(2):98–102.

Unesco, W. (2019). The united nations world water development report 2019: Leaving no one
behind. The United Nations world water development report 2019: leaving no one behind.

Van Bavel, C., Damagnez, J., and Sadler, E. (1981). The fluid-roof solar greenhouse: energy budget

analysis by simulation. Agricultural meteorology, 23:61–76.

Van der Bruggen, B., Vandecasteele, C., Van Gestel, T., Doyen, W., and Leysen, R. (2003). A review
of pressure-driven membrane processes in wastewater treatment and drinking water production.
Environmental progress, 22(1):46–56.

Van Henten, E. (1994). Validation of a dynamic lettuce growth model for greenhouse climate

control. Agricultural System, 45(1):55–72.

Van Henten, E. and Van Straten, G. (1994). Sensitivity analysis of a dynamic growth model of

lettuce. Journal of Agricultural Engineering Research, 59(1):19–31.

Van Holsteijn, H. M. (1981). Growth and photosynthesis of lettuce. Wageningen University and

Research.

Van Krevelen, D. and Hoftijzer, P. (1948). Kinetics of simultaneous absorption and chemical

reaction. Chemical Engineering Progress, 44(7):529–536.

Varol, Y. and Oztop, H. F. (2008). A comparative numerical study on natural convection in inclined

wavy and flat-plate solar collectors. Building and environment, 43(9):1535–1544.

Velmurugan, V. and Srithar, K. (2011). Performance analysis of solar stills based on various factors
affecting the productivity—a review. Renewable and sustainable energy reviews, 15(2):1294–
1304.

Waller, R., Kacira, M., Magadley, E., Teitel, M., and Yehia, I. (2022). Evaluating the performance
of flexible, semi-transparent large-area organic photovoltaic arrays deployed on a greenhouse.

204

AgriEngineering, 4(4):969–992.

Watmuff, J., Charters, W., and Proctor, D. (1977). Solar and wind induced external coefficients-solar

collectors. Cooperation Mediterraneenne pour l’Energie Solaire, page 56.

Weyl, P. K. (May 14, 1964). Recovery of demineralized water from saline waters.

Whillier, A. (1964). Performance of black-painted solar air heaters of conventional design. Solar

Energy, 8(1):31–37.

Willits, D. (2003). The effect of cloth temperature on the cooling efficiency of shade cloths in

greenhouses. Transactions of the ASAE, 46(4):1215.

Wu, G., Zheng, H.-F., Wang, F., and Chang, Z.-H. (2017). Parametric study of a tandem desalination
system based on humidification-dehumidification process with 3-stage heat recovery. Applied
Thermal Engineering, 112:190–200.

Xu, G., Ming, T., Pan, Y., Meng, F., and Zhou, C. (2011). Numerical analysis on the performance
of solar chimney power plant system. Energy Conversion and Management, 52(2):876–883.

Yamalı, C. and Solmuş, İ. (2007). Theoretical investigation of a humidification-dehumidification
desalination system configured by a double-pass flat plate solar air heater. Desalination, 205(1-
3):163–177.

Yano, A., Onoe, M., and Nakata, J. (2014). Prototype semi-transparent photovoltaic modules for

greenhouse roof applications. Biosystems Engineering, 122:62–73.

Yuan, G., Wang, Z., Li, H., and Li, X. (2011). Experimental study of a solar desalination system

based on humidification–dehumidification process. Desalination, 277(1-3):92–98.

Yuan, Y., Fang, H., Wu, G., Yang, Q., Ma, Q., Ji, Y., Cheng, R., Zhang, Y., and Tong, Y. (2022).
Experimental investigation of full solar spectrum utilization based on nanofluid spectral splitter
for greenhouse applications. Energy Conversion and Management, 254:115215.

Zamen, M., Amidpour, M., and Soufari, S. M. (2009). Cost optimization of a solar humidification–
dehumidification desalination unit using mathematical programming. Desalination, 239(1-
3):92–99.

Zech, J. and Mersmann, A. (1979). Liquid flow and liquid phase mass transfer in irrigated packed

columns. In Inst. Chem. Eng. Symp. Ser, volume 56, page 39.

Zhang, X., Zhao, W., Zhang, Y., and Jegatheesan, V. (2021). A review of resource recovery from
seawater desalination brine. Reviews in Environmental Science and Bio/Technology, 20:333–361.

Zhao, Y., Li, Z., Deger, C., Wang, M., Peric, M., Yin, Y., Meng, D., Yang, W., Wang, X., Xing,

205

Q., et al. (2023). Achieving sustainability of greenhouses by integrating stable semi-transparent
organic photovoltaics. Nature Sustainability, 6(5):539–548.

Zhou, X., Wang, F., and Ochieng, R. M. (2010). A review of solar chimney power technology.

Renewable and Sustainable Energy Reviews, 14(8):2315–2338.

Zhou, X. and Yang, J. (2008). Temperature field of solar collector and application potential of solar

chimney power systems in china. Journal of the Energy Institute, 81(1):25–30.

Zhou, X., Yang, J., Xiao, B., and Hou, G. (2007a). Experimental study of temperature field in a

solar chimney power setup. Applied Thermal Engineering, 27(11-12):2044–2050.

Zhou, X., Yang, J., Xiao, B., and Hou, G. (2007b). Simulation of a pilot solar chimney thermal

power generating equipment. Renewable Energy, 32(10):1637–1644.

Zou, H., Wang, C., Yu, J., Huang, D., Yang, R., and Wang, R. (2023). Eliminating greenhouse heat

stress with transparent radiative cooling film. Cell Reports Physical Science, 4(8).

Zuo, L., Yuan, Y., Li, Z., and Zheng, Y. (2012). Experimental research on solar chimneys integrated

with seawater desalination under practical weather condition. Desalination, 298:22–33.

Zuo, L., Zheng, Y., Li, Z., and Sha, Y. (2011). Solar chimneys integrated with sea water desalination.

Desalination, 276(1-3):207–213.

206