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This is to certify that the

thesis entitled
"Drying Rate of Individual Ears of Corn"

presented by

Nicholas Robert Friant

has been accepted towards fulfillment
of the requirements for

 

M. S . degree in Biosystems Engineering

     

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-.

ajor professor

Date 2/%%>

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

LIBRARY ‘
Michigan State
University

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 c:IClRC/DatoDu9.p65-p.15

DRYING RATE OF INDIVIDUAL EARS OF CORN
By

Nicholas Robert Friant

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Department of Agricultural Engineering

2002

ABSTRACT

DRYING RATE OF
INDIVIDUAL EARS OF CORN

By

Nicholas Robert Friant

The current drying process for seed corn relies primarily on the experience
of the dryer operator. However, manual control of an ear-corn dryer can result in
an inefficient process, with respect to dryer capacity and energy consumption.

Development of an automatic controller will allow dryer operators to
operate seed-corn dryers more effectively and efficiently. However, development
of a controller will require a drying model, and a thin-layer equation for ear-corn
drying is an essential component of any ear-corn drying model.

Thin-layer ear-corn drying was performed experimentally, and a thin-layer
drying rate model was parameterized for ear corn. The calibration data set
consisted of 127 data sets (1,206 data points) and was made up of laboratory
data (nsets = 65, npoims = 901) and field data (nsets = 62. "points = 305). Tests were
run with drying air temperatures between 35 and 45°C (95 and 115°F). Relative
humidity ranged from 5 to 35%. The resulting thin-layer model was validated
against an independent validation set (nsets = 30, npomts = 152). Validation of the
model against field data resulted in a standard error of prediction of 0.1147 for
the moisture ratio and 3.8% (dry basis) for the moisture content. The ratio of
standard error of calibration to standard error of prediction resulted in a value of

1.4, indicating good robustness of the model.

For Stephanie, my light, my life, my love.

ACKNOWLEDGEMENTS

The author wishes to acknowledge Professor Fred W. Bakker-Arkema for
all of his guidance, help, and friendship. Without him, much of my success and
direction would not have come so easy to me.

I would also like to thank Professor Bradley P. Marks for his guidance and
assistance, and most importantly, for taking on the responsibility of being my
major professor. The knowledge and wisdom Dr. Marks has imparted upon me
is invaluable.

Gracious appreciation is extended to Professor Larry Copeland from Crop
and Soil Sciences and Professor Craig Somerton of Mechanical Engineering,
both of Michigan State University, for serving on the guidance committee.

The financial support of Pioneer Hi-bred International, Inc., and Dr. Jim
Hunter’s involvement with the MSU/Pioneer Project is greatly appreciated.

To all of the friends and colleagues I have met and worked with at
Michigan State University, too numerous to mention here - thank you.

Thank you to my family for supporting me and being there for everything,
especially during my time at MSU. I can never repay the caring and support you
have shown me, I can only hope to make you proud — thank you!

Lastly, a heart felt thank you to my Stephanie. Without you in my life, I
fear I would be lost. Thank you for putting up with me and continuing to be there

for me.

TABLE OF CONTENTS

List of Tables ............................................................................................ vii
List of Figures ............................................................................................ ix
Nomenclature ........................................................................................... xii
1. Introduction ........................................................................................... 1
2. Review of Literature .............................................................................. 6
2.1 Seed Technology ........................................................................... 6
2.2 Corn Hybridization ......................................................................... 6
2.2.1 Traditional Corn Hybridization .............................................. 6

2.2.2 Genetic Modification (Plant Biotechnology) ....................... 19

2.3 Seed Production Practices .......................................................... 12
2.4 Thin-Layer Drying ........................................................................ 13
2.5 The OSU Model ........................................................................... 16
2.6 Cob-Kernel Moisture Content Relationship ................................. 22

3. Experimental Procedures .................................................................... 23
3.1 Overview ...................................................................................... 23
3.2 Field Experimentation .................................................................. 23
3.2.1 Data Collection ................................................................... 23

3.2.2 Moisture Content Sample Collection .................................. 24

3.3 Laboratory Experimentation ......................................................... 25
3.3.1 Data Collection ................................................................... 25

3.3.2 Thin-Layer Tests ................................................................ 26

3.3.3 Calibration Tests ................................................................ 28

3.3.4 Single Kernel Moisture Tests ............................................. 30

3.3.5 Data Analysis ..................................................................... 30

4. Equation Development ........................................................................ 35
4.1 Thin-Layer Equations .................................................................. 35
4.1.1 ASAE Standards Thin-Layer Model ................................... 35

4.1.2 Sharaf-Eldeen Thin-Layer Model ....................................... 36

4.1.3 Equilibrium Moisture Content ............................................. 37

4.2 Ear-Kernel Moisture Relationships .............................................. 38
4.3 Psychrometrics ............................................................................ 38
4.3.1 Relative Humidity ............................................................... 39

4.3.2 Humidity Ratio .................................................................... 39

4.3.3 Vapor Pressure .................................................................. 39

4.3.4 Dry-Bulb Temperature ....................................................... 40

4.3.5 Wet-Bulb Temperature ....................................................... 41

4.3.6 Specific Volume ................................................................. 41

4.3.7 Enthalpy ............................................................................. 42
4.3.8 Relative and Absolute Humidity Calculations ..................... 42

4.4 Application and Implementation of the Thin-Layer Equation into
The Deep—Bed Model ................................................................... 45
5. Results and Discussion ....................................................................... 48
5.1 Laboratory Experiments ............................................................... 48
5.1.1 Equilibrium Moisture Content ............................................. 48
5.1.2 Thin-Layer Tests ................................................................ 49
5.1.3 Individual Kernel Moisture Content .................................... 52
5.2 Field Experiments ........................................................................ 54
5.3 Regression Results ..................................................................... 58
5.3.1 Nonlinear Regression ........................................................ 58
5.4 Equation Comparisons ................................................................ 71
5.4.1 Experimental Data and the Sharaf Model .......................... 71
5.4.2 Friant and Sharaf ............................................................... 72
5.5 Model Sensitivity to Varying Drying Conditions ........................... 77
5.6 Hybrid Effects .............................................................................. 84
5.7 Thin-Layer Effects on the Deep-Bed Model ................................. 85
6. Conclusions ........................................................................................ 88
7. Recommendations for Further Study .................................................. 90
References .............................................................................................. 91
Appendices .............................................................................................. 95
A. Experimental Data and Validation Tables ..................................... 96
B. FORTRAN Code ......................................................................... 142
C. Equipment Specifications ............................................................ 151

vi

Table 1.1
Table 3.1

Table 3.2

Table 3.3

Table 4.1

Table 5.1

Table 5.2

Table 5.3

Table 5.4

Table 5.5

Table 5.6

Table 5.7

Table 5.8

LIST OF TABLES

Description of common grain dryer types ............................. 3
Calibration data for the GAC 2000 moisture meter ............. 29
Calibration data for the PQ-100 single-kernel moisture

meter .................................................................................. 29
Example of JMP Spreadsheet ............................................ 32

Verification of psychrometric equations for relative humidity
given wet-bulb and dry-bulb temperature ........................... 44

Comparison of experimental and predicted equilibrium
moisture contents at 40°C .................................................. 49

Calculations of the equilibrium moisture content using
laboratory conditions, psychrometric equations and
equation (4.8) ..................................................................... 50

Example of drying data at 40°C (104°F) and 24.3%
relative humidity ................................................................. 58

Example of the validation set for moisture content and
moisture ratio ...................................................................... 64

Spreadsheet used to calculate predicted moisture content,
moisture ratio, and drying time using the Friant and Sharaf
equafions ............................................................................ 73

SEP values for the Friant and Sharaf models during the
first half of drying (MRAT20.5) and the SEP values during
the second half of drying (MRAT<0.5) ................................ 74

Time (h) for the moisture content in the Friant and Sharaf
Models to predict 22 and 12.5% Mb.) at different
temperatures and initial moisture contents at 15% relative
humidity .............................................................................. 77

Drying rate (kg/tonne/h) differences for each initial condition

to determine which initial condition has the greatest effect
on drying rate (kg/tonne/h) ................................................. 83

vii

Table 5.9

Table 5.10

Bias of the hybrid effect on the moisture ratio (a) and the
moisture content (b) (NS = not significant at a = 0.05) ....... 84

Comparison of the reversal time, dryer shut-off time, and

final moisture content gradient for the Friant and Sharaf
thin-layer models in the deep-bed ear-corn drying model... 86

viii

Figure 1.1
Figure 2.1

Figure 2.2

Figure 3.1
Figure 3.2
Figure 3.3

Figure 4.1

Figure 4.2

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

LIST OF FIGURES

Schematic diagram of a fixed-bed ear-corn dryer
(Cabrera, 2001) .................................................................... 4

Types of Hybrid crosses (U of W, 2001) ............................... 7

Comparison of traditional plant breeding and modern
plant biotechnology (Adapted from the Council for

Biotechnology lnforrnation, 2000) ....................................... 11
Ear corn samples in plastic mesh on oven drying rack ....... 27
Shelled corn and cobs on drying rack for 72h drying .......... 27
Typical output for JMP nonlinear regression ...................... 33

Example of a thin-layer in a deep-bed simulation model
(Adapted from Brooker et al., 1992) ................................... 46

Flow diagram of deep-bed ear-corn drying simulation
model .................................................................................. 47

Moisture content versus time for two ears of corn dried in
the laboratory at 35°C (95°F) and 11 .4% relative humidity. 51

Moisture ratio versus time for two ears of corn dried in
the laboratory at 35°C (95°F) and 11.4% relative humidity. 51

Average axial moisture content for each row around one
ear of corn .......................................................................... 52

Average radial moisture content for each vertical row of
kernels on one ear of corn .................................................. 53

Moisture content versus time for field up-air bottom-layer
data (375°C [99.5°F], 34.72% relative humidity) and thin-
layer laboratory data (40°C [104°F], 24.3% relative

humidity) ............................................................................. 56

Moisture content versus time for field up-air bottom-layer
data (379°C [100.2°F], 34.89% relative humidity) and
thin-layer laboratory data (40°C [104°F], 24.3% relative
humidity) ............................................................................. 56

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Figure 5.11

Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

Figure 5.16

Figure 5.17

Figure 5.18

Moisture content versus time for field down-air top-layer

data (394°C [102.9°F], 11.62% relative humidity) and
thin-layer laboratory data (40°C [104°F], 24.3% relative
humidity) ............................................................................. 57

Moisture content versus time for field down—air top-layer

data (413°C [106.4°F], 16.17% relative humidity) and
thin-layer laboratory data (40°C [104°F], 24.3% relative
humidity) ............................................................................. 57

JMP output for the parameter values of Equation (4.6) ...... 60

Experimental moisture ratio versus predicted moisture
ratio for 1,206 data points ................................................... 62

k-value versus temperature for Equation (4.5) at 42.9%
(d.b.) initial moisture content .............................................. 63

Experimental ear-corn moisture ratio versus predicted
moisture ratio for the model based on the unmodified
calibration data set ............................................................. 67

Experimental ear-corn moisture content versus predicted
moisture content for the model based on the unmodified
calibration data set ............................................................. 68

Experimental ear-corn moisture ratio versus predicted
moisture ratio for the model based on the jackknife-
modified calibration data set ............................................... 69

Experimental ear—corn moisture content versus predicted
moisture content for the model based on the jackknife-
modified validation data set ................................................ 70

Moisture ratio versus time for a comparison of the Sharaf
model to experimental data for moisture ratio dried at
40°C and 7% relative humidity ........................................... 71

Kernel moisture content versus time for a comparison of
the Sharaf model to the experimental data for moisture
content dried at 40°C and 7% relative humidity .................. 72

Moisture content versus time for the two thin-layer
models and the experimental data dried at 40°C, 7% r.h. .. 75

Figure 5.19

Figure 5.20

Figure 5.21

Figure 5.22

Figure 5.23

Moisture ratio versus time for the two thin—layer models
and the experimental data dried at 40°C, 7% r.h. ............... 76

Moisture content versus time to reach 25.6% ear

moisture content (w.b.) for the new thin-layer model at

three temperatures: 35, 40, and 45°C. Initial ear

moisture content = 35.6% (w.b.), relative humidity = 20%.. 79

Moisture content versus time to reach 25.6% ear

moisture content (w.b.) for the new thin-layer model at

three relative humidities: 15, 20, and 25%. Initial ear
moisture content = 35.6% (w.b.), temperature = 40°C ........ 79

Ear moisture content versus time for the new thin-layer
model at three initial moisture contents: 29.4, 35.6, and
41.4% (w.b.). Temperature = 40°C, relative humidity =
20% .................................................................................... 81

Drying rate versus time for the new thin-layer model at

three initial moisture contents: 29.4, 35.6, and 41.4%
(w.b.). Temperature = 40°C, relative humidity = 20% ........ 81

xi

NOMENCLATURE

Friant and Sharaf (Section 2.4 and Chapters 4 and 5)

 

Mo
Me
l\_/l

MRAT

A, BC
D,n

Tabs

r.h.

(LB

Initial moisture content [decimal, dry basis]
Equilibrium moisture content [decimal, dry basis]
Average moisture content [decimal, dry basis]
Moisture ratio

Drying parameter [h'1]

Time [h]

Experimentally determined parameter values
Absolute temperature [K]
Relative Humidity [%]

Experimentally determined constants for drying

Hamdy and Barre, 1969 (Section 2.5)

 

M9
Me
Ma

M

Kernel average moisture concentration [%, dry basis]
Grain equilibrium moisture content [%, dry basis]
Moisture content in air [%, dry basis]

Moisture concentration inside the kernel [%, dry basis]
Moisture concentration in kernel surface [%, dry basis]
Air temperature [° F]

Kernel average temperature [°F]

Specific heat of dry air [0.24 Btu/lb °F]

Specific heat of water vapor [0.44 Btu/lb °F]

xii

 

Grain equilibrium moisture content [%, dry basis]

SW Specific heat of water [1 Btu/lb °F]

89 Specific heat of dry grain [Btu/lb °F]

y Kernel depth in drying bed [ft]

r Radial position inside the kernel [ft]

t Time [h]

p bulk density of grain [Ib/ft3]

a film coefficient (moisture) [ft/h]

B Constant of heat transfer to grain [h'1]

L Latent heat of vaporization [Btu/lb]

D Moisture diffusion coefficient [ftzlh]

R Kernel radius [ft]

G Airflow rate per unit area of dryer [lb/ft2 h]
Bagqhman et al., 1970 (Section 2.5)

C Grain moisture ratio

D Dimensionless depth variable

G Mass flow rate of drying air [lb of dry air/h ftz]
K Drying constant [h"]

L Latent heat of moisture evaporation [Btu/lb]
M Grain moisture [%, dry basis]

Mo Initial grain moisture [%, dry basis]

Mt Grain moisture at the dryer inlet [%, dry basis]
Me

83 Specific heat of air [Btu/lb °F]

Te Equilibrium air temperature [°F]

xiii

'To

9
Q

Inlet drying air temperature [°F]
Kernel depth in drying bed [ft]
Time [h]

bulk density of grain [lb/ft3]

Grain flow rate [lb/h ftz]

Ear-Kernel Moisture Relationships LSection 4.2)

 

MCEar

MCKernel

Ear corn moisture content [%, d.b.]

Kernel moisture content [%, d.b.]

Psychrometrics (Section 4.3)

 

mg
F’ann
F’v
F’vs

vawb

vadb

Tabs
Tdb

wa

Latent heat of vaporization [J/kg]

Atmospheric pressure [101,325 Pa]

Partial pressure of water vapor [Pa]

Partial pressure of water vapor at saturation [Pa]

Partial pressure of water vapor at saturation with wet-bulb
temperature [Pa]

Partial pressure of water vapor at saturation with dry-bulb
temperature [Pa]

Absolute temperature [K]

Dry-bulb temperature [K]

Wet-bulb temperature [K]

Specific volume of moist air [m3/kg]

Humidity ratio of moist air [kg H20/kg dry air]

Relative humidity [decimal]

xiv

CHAPTER 1

INTRODUCTION

Corn1 is an important commodity grown in the United States of America,
accounting for 254 million metric tonnes and approximately $26.5 billion in raw
product value (USDA, 2000). Therefore, production, harvesting, drying, and
storage of corn seed are a critical part of this market sector.

Corn is primarily harvested by two means: combining, which separates the
seed from the cob (shelled corn) and picking as ear corn. To prevent mold
growth and to preserve viability, corn must be dried to a moisture content of 10 to
15%, wet basis (w.b.) (11 to 18%, dry basis)? This is accomplished primarily by
using mechanical grain dryers.

There are two main methods of corn drying: fixed-bed drying and
continuous-flow drying (Brooker et al., 1992). Brief descriptions of the major
types are given in Table 1.1.

Corn is produced as grain, for food or feed and seed for planting in
subsequent growing seasons. In the production of corn for seed, ear corn is
picked at a moisture content of 30 to 40%. The seed is then dried to
approximately 12% moisture content for safe storage. A main difference in the
production of seed corn versus grain is the end-user definition of quality. For the
livestock producer, nutrient value is important; in the cereal industry, minimum

stress cracking is desirable; and, in seed production, the viability is paramount.

 

1 In this thesis, the word corn is used in the American sense, referring to Zea Mays.
2 In this thesis, the moisture contents are expressed in wet basis, unless specified differently.

In the process of seed-corn production, drying the seed to a moisture
content of 12 to 13% is essential to prevent spoilage during storage. The seed is
dried while still on the ear. Ear-corn dryers are manually controlled and
marginally efficient with respect to capacity and energy usage (i.e., capacity
could be increased, and energy usage could be reduced). Figure 1.1 shows the

schematic of a typical ear-corn drying system.

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Figure 1.1 Schematic diagram of a fixed-bed ear-corn dryer (Cabrera, 2001).

 

A fixed-bed ear-corn drying unit consists of a two-plenum system with
drying bins on each side of the plenum as seen in Figure 1.1. Several drying
units are combined to form one ear-corn dryer, which uses one set of fans and
burners for heating and circulating the drying air.

Ear corn is transported to the desired bin by a conveyor belt system. The
corn is loaded into the appropriate bin through the top loading doors. The ear
corn is piled on the slanted floor of the bin and filled to a depth of 2 to 3.5 m (7 to
11 feet). During the first stage of drying, the “up-air” drying air passes from the
lower plenum through doors upwards through the drying bed, as indicated by the
arrows, and is exhausted to the ambient through the loading doors. At the
desired “reversal” time in the drying cycle, the airflow is reversed by closing the
doors in the bin ceiling, and opening the doors of the upper plenum. The “down

air” passes downward through the drying bed into the lower plenum, as indicated

by the arrows. The air is recycled and used as the “up air” in other bins. When
the correct final moisture content is reached (i.e., 12.5 :1: 0.5%), the corn is
unloaded through the unloading doors at the bottom of the drying bin.

To optimize the operation of an ear-corn dryer, a model of the drying
process should be developed. Subsequently, formal control theory can be
applied to find the optimum values of the main drying parameters (i.e., air
temperature, bed depth, airflow, reversal time, shut-off time), which will result in
the maximum production or minimum energy use of the dryer.

Historically, there has been little formal research aimed at ear-corn drying
theory. Therefore, this thesis project was part of a larger research program with
the overall goal of modeling, optimizing, and controlling fixed-bed ear-corn
drying. However, before that overall goal can be achieved, it is first necessary to
develop and validate various core elements that comprise a deep-bed drying
model, including psychrometric routines, equilibrium moisture models, and thin-
Iayer drying equations.

Therefore, in that context, the primary objectives of this research were: 1)
to develop and validate a drying model for an individual ear of corn and 2) to
contribute that model to a larger effort in developing a deep-bed model for the

drying of ear corn.

CHAPTER 2

REVIEW OF LITERATURE

2.1 SEED TECHNOLOGY

Great strides have been made in the seed-production industry in the last
50 years. Copeland and McDonald (2001) listed six factors that have contributed
to the growth of the seed industry:

1) An increased number of new varieties.

2) New seed-certification and seed-law enforcement programs.

3) Improved cleaning and conditioning technology.

4) Better understanding of seed quality.

5) Specialization of seed growers.

6) Greater seed industry sophistication.
The Hatch Act of 1875 laid the groundwork for the seed industry by establishing
a network of experimental stations throughout the United States. A direct effect
of the Hatch Act was the development of the seed certification program.
2.2 CORN HYBRIDIZATION
2.2.1 TRADITIONAL CORN HYBRIDIZATION

The hybridization of corn was a major step in the production of seed. In
1908, the advantages of hybrid corn compared to open-pollinated corn were first
published. Double-cross seed was produced in 1917; its acceptance grew

rapidly, leading to nearly 100% use today (Copeland and McDonald, 2001).

There are good reasons for using hybrid seed instead of inbred lines. As
corn is inbred, the general characteristics soon become apparent, resulting in
smaller, less vigorous, later maturing, lower yielding plants. There is also an
increase in uniformity with subsequent generations. Conversely, the first
progeny of hybrid seed is more vigorous, taller, higher yielding and earlier
maturing than those of inbred seed. Hybrid seed is produced by cross-pollinating
two inbreds or a series of inbreds and hybrids (U of W, 2001).

Currently, there are four main types of cross-pollination hybrids on the
market: a) single-cross, b) modified single cross, 0) double-cross, and d) three-

way cross (Copeland and McDonald, 2001) (Figure 2.1).

 

Single Cross

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AxB % AB

Modified Single Cross 1
A x A' -> AA' AA' x 88' -> AA'BB'
B x B' -> 88' Or

B = Pure inbred AA' x B -> AA'B
Double Cross

AxB-> AB ABxCD->ABCD
C x D -> CD

 

 

 

 

 

Three-way Cross
AxB-éAB ABxC->ABC ]

 

 

 

 

Figure 2.1 Types of hybrid crosses (U of W, 2001)

In each of the commercially available crosses illustrated in Figure 2.1, the inbred
lines have been in development for at least five successive generations. Thus,

hybrids go through a rigorous selection process to ensure quality seed for

different growing conditions. Therefore, hybrid seed has to be produced under a
variety of conditions (e.g., low fertility, no-till, or irrigation). Seed is also
evaluated for disease and insect resistance (U of W, 2001).

For many years, double-cross pollination was the standard hybrid corn
(See Figure 2.1). These hybrids have many desirable characteristics (Copeland
and McDonald, 2001), such as:

1) greater genetic variability than single or three-way crosses, which may

help the plant during unfavorable growing conditions,

2) longer pollination period for improved seed fill on the ear, which leads

to higher yield,

3) lower cost when the yield is equal to or better than single and three-

way crosses, and

4) higher seed quality than single-cross hybrids.

In recent years, the use of single-cross hybrids has become more
common. In these hybrids, two parent plants are cross-pollinated to yield one
offspring (See Figure 2.1). The seed produced from this cross has the following
desirable traits: a) a good plant uniformity in plant height, ear height, tasseling
time, silking, and pollen shed; b) higher disease and insect resistance; and c)
higher genetic yield potential than the best double cross. Disadvantages of the
single-cross hybrid are a lower seed yield and a relatively low seed quality,
because seed is produced on inbred parents (Copeland and McDonald, 2001).

In modified single-cross corn (Figure 2.1), two related sister-inbred lines

(A and A’) are crossed to produce the female (seed) parent. Also, two other

related sister-inbred lines (B and B’) can be cross-pollinated resulting in the male
(pollen) parent. The female parent is then cross-pollinated with the male parent
or a straight inbred (B). Figure 2.1 shows the crosses and progeny in modified
single-cross hybridization. These hybrids are more vigorous and produce higher-
quality seed than full inbreds.

In three-way cross-pollination, a single-cross parent is crossed with an
unrelated parent inbred (Figure 2.1). In general, three-way crosses tend to fall in
between single- and double-crosses with respect to cost, yield and variability
(Biotech-Monitor, 2001). Three-way crosses are usually less uniform than single-
cross hybrids and normally have higher yields than double cross hybrids
(Heiniger, 2001).

2.2.2 GENETIC MODIFICATION (PLANT BIOTECHNOLOGY)

Modern hybrid development is aided by genetic modification. Plant
biotechnology allows for the transfer of a variety of genetic information in a
precise, controlled manner (Monsanto, 2000). Figure 2.2 shows the comparison
between traditional plant breeding and modern plant biotechnology (Adapted
from the Council for Biotechnology Information, 2000).

In plant biotechnology, enzyme “scissors” are used to cut a desired gene
segment from a chain of DNA (deoxyribonucleic acid) followed by cutting an
opening in the plasmid1 of the DNA chain into which the desired gene segment is
inserted. The desired gene is placed in the plasmid. The chemical make-up of

the cut ends of the gene segment and the plasmid bond to form a new plasmid

 

' The plasmid is the rind of DNA found in the bacteria outside of a cell.

(Monsanto, 2000). Many new corn hybrids have been a direct result of the

enzyme scissors technology

10

Traditional Plant Breeding

Traditional Commercial
Donor Variety

New Variety
(Many genes
transferred)

(88“ X Wq/

Desired
Gene

Modern Plant Biotechnology

Desired Gene Commercial
Variety

' The

Desired
Gene

New Variety
(One gene
transferred)

its...

Desired
Gene

Figure 2.2 Comparison of traditional plant breeding and modern plant
biotechnology. (Adapted from the Council for Biotechnology

Information, 2000)

11

2.3 SEED PRODUCTION PRACTICES

Seed-production practices vary widely, depending upon location, climate,
seed cost, hybrid-development rate, seed type, and grower planting practice
(Hunter, 2002). This section explains the common choices of cross-type and
row-pattern selections.

As shown previously, single-cross hybrids have become common in recent
years. These hybrids are generally grown in temperate, low-stress
environments. Three-way hybrids are commonly produced where challenging
growing conditions are present (e.g., the tropics). Decisions for producing a
double-cross hybrid depend on: the seed price, and low production of new
hybrids. The value of higher yielding seed lines is offset by the higher potential
seed yields of double-crosses (Hunter, 2002).

The row pattern in seed production varies greatly. The basic row patterns
are 4:1 (i.e., four rows of female (seed) parent to one row of male (pollen) parent),
4:2, 6:1, and 6:2. Regardless of the planting pattern, the female rows are
detasseled, allowing the male rows to pollinate the female rows. Female plants
may also be male-sterile (i.e., the male portion of the plant, the tassel, is sterile
and thus the plant does not pollinate itself). It should be noted that these plants
have a self-restoring mechanism, and thus the next generation of seed produces
both pollen and seed again (Copeland and McDonald, 2001).

Four general attributes govern the row-pattern selection in seed
production: the number of row units on the grower’s planter, the use of a split-

planted male (i.e., the male seed is planted after the female seed), the strength

12

(vigor) of the male, and the row width. Generally, an attempt is made to balance
the multiple considerations, so that the best combination of management
practices is selected (Hunter, 2002).

Once seed corn is produced, it is important to understand and model the
subsequent drying process.

2.4 THIN-LAYER DRYING

It is assumed that in the thin-layer drying of corn, liquid water in the corn
kernel and/or cob diffuses to the surface where it is evaporated. This follows
F ick’s law of diffusion, which states that mass flux per unit area is proportional to
the concentration gradient (Holman, 1997). This process is known as falling-rate
drying, where the drying rate is dependant on the rate of moisture transfer from
the interior to the surface of the grain (Laws and Parry, 1983).

Thin-layer drying is a process during which drying air is passed though a
thin layer of corn for a given interval (Thompson et al., 1968). During the time
interval, moisture is evaporated from the corn into the air. The point of thin-layer
drying is to keep the grain in contact with constant air conditions (e.g., air
temperature and relative humidity).

Fickian diffusion principles have been applied to the drying of corn by
numerous researchers (Laws and Perry, 1983; Thompson et al., 1968;
Henderson and Henderson, 1968; Chu and Hustrulid, 1968; Tolaba et al., 1997;
Mourad et al., 1996; and Parti and Dugmanics, 1990). However, the application
of Fick’s Law to drying ear corn considers questionable assumptions: ears of

corn and kernels are a regular shape (i.e., spheres) and the kernels are

13

homogeneous. When applied to single kernels of corn, this process can be
theoretically modeled. Practically, the use of F ickian diffusion is time consuming
and difficult, because of the non-homogeneity of corn, especially ear corn, which
necessitates numerical solutions.

Because of the difficulty applying Fickian diffusion to corn drying,
researchers have tended to work more with empirically derived models.
Examples of empirical models are those developed by Lewis (1921), Page
(1949), and Sharaf-Eldeen et al. (1980). The Lewis model is a simple

exponential model:

MRAT = 6’“ (2,1)

The Page model incorporates a second variable, n:

MRAT = exp(—kt") (2.2)

The Sharaf-Eldeen model is a two-term model using two constants, A and B, as
well as the drying parameter k. The Sharaf model will be discussed later in this
secflon.

Thompson et al. (1968) performed thin-layer tests with shelled corn to
investigate the effects of drying air temperature. The experimental thin-layer
dryer for these tests simply consisted of a fan blowing heated air upward through
a screened tray holding the corn samples. The tests of Thompson et al. showed
that air temperature was the main factor affecting the drying rate.

Li and Morey (1984) performed thin-layer tests to fit Page’s equation to
shelled corn drying data. The thin-layer drying apparatus used by Li and Morey

delivered air with set temperature and relative humidity to a sample that was

14

being dried on an automatic weighing rack constructed of sheet metal and wire
mesh. To correct for the buoyancy effect of the airflow over the sample, weights
with air flowing and no air flowing were recorded and used to correct the
recorded weights. The weight was recorded every 10 seconds.

The experiments of Li and Morey (1984) produced five important
conclusions:

1) drying air temperature has the most significant effect on the drying rate
of corn in thin-layers,

2) airflow rates over 0.1 to 0.5 m/s have little effect on the drying rate,

3) initial moisture content significantly affects the moisture ratio,

4) relative humidity has a minor affect on the moisture ratio and can be

neglected, and

5) Page’s model provides a suitable description of thin-layer drying rates

for corn at 27 to 116°C and 23 to 26% (db).

Sharaf-Eldeen et al. (1980) performed thin-layer drying experiments to
develop a two-term thin-layer drying model for ear com. A laboratory dryer was
equipped with temperature, relative humidity, and air velocity controls. The
weight of the drying samples was recorded using an automatic weight system
comprised of cantilever beams with strain gages attached. The cantilever beams
were calibrated using weights up to 500 g to compensate for the buoyancy
effects of the airflow. Air temperatures and relative humidities for the test were

35.2, 54, 74°C and 13.4, 16.0, and 5.0%, respectively.

15

From experimental data, Sharaf-Eldeen et al. (1980) developed the

following thin-layer equation for the drying of ear corn:

 

f4—M2 _ —kr —-Bkr
M)—M, —Ae +(1—A)e (2.3)

The constants A and B were chosen to fit the experimental data. The
assumption was made that the drying curves of fully exposed ear corn can be
simulated by two straight lines on a semi-log plot. Equilibrium moisture content

was calculated from:

M = {—1110 _ r'h'qw

 

V 7:1/73' (24)
The drying parameter (k) was determined from:
2
k Z €XP[6.8 + “1019571,”. — 9'75)M() — g (2.5)
ubx

Equations (2.3), (2.4), and (2.5) comprise the two-term, Sharaf thin-layer
drying model.
2.5 THE OSU MODEL

A deep-bed simulation model of grain drying was developed in the 19605
and 1970s by Barre and associates at The Ohio State University (Hamdy and
Barre, 1969; Baughman et al., 1970; and Barre et al., 1971). The logarithmic
model combines an empirical approach with some fundamentals of heat and

mass transfer.

16

The drying process is modeled by a series of five partial differential
equafions:

1) air temperature,

2) absolute humidity,

3) grain temperature,

4) local grain moisture content, and

5) average grain moisture content.
The five simultaneous equations have five unknowns, which results in a unique
solution for a given set of boundary conditions. The boundary conditions are
Equations (2.11) to (2.14).

Equation List 2.1 Deep-bed drying equations and boundary conditions (Hamdy
and Barre, 1969)

 

 

 

 

     

58 p 517 fig?
S +m S, ‘ —— G) —-G) S —S
( . . .)— 5y =.G( A a, (2..)
8m” _ p 8m
8y — G at (2 7)
5G) ,
(SK + mgSw) a; : _I8Sg (Gs: _ 6)“) at“ (2.8)
_8_m_ D 203 in?)
St r 6r ar (2°)
3 R 2
I’I’lg : FL mr dl’ (2.10)

®cr(t’0) : 6)I

(2.11)

17

ma (t,0)= MI (2.12)
9g (0’)”): E90 (2.13)
"7(an2"): M0 (2.14)

5,, [:0 (2.15)
am

D— =— m.—m
6r ,-=R a( ° ") (2.16)

The equilibrium moisture content (EMC) in Equation (2.17) is a function of

the air temperature and moisture content

"1.. = m.’(®.am.) (2.17)

The equations in Equation List 2.1 became the basis for a computer
simulation model (Hamdy and Barre 1969). The solution to the model gives
transient temperature and moisture profiles for the drying air and grain. Due to
the complicated nature of solving the system of equations, Hamdy and Barre
developed a computer program. This program assumed that the deep-bed
drying can be modeled as a series of thin layers. An important assumption in the
model is that the temperature and moisture content of each layer is uniform, but

changes with respect to time and from layer to layer.

18

Because of the two independent variables, t and r, in the equations for
moisture transfer in the grain layer (Equations [2.8] to [210]); r was eliminated as
a variable. This was done by treating individual kernels as 10 concentric
spherical shells. This process yields 10 simultaneous ordinary differential
equations. The equations for the air temperature and moisture were solved by
finite differences. Equation List 2.2 shows the modified equations for the deep-
bed drying simulation.

Equation List 2.2 Modified deep-bed equations and boundary conditions
(Hamdy and Barre, 1969).

 

. d
d: = mg(®a_®g)+l’% +(Sg+mgsw) (2.18)

i+l
@2- ___100% Z al./.mj;f0r —> i = 0,1,...,9

dt (2.19)

PM

9
m , = me.
,g z I (2.20)

 

 

dt R2 [:0 i i (2.21)
_ 301) 101) 1 80D
ms - ZR— — 3 ms +mc “ 3751? (2.22)
L = LInfg) (2.23)
D 1
R2 _ FDImg) (2.24)

19

i+l

CI. = ijafl;f0r—9i=0,l,...,9

 

. . (2.25)
./=I-I
_ p M
_ p dmg
Amu — _AyE dt (2.27)
The boundary conditions are:
9.. (1,0) = ®I (2.28)

ma(t,()) = M (2.29)
6) MOW) : (2.30)

m.=0(0,y) M0;i=0,,..I ,9 (2.31)

l

Baughman et al. (1970) expanded on the work of Hamdy and Barre
(1969). A diffusion model replaced the thin-layer equation in the logarithmic
model. The following assumptions were made:

1) Change in sensible heat of the air due to moisture gain is negligible.

2) Sensible heat required to raise the grain temperature is negligible

compared to the latent heat of moisture vaporization.

3) Sensible heat used to raise the temperature of removed water vapor to

air temperature is very small.

20

4) The grain bulk density (p) and the latent heat of vaporization (L) are
assumed not to change with grain moisture or temperature.

Using these assumptions, the heat transfer equation of Hamdy and Barre (1969)

(Equation [226]) was reduced to:

SUGQ]; : pLafi

6y 6t (2.32)

Next, Baughman et al. (1970) introduced the concept of the travel rate (Q)

of the drying front with respect to the airflow rate. Then, from Equation (2.32):

 

8T 8M
GS“ :— I "QL “T (2.33)
(2y (2})
where:
_ T. - T. 5.0
Mu _ M, L (2.34)

Substitution of Equations (2.32) and (2.33) into Equation (2.34) and simplification

by use of dimensionless variables leads to:

 

 

6C _ —1 6C
86) 1—C(0,®)aD (2.35)
where:
C_ M) _M.
Moisture ratio —> T —T

Time variable -9 G) = kt

21

LIM. -M.)kyp

Depth variable —> _ GS (T —T )

 

The results of Baughman et al. (1970) show that the diffusion model is
more accurate than the logarithmic model (i.e., the measured and computed
moisture ratios show closer agreement).

The general drying model developed by Hamdy and Barre (1969),
Baughman et al. (1970), and Barre et al. (1971) was subsequently adapted for
ear-corn drying. Internal reports of this research have been made available to
the author, but due to the confidentiality of these reports, they cannot be
incorporated into this thesis. Islam (2002,b) showed that the standard error for
predicting dryer shut-off time with the OSU model is greater than 20 h.

2.6 COB-KERNEL MOISTURE CONTENT RELATIONSHIP

During drying, the drying of the corn cob lags behind the drying of the
kernels, which affects the normal cob-kernel moisture relationship. However, the
effect is not unduly severe. The cob and kernel moisture content, if given the
chance, will equilibrate (Schmidt, 1948). A conversion chart to determine the
cob-kernel moisture relationship can be found in Schmidt (1948). In this study,
moisture content for the entire ear (i.e., cob and kernels) is used for the
laboratory data. Field data were recorded as kernel moisture content and
converted to ear moisture content using an equation regressed from the data
presented in Schmidt (1948). The conversion equation from kernel to ear

moisture content is discussed in Chapter 4.

22

CHAPTER 3

EXPERIMENTAL PROCEDURES

3.1 OVERVIEW

In the development and validation of the computer simulation model for ear-
corn drying, two primary types of experimental data were collected: field data and
laboratory data. Field data were collected in Constantine, Michigan at the
Pioneer Hi-bred International, Inc. seed production plant. The data were used in
the development and validation of the thin-layer, ear-corn drying equation and
deep-bed, ear-corn drying model. Ear corn samples taken from the research site
(at 25 to 38% [w.b.] moisture content) were also used in laboratory thin-layer
drying.

The complete data set (nsets =157, npoints =1 ,358) was separated into a
calibration set (nsets =127, npoints =1 ,206) and a validation set (nsets =30, npoims
=152). The calibration set consisted of laboratory data (nsets =65, npoints =901)
and field data (nsets =62, npoims =305). The 30 data sets used in the validation set
were removed from the set of field data using a random number generator and
were used to determine the standard error of prediction of the parameterized
thin-layer model.

3.2 FIELD EXPERIMENTATION
3.2.1 DATA COLLECTION
Data collected in Constantine, Michigan consisted of transient data for the

deep-bed drying cycle. Three drying bins were designated as research bins for

23

the MSU research team. During the drying season, which began on September
1, 2002 and ended October 30, 2002, the researchers were given control of the
three designated bins. For each drying cycle, initial and final moisture content
data, as well as transient moisture content data were collected.

To monitor drying, moisture content samples were taken at the bottom and
top of the drying bed prior to unloading. If the samples were within the
recommended moisture content range for shelling (12.5% t0.5%), the bin was
unloaded. If sample moisture contents were not within the acceptable range, the
dryer was restarted.

3.2.2 MOISTURE CONTENT SAMPLE COLLECTION

Moisture content data consisted of three sets: 1) initial moisture content,
2) transient moisture content, and 3) final moisture content. Initial moisture
content was determined by Pioneer employees during bin loading. Samples for
transient moisture content analysis were collected by MSU researchers at eight-
hour intervals during the drying cycle. Final moisture content was taken from the
moisture content metered by Pioneer employees during corn shelling.

During bin loading, random samples were shelled by Pioneer employees,
and the moisture content of these samples was measured using a Dickey-John
GAC 2000 moisture meter (Dickey-John Corp., Auburn, IL). Specifications and
operation parameters for the GAC 2000 are in Appendix C.

Two methods were employed to collect moisture content samples during
the drying cycle. Samples from the bottom of the drying bed were removed

directly from the unloading doors at eight-hour intervals. Samples to be collected

24

from the top of the drying bed were placed in plastic mesh bags during bin
loading. Mesh bags were selected for use, because they minimally disturbed the
airflow around the ear corn. After loading was complete, ropes were tied to the
sample bags. The bags were then placed on top of the drying bed in a linear
pattern at three sampling points. The bags were removed approximately every
eight hours, during the drying cycle, and ears were taken from each bag to check
moisture content. Moisture content samples were shelled from the cob and
moisture content was measured with the Dickey-John GAC 2000.

Final moisture content for each drying cycle was taken from the moisture
content determined during shelling. During shelling, moisture content was
continuously monitored using a GAC 2000 moisture meter. The final moisture
content that was recorded was the average moisture content measured for the
entire bin. In situations where the initial data showed that com was under-dried,
shelling was stopped, and airflow was returned to the unshelled corn remaining
in the bin.

3.3 LABORATORY EXPERIMENTATION
3.3.1 DATA COLLECTION

Experimentation and data analysis were carried out in the laboratory using
samples taken from the research bins in Constantine, Michigan at the start of
drying (27 to 36% moisture content, wet basis). Thin-layer tests were performed
to develop and validate the thin-layer drying equation to be used in the deep-bed

simulation of ear-corn drying.

25

3.3.2 THIN-LAYER TESTS

Thin-layer drying tests were performed in a DX-400 gravity-convection
oven (Yamato Scientific America Inc., Oragenburg, NY). Specifications for the
oven are in Appendix C. Thin-layer tests were conducted at three drying
temperatures: 35, 40, and 45°C (95, 104, and 113°F, respectively).

Before drying, the oven was set to the desired temperature and allowed to
reach steady state. To achieve airflow of 0.3 m/s specified in ASAE Standards
(2000, a), a fan was placed in the oven. The airflow was measured using an air
velocity probe for the Solomat MPM 500e (Lumidor Safety Products, Miramar,
FL). Each sample was wrapped in a plastic mesh cloth. Similar to the field tests,
this insured that no kernels broke off the ear corn during drying. Each sample
was weighed and placed in the oven. Samples were arranged in a pattern such
that no samples were placed directly over the fan. Figure 3.1 shows the pattern
of the ears on the drying rack and the mesh covering used to contain the shelled
kernels.

During drying, the weight of each sample was recorded hourly for the first
eight hours of drying. After that, samples were weighed periodically until weight
loss became negligible. At the end of the thin-layer drying test, an oven test
(103°C, 72 h) was performed to determine the final moisture content of the ear
corn (ASAE, 2000, b) (Figure 3.2). The moisture contents for the thin-layer
drying cycle were then back calculated from this value and the associated weight
changes during drying. The moisture contents and moisture ratios from the thin-

layer tests were used to develop the thin-layer drying equation.

26

 

.1 Ear corn samples in plastic mesh on oven drying rack.

3

Figure

 

Figure 3.2 Shelled corn and cobs on drying rack for 72 h drying.

27

The temperature and relative humidity were monitored in the laboratory
with a Bionaire digital thermo/hygrometer (The Holmes Group, Inc., Milford
Massachusetts). Each time the sample weights were taken, the laboratory
temperature and relative humidity were recorded. During two tests, the relative
humidity in the oven was recorded with a Solomat MPM 500e for use in the
validation of the equilibrium moisture content equation used by Sharaf-Eldeen et
al. (1980). This will be discussed further in Chapters 5. During the 35°C (95°F)
tests, temperature was recorded in the oven with a Solomat MPM 500e, because
the oven is only calibrated for temperatures greater than 40°C (104°F).

3.3.3 CALIBRATION TESTS

Ear corn samples were taken at the Constantine research location and
dried in the laboratory to determine a calibration constant for the GAC 2000 and
the PQ-100 single kernel moisture meter (Seedburo Equipment Company,
Chicago, IL). Two ears of corn for each sample were shelled and placed back in
the sample bag. The shelling and mixing of two ears from each sample reduced
the effects of individual seed moisture content variability. The individual seed
moisture content variability will be discussed later in this chapter. Moisture
content was determined via an oven test (ASAE, 2000, b).

Table 3.1 shows the calibration data for the GAC 2000 moisture meter and
the calibration bias of -0.2% (i.e., the actual moisture content is the moisture
content measured by the GAC 2000 minus 0.2%). Table 3.2 shows the

calibration data for the PQ-100 and the calibration bias of + 1.8% (i.e., the actual

28

moisture content is the moisture content measured by the PQ-100 plus 1.8%).

Specifications for the PQ-100 are in Appendix C.

Table 3.1 Calibration data for the GAC 2000 moisture meter.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Oven GAC 2000

Moisture Content Moisture Content Difference

Sample (%, w.b.) (%, w.b.) (%, w.b.)
1 16.1 17.1 -1.0
2 17.0 15.2 1.8
3 17.8 20.1 -2.3
4 17.9 17.6 0.3
5 18.4 21.7 -3.3
6 20.5 20.6 -0.1
7 21.0 25.4 -4.4
8 21.3 21.0 0.3
9 23.4 22.0 1.4
10 24.2 22.8 1.4
11 24.7 23.6 1.1
12 27.6 25.2 2.4
Average Difference -0.2

 

 

 

Table 3.2 Calibration data for the PQ-100 single-kernel moisture meter.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Oven PQ-100

Moisture Content Moisture Content Difference

Sample (%, w.b.) (%, w.b.) (%, w.b.)
1 15.3 14.7 0.6
2 16.4 14.5 1.9
3 17.3 15.9 1.4
4 17.4 15.6 1.8
5 18.2 16.7 1.5
6 18.4 16.5 1.9
7 18.5 16.5 2.0
8 18.8 16.5 2.3
9 19.2 17.3 1.9
10 20.9 18.1 2.8
Average Difference 1.8

 

 

 

29

3.3.4 SINGLE KERNEL MOISTURE TESTS

Two separate sets of single kernel moisture content data were used to
show the variability of moisture content of individual kernels on the same ear of
corn. In both tests, the PQ-100 single-kernel moisture meter was used. To
demonstrate the moisture content variability, the single-kernel moisture content
was measured for each kernel on an ear of corn. Corn kernels were shelled from
a sample one row at a time, keeping the kernels in the same order they came off
the cob. The moisture content of each individual kernel was measured and
recorded. Variability of the individual kernel moisture content will be further
discussed in Chapter 5.
3.3.5 DATA ANALYSIS

Data from the thin-layer tests were arranged in a spreadsheet in the
following order: sample code number, drying time, moisture ratio, initial moisture
content, and drying-air temperature. For the nonlinear regression, the nominal
temperatures were used for the laboratory data and the average temperatures for
each drying run were used for the field data. For the laboratory data, the
average temperature for each experiment differed from the nominal value by less
than :|:1.5°C. For the field data, the average temperature for each data set
differed from the temperature calculated by Pioneer by less than :l:1.5°C. The
complete data set, less the 30 validation sets, can be found in Appendix A.

An iterative process was used to calculate the least-squares estimates of
model parameters for the specified equation form (equation forms are discussed

in Chapter 4). The iterative process consists of the Gauss-Newton method with

30

stephalving (SAS Institute, 2001). The analytical derivatives of the prediction
formula, with respect to the parameters, are taken to calculate the least-squares
estimates of the parameters. If the analytical derivative cannot be calculated, the
numerical derivative must be calculated. The Newton-Raphson method is used
when the parameter values do not have a linear relationship; the Newton-
Raphson method utilizes the second derivatives of the prediction formula (SAS
Institute, 2001).

The nonlinear regression procedures were implemented via JMP
statistical software (SAS Institute, 2001). The Nonlinear Fit Platform (nonlinear
regression user interface in JMP) automatically calculates the derivatives of the
prediction formula with respect to the parameter values. When using the second
derivative option, JMP automatically calculates the second derivatives of the
prediction formula and uses the Newton-Raphson method (SAS Institute, 2001).

The data were imported into the JMP program along with the thin-layer
model. Initial guesses for the parameters were made before the JMP nonlinear
regression was run. The JMP software was run until the parameter values
converged. The converged parameter estimates formed the basis for the new,
thin-layer model described in Chapter 4. Table 3.3 shows the form of the
spreadsheet used in the JMP software. Columns one through five contain the
code number and input data used for the nonlinear regression. Column 6 shows

the output of the thin-layer model when using the parameter values.

31

Table 3.3 Example of JMP spreadsheet

 

Initial Thin-layer
Drying Moisture MC. Model

Code Time Ratio (%) Temp. C MRAT

0 1.0000 45.6 40.0 1.0000
1 0.9855 45.6 40.0 0.9677
2 0.9662 45.6 40.0 0.9374
3 0.9444 45.6 40.0 0.9083
4 0.9154 45.6 40.0 0.8804
5

7

8

 

 

 

 

 

 

0.8961 45.6 40.0 0.8534
0.8550 45.6 40.0 0.8023
0.8405 45.6 40.0 0.7781
22 0.6206 45.6 40.0 0.5092
25 0.5796 45.6 40.0 0.4655
45 0.3403 45.6 40.0 0.2570
53 0.2461 45.6 40.0 0.2030
72 0.1470 45.6 40.0 0.1163
94 0.0673 45.6 40.0 0.0613

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.3 shows the typical output produced by the JMP software. When
the nonlinear fit is used, the text appearing below the word “Report” tells the user
the status of a run. In the case of Figure 3.3, the data yielded converged
parameters. The iteration row shows the number of iterations and the stop limit
for the number of iterations. In the case of Figure 3.3, the total number of
iterations was 17, and the stop limit was 60. If 60 iterations are performed, and
the parameter values do not converge, the program stops running. The “Current
Value” column displays the values of the parameters while the software is

running.

32

 

 

NonfinearFfi

 

 

Control Panel

 

 

 

Repon
Converged in the Gradient

 

 

Criterion Current Stop Limit
Iteration 1 7 60
Shortening 0 1 5

 

Obj Change 5.41 15935-9 0.0000001
Prm Change 000862521 1 7 0.0000001
Gradient 1 .91 451 558-8 0.000001

 

 

 

 

 

Parameter Current Value Lock

 

 

 

 

 

 

 

 

 

 

 

 

A 533851043 l— SSE 34387505943
5 02450542753 l" N 871
.3 0148025225 r'

0 9052231415 l"
n 09102255594 I"
Edit Alpha 0.050
Convergence Criterion 0.05
rGoal SSE for CL
Solution
SSE DFE MSE RMSE
3.4387606943 866 0.0039709 0.0630147
Parameter Estimate ApproxStdErr Lower CL Upper CL
.4. -5.88861 043 203503403
El 02450542763 084725309
C 0 .1 48025225 1 49431 .01 2
0 9.062231 416 438272098
n 0 9702265594 0.01 1 1 2992

Figure 3.3 Typical output for JMP nonlinear regression.

33

The Sum of Squares Error and the number of data points used are displayed to
the right of the parameter values. Root Mean Square Error (RMSE) is shown in
the solution.

Sum of squares error (SSE) is the sum of the residual values (the
difference between actual values and predicted values) squared. As this number
gets smaller, the predictive model is more closely predicting the experimental
values. The mean squared error (MSE) is the SSE divided by the number of total
data points (n) minus 1 (n-1). As with the SSE, as the MSE decreases, there is a
closer fit between the predicted data and experimental data. RMSE, the root
mean square error, (standard error of calibration [SEC]) describes the error of the
predicted data versus the experimental data used to develop the parameter
values. When the RMSE decreases, the prediction model is more accurately

modeling the experimental data.

34

CHAPTER 4

EQUATION DEVELOPMENT

4.1 THIN-LAYER EQUATIONS

In this research, two main forms of the thin-layer drying equation were
investigated: one form recommended in the ASAE Standards (2000, a), and one
form developed by Sharaf-Eldeen et al. (1980). The form in the ASAE Standards
is a one-term model containing the drying constant (k), the time in the drying
cycle (t), and an exponent (n). The Sharaf-Eldeen equation contains two
coefficients (A, B), as well as the drying constant (k) and time (t).
4.1.1 ASAE STANDARDS THIN-LAYER MODEL

The general form of the thin-layer equation in ASAE Standards (2000, a) is

the one-term Page (1949) model:

 

MRAT: M M M=exp(—kt")

M0 _ (4.1)

An equation for the drying constant (k) was derived by Chu and Hustrulid

(1968); it has the following form:

k = a exp (flMO) (4.2)
For ear com, the following expressions were used for constants o and B:
B
a = A €XP[- —] (4.3)
' (lbs
and

35

fl: CT abs _D (4.4)

By substituting Equations (4.3) and (4.4) into Equation (4.2), the equation

for the drying parameter (k) becomes:

k : app + (CTA + D)M + 1:) (45)

(1b.)
The resulting equation for the moisture ratio is:
B
)M + — * t”

abs

abs

MRAT: eXp[— exr{A+(CT +1) (4.6)

The parameters of Equation (4.6) were estimated via nonlinear regression
of the model against the calibration set of the experimental drying data.
Be rearranging Equation (4.1) the average moisture content of the ear

corn at any time during the drying cycle can be calculated:

M: exp(—kt)*( M M)+M,, (47)

where k is given Equation (4.5).
4.1.2 SHARAF-ELDEEN THIN-LAYER MODEL

A different model to simulate thin-layer drying of ear corn was developed
by Sharaf-Eldeen et al. (1980). The model is a two-term model and incorporates

two coefficients, A and B. The form of the two-term model is:

 

_ — M
M e Z Ae—kmt + (1 _ A)e—Bk(./,l
M _ Me (4.8)

36

The value of the drying constant, ksh, in the Sharaf-Eldeen thin-layer
equation was calculated using Equation (4.2). To find the coefficients for
Equation (4.5), Sharaf-Eldeen plotted the drying parameter versus the initial
moisture content for three different air temperatures and relative humidities. By
least squares fitting of Equations (4.3) and (4.4) to the experimental data, Sharaf-

Eldeen et al. (1980) reported the following equation:

2619

 

km = exp 6.8 + (0.0195 Tum. — 9.75)MU —[ (4.9)

(lhx

A comparison of Equations (4.5) and (4.6) versus Equations (4.8) and
(4.9) will be made in Chapter 5.
4.1.3 EQUILIBRIUM MOISTURE CONTENT

In the calculation of the moisture ratio, knowledge of the equilibrium
moisture content is essential. The equation for equilibrium moisture content of
ear corn used in Equations (4.1) and (4.8) was derived by Sharaf-Eldeen as

discussed in Chapter 2. It has the form:

0.55

— ln(l — r.h.)

 

M, = 5.69 (4.10)

uhs

The validation of the equilibrium moisture content equation will be given in

Chapter 5.

37

4.2 EAR-KERNEL MOISTURE RELATIONSHIPS

It was shown by Schmidt (1948) that there is a relationship between the
kernel moisture content and the ear (cob and kernels) moisture content. The
relationship shown by Schmidt was used to develop an equation to convert the
field data (kernel moisture content) to the same form as the laboratory data (ear
moisture content). Pairs of ear and kernel moisture contents (n = 8) were read
from the graph of Schmidt (1948), and polynomial regression (R2 = 09996)

yielded the following equation:

MC , = —O.OOOZMC,‘ZW, + 0.0196 MC ,, + 0.8334MC,,,,.,,,,, — 0.5675

(4.11)
which was used to relate kernel moisture content (%, d.b.) to total ear (cob and
kernels) moisture content (%, d.b.).

4.3 PSYCHROMETRICS

To correctly model the drying process, it is necessary to model the
psychrometric relationships. The air properties that affect the drying process
include: relative humidity, humidity ratio, vapor pressure, dry-bulb temperature,
wet-bulb temperature, specific volume, and enthalpy (Brooker et al., 1992).
There are two ways to establish the psychrometric properties of air: 1)
psychrometric charts, and 2) psychrometric equations.

For simple calculations that require psychrometric properties, a
psychrometric chart can be used if two independent air properties are known.
For the computer simulation of deep-bed grain drying, it is not possible to use

psychrometric charts. For this reason, a computer program to calculate

38

psychrometric properties was developed by Lerew (1972). The following
sections will provide a short description of the importance of each of the
psychrometric properties and the associated equations in SI units. It should be
noted that the equation constants reported in Brooker et al. (1992) are only given
to three decimal places. Therefore, a more accurate psychrometric model was
developed, based on values published in ASAE Standards (2000, c), for use in
the deep-bed ear-corn drying simulation model.
4.3.1 RELATIVE HUMIDITY

Relative humidity is the ratio of the water vapor pressure in air to the
saturated water vapor pressure at the same temperature. It is particularly
important in the calculation of the equilibrium moisture content (Brooker et al.,
1992)

,5:

(4.12)

.56 [:6

4.3.2 HUMIDITY RATIO

Also known as absolute humidity or specific humidity, the humidity ratio
(W) is the mass of water vapor per unit mass of dry air. This value is used to
determine the relative humidity of the drying air, as well as the values associated

with relative humidity (Brooker et al., 1992).

 

W ¢P..
= 0.622 ‘*
PU“)? — (¢va ) (4'13)

4.3.3 VAPOR PRESSURE

39

Vapor pressure (PV) is the partial pressure exerted by the water vapor
molecules in moist air. Vapor pressure in air fully saturated with water vapor is
known as the saturation vapor pressure. The P, values are used in the
calculation of the relative humidity when given certain input values (Brooker et
al., 1992). The equation presented is for saturation vapor pressure (va).

Calculation of the vapor pressure (Pv) is discussed in Section 4.4.8.

(A+T*(B+T*(C+T*(D+T*E))))
(T*(F—G*T)) (4.14)

 

PM = R * ex

Where
273 < T (Kelvin) < 533
R = 2.2105847380E+07
A = 2740552583610 x 104
B = 9.754129373 x 101
c = -1 .46244044 x 10‘1
o = 1255753189 x 10'4
E = -4.85017 x 10'8
F = 4349028978 x 100
e = 3938107171 x 10'3
4.3.4 DRY-BULB TEMPERATURE
Dry-bulb temperature (Tdb) is the temperature shown on a normal
thermometer in air. This value, along with the wet-bulb temperature, is used to

easily determine other air properties with the psychrometric relationships

40

(Brooker et al., 1992). Dry-bulb temperature is a measured value in ear corn
drying, and therefore no equation will be presented.
4.3.5 WET-BULB TEMPERATURE

Wet-bulb temperature (wa) is the steady-state temperature of air indicated
by a thermometer with a wet wick covering the bulb in a psychrometer in a
moving air stream. This temperature, along with the dry-bulb temperature, is
used to calculate other air properties using the psychrometric relationships
(Brooker et al., 1992). Similar to dry-bulb temperature, wet-bulb temperature is a
measured value in ear corn drying. However, there is an equation to calculate
the wet-bulb temperature:

7:177 : —l— (wab _ P )+ T'uhs

3’ v (4.15)

where

_ 1006‘9254(vawb — Palm X1 + 015577R/B’M7)
06219472,, (“9

BI

 

4.3.6 SPECIFIC VOLUME
Specific volume (0) is the volume per unit mass of dry air. This value
affects the amount of power required for the fan on a drying system. Specific

density is the reciprocal of the specific volume (Brooker et al., 1992).

RUTH/vs '
101 .325 _ (¢pm ) (Lerew, 1972) (4.17)

 

where

41

Ra = Gas constant for dry air, 287.09 kg m2/(s2 kg K)
4.3.7 ENTHALPY

Enthalpy (h) is the heat content of the moist air per unit mass of dry air
above a certain reference temperature. Reference temperature is generally
inconsequential, because the difference in enthalpy is the usual value of interest.
In grain drying, the latent heat of vaporization, hfg, is the enthalpy value of
importance. This value is used in determining the burner size in a given drying

system (Brooker et al., 1992).

abs

11,, = 2502535259 — 2385.76424(T — 273.16) (4.18)

4.3.8 RELATIVE AND ABSOLUTE HUMIDITY CALCULATIONS

Due to the nature of the data collected on deep-bed ear-corn drying, it is
necessary to be able to calculate the relative humidity and absolute humidity of
the drying air given the dry-bulb and wet-bulb temperatures.

The calculation of relative humidity begins by solving Equation (4.13)
using dry-bulb temperature and wet-bulb temperature. Equations (4.14) and

(4.15) are then solved for vapor pressure:

”-10 62197419.? ]— [1006.9254(P ...—.,, meX M T11)?
.. (0 62194111,, ),,,,,)+0.15577[10069254(p T)] (419)

R m h arm

 

RPM/7 PlthT wh— db)

For ease of calculation, Equation (4.18) is broken down using three simplified

equations; A, B, and C.

A = vawb (4.198)
B = 0.62194(Hfg) Patm (4.19b)
C = 1006.9254(PVSW1J — Patm)(wa - Tdb) (4.190)

42

The resulting equation for PV becomes:

AB—CP

(11111

" _ B + 0.15577C (4'20)

 

The relative humidity is calculated using Equation (4.12) and the absolute
humidity using Equation (4.13). Table 4.1 shows the spreadsheet setup to
calculate the relative humidity and absolute humidity (values chosen are
arbitrary).

A modified FORTRAN program based on the model of Lerew (1972) has
been developed by the author to calculate psychrometric properties with either
the dry-bulb and wet-bulb temperatures or the dry-bulb temperature and relative

humidity. Syntax for the program can be found in Appendix B.

43

Table 4.1 Verification of psychrometric equations for relative humidity given wet-
bulb and dry-bulb temperature.

   
     

Constants for Saturation Pressure Enter T

   

     
  

T
Wet-Bulb

F
75.00
105.00

Kelvin
297.05
313.72

Slunns
05847380E+O7
740552583610E+04
754129373E+01
146244044
.255753189E-O4
.85017E-08

         
  
   
   
   
   
 
   
 
   
   
           

     

O7171E—03

variables are used in the calculation of

Taken from LE. Lerew 1972

1.54113E+11

  
   
   
   
 
      
 
 

91850220345
1874.51
17876

   

RH. .6812112 %

     

Abs. Hum. 1722041

44

4.4 APPLICATION AND IMPLEMENTATION OF THE THIN-LAYER MODEL

INTO THE DEEP-BED MODEL

Four partial differential equations are used in the simulation of deep-bed ear
-corn drying (Bakker—Arkema et al., 1974):

1) air temperature — air temperature at any location

2) ear corn temperature — ear corn temperature at any time

3) air humidity — air humidity at any location

4) ear corn moisture — ear corn moisture content at any time (Section 4.1)
The system of four equations cannot be solved analytically. A numerical solution
technique, such as finite differences or finite elements must be used (Brooker et
al., 1992). The focus of this thesis is the thin-layer model for ear corn moisture
content. For this research project, the deep-bed simulation model was co—
developed with a fellow student, and was based on the MSU deep-bed drying
model (Islam, 2002, a).

To simultaneously solve the partial differential equations for deep-bed
drying, it is assumed that the bed can be modeled as a series of thin layers.
Nthin short time periods (At), the air and corn temperature and the air and corn
moisture content are assumed to be constant in thin layers (Ax) of the ear corn.
When the layers form a deep bed, the output values from one layer — air humidity
ratio and air temperature — become the input values for the next layer. The
model generates output for the average moisture content, air and corn
temperature, and air humidity for all of the layers at a particular time step. Figure

4.1 shows a thin-layer within the deep bed.

45

 

 

 

/

W1 T1 Va: pa: Ca 61 Mi Cpa pp

 

 

 

Figure 4.1 Example of thin-layer in a deep-bed simulation model
(Adapted from Brooker et al., 1992).

The deep-bed model was implemented via FORTRAN. This was done for
continuity, because the original MSU drying models (Bakker—Arkema et al., 1974)
were written using FORTRAN. Figure 4.2 shows the flow diagram of the deep-
bed, ear-corn drying simulation model. Appendix B contains the FORTRAN code
for the psychrometric properties of air, the equilibrium moisture content of ear
corn, and the new thin-layer model, including the drying parameter (k), described
in Chapter 5. The complete ear-corn drying simulation model can be found in the

Ph.D. Dissertation of Md. Taufiqul Islam (Islam, 2002, b).

46

fl

ct T
Q1)
l—ln__puts

 

 

 

Unit conversion

 

 

 

 

 

Property values

 

 

 

 

 

 

Initialize starting values

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculate:
Depth Air Temperature
Ear corn denstiy Air humidity
Ear corn Temperature
Ear corn moisture content (<.\
\x
NO \\
Is ear corn lvlC. N0 ls ear corn MC. Yes Reverse 1
< Final lvl.C. < reversal IvIC. airflow
YES /
Outputs 903V?” Equation developed
”U pu S in this thesis
End) Print

 

 

 

Figure 4.2 Flow diagram of deep-bed ear-corn drying simulation model.

47

CHAPTER 5

RESULTS AND DISCUSSION

Experimental data were collected from both laboratory tests and field
tests. Laboratory experiments included equilibrium moisture content, thin-layer,
and individual kernel moisture content tests. Field experiments consisted of the
collection of moisture content data during deep-bed, ear-corn drying.

5.1 LABORATORY EXPERIMENTS
5.1.1 EQUILIBRIUM MOISTURE CONTENT

Laboratory data for the equilibrium moisture content were taken to validate
the equation for equilibrium moisture content derived by Sharaf-Eldeen (1980)
(Equation [410]). To measure equilibrium moisture content, samples were
allowed to dry until weight loss was negligible. At this time, the samples were
considered to be at equilibrium moisture content. During drying, the relative
humidity and temperature in the laboratory and oven were recorded. Table 5.1
shows a comparison of the experimental equilibrium moisture content values and
the equilibrium moisture content values predicted by Equation (4.10). The root
mean squared error (RMSE) value is 0.54. Therefore, the prediction model

predicted the equilibrium moisture content at 40°C to within :I: 0.54 d.b. 0/01.

 

1 Moisture contents in this Chapter are reported in percent dry basis, because dry basis is
generally used in engineering calculations (CIGR Handbook of Agricultural Engineering, Vol. 4,
1999)

48

Table 5.1 Comparison of experimental and predicted equilibrium moisture
contents at 40°C.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Experimental Predicted Difference
EMC (%, d.b.) EMC (%, d.b.) Difference (%) Squared

6.8 7.6 -0.8 0.64
8.3 7.6 0.7 0.49
7.6 7.6 0.0 0.00
7.5 7.6 -0.1 0.01
8.4 7.6 0.8 0.64
7.7 7.6 0.1 0.01
7.6 7.6 0.0 0.00
8.5 7.6 0.9 0.81
7.7 7.6 0.1 0.01
5.1 5.6 -0.5 0.25
5.3 5.6 -0.3 0.09
5.3 5.6 -0.3 0.09
6.3 5.5 0.8 0.64
6.0 5.7 0.3 0.09
6.1 5.7 0.4 0.16
5.6 5.7 -0.1 0.01
6.2 5.7 0.5 0.25
5.9 5.7 0.2 0.04
6.5 5.7 0.8 0.64
6.5 5.7 0.8 0.64

SSE = 5.51

MSE = 0.29

RMSE = 0.54

 

 

 

5.1.2 THIN-LAYER TESTS

Complete data from the thin-layer tests can be seen in Appendix A. An
illustrative example of the thin-layer data can be seen in Figures 5.1 and 5.2.
The samples in Figures 5.1 and 5.2 were dried at 35°C (95°F), 11.4% relative
humidity, and initial moisture contents of 38.5 and 38.4% (d.b.), respectively.

Samples were also dried at 35, 40, and 45°C (95, 104, and 113°F), in the 5 to

49

15% relative humidity range at varying initial moisture contents. Initial moisture
contents ranged from 28.6 to 60.5% (d.b.).

The equilibrium moisture content was calculated using the laboratory
conditions for each test and the psychrometric equations (see Table 5.2). For
the tests illustrated in Figure 5.1 and 5.2, the equilibrium moisture content was
7.6% (d.b.). The moisture ratio curve for Ear #1 becomes negative after 80 h of
drying; this suggests that the ambient drying conditions (i.e., the relative
humidity) may have varied slightly at the end of the drying cycle, causing the
equilibrium moisture content to fluctuate, or, more likely, the EMC equation was

simply not accurate for that particular ear of corn.

Table 5.2 Calculation of the equilibrium moisture content using laboratory
conditions, psychrometric equations, and Equation (4.10).

 

 

 

 

 

Known:
Laboratory Laboratory Oven
Temperature r.h. Temperature
22.7 °C 24.1% 358°C

 

 

Using the Lerew Psychrometric Program

 

 

 

 

 

 

 

 

 

 

 

 

Inputs Output
Temperature 22.7°C Humidity ratio 10.00411
r.h. 24.10/0
Inputs Output
Temperature 358°C r.h. I 11.39%
Humidity ratio 0.00411

 

 

Equilibrium moisture content (Equation [4.101)

Inputs Output
Temperature 358°C EMC (%, d.b.)L 7.6
r.h. 11.39%

 

 

 

 

 

 

 

 

50

 

+ Ear #1
+Ear #2

 

 

 

 

 

 

Moisture Content (%, w.b.)
a:
O

 

 

 

 

 

0 20 40 60 80 100 120
Time (h)

Figure 5.1 Moisture content versus time for two ears of corn dried in the
laboratory at 35°C (95°F) and 11.4% relative humidity.

1.0000

 

+Ear #1

0.8000 - Ear #2 -—

 

0.6000

0.4000 \\
0.2000

0.0000

 

 

Moisture Ratio

 

 

 

 

'O.2000 T I I I I I I I I I I I I I I I I I I
O 20 40 60 80 100 120

Time (h)

 

Figure 5.2 Moisture ratio versus time for two ears of corn dried in the laboratory
at 35°C (95°F) and 11.4% relative humidity.

51

Appendix A contains the same drying rate data for all the samples dried in
the laboratory. Each sample is labeled with a code number (printed in bold on
the table). In the laboratory experiments, 65 sets of data were collected. The
data sets contain 10 to 20 individual data points (totaling 901 data points),
depending on the total drying time of the experiment.

5.1.3 INDIVIDUAL KERNEL MOISTURE CONTENT

Variability in individual kernel moisture content is important. Figures 5.3
and 5.4 show the distribution of moisture content for one ear of corn harvested in
1999. Figure 5.3 shows the average axial kernel moisture content for each row
around, from tip to bottom, of one ear of corn. The kernels around the tip and
bottom of the ear have lower moisture contents, while the kernels near the

middle of the ear have higher moisture contents.

19.5

 

19.0

 

18.5

 

 

18.0

 

 

17.5

 

 

LLL All.

 

17.0:

 

 

Moisture Content (%, w.b.)

16.5:

16.0 ‘

 

 

 

 

9111

15.5

 

O 5 1O 15 20 25 30 35 40 45 50

Row Number

Figure 5.3 Average axial moisture content for each row around one ear of corn.

52

The radial variation of the average kernel moisture content can be seen in
Figure 5.4. The kernels in vertical rows one to eight have lower moisture content

then the kernels in rows nine to fourteen.

 

 

Figure 5.4 Average radial moisture content for each vertical row of kernels on
one ear of corn (center point is 16.5%, w.b., outer gridline is 18.5%,
w.b.).
This variability shows that care must be taken when determining moisture
content. If a limited number of kernels are used to determine moisture content,

the moisture content average determined may not reflect the actual average

moisture content

53

5.2 FIELD EXPERIMENTS

Data taken at the Constantine research site were used in the development
and validation of the thin-layer drying model. It was hypothesized that the bottom
layer of ear corn in the deep-bed dryer could be considered to be a thin layer
during the up-air part of drying. Figures 5.5 and 5.6 are an illustrative
comparison of two thin-layer experiments to two sets of data taken at the bottom
of the drying bin.

It was hypothesized that the top sampling points of the Constantine data can
also be considered to be a thin layer during the down-air part of drying.

Figures 5.7 and 5.8 are an illustrative comparison of two thin-layer
experiments to two sets of top-layer data. Because the sampling points on the
top of the drying bed usually showed different moisture contents due to varying
drying conditions (e.g., air channeling during up-air drying), each sampling point
was used individually for comparison in thin-layer modeling.

Based on the above comparisons, the field data were included in the
calibration and validation data sets. After the thin-layer model is described this
assumption will tested by evaluating whether there is a significant bias between
the two types of data (i.e., laboratory data and field data).

Appendix A contains the complete set of field data included in the entire data
set. Each data set is labeled with a code number and, in the case of the down-
air samples, a location number (both printed in bold on the upper left-hand side

and right-hand side, respectively, in the data tables). Field data includes the

54

drying-air temperature for each data point. In the nonlinear regression analysis,

the average temperature for each portion of the drying cycle was used.

55

 

-+- Laboratory

 

+ Field

 

 

 

 

Morsture Content (%, d b )
00
O

 

 

 

 

0 I T I I I l I I I I I I I I 1 I I I I I I I I I I I I I r 'I' I I I I

0 10 20 30 40 50 60 70
Time (h)
Figure 5.5 Moisture content versus time for field up-air bottom-layer data (375°C

[99.5°F], 34.72% relative humidity) and thin-layer laboratory data
(40°C [104°F], 24.3% relative humidity).

50

45 \ +LaboFatory _
40 +Field a
35 \\

30 '\\.\

25 \I\\

20 \I\\

15 f \a

10f

 

 

 

 

 

 

 

 

Moisture Content (%, d.b.)

 

d
5 ‘
d
u

 

 

 

 

O I ‘l I I I I I I T I I I I I I I I 1 I I I T

0 10 20 30 40 50
Time (h)

Figure 5.6 Moisture content versus time for field up-air bottom-layer data (379°C
[100.2°F], 34.89% relative humidity) and thin-layer laboratory data
(40°C [104°F], 24.3% relative humidity).

56

50

 

45 + Laboratory

, +Field
40 5 7 *
35 3

 

 

 

 

 

 

 

 

 

 

 

 

 

32‘

U 1

3°: 5 \\

:30.

5 = \l.'\

*5 25: -

8 : \

e 20-

3153

= I
10:
55
O: I I I I I I I I I I I If? T I I I I I I I I

O 10 20 30 4O 50

Time (h)

Figure 5.7 Moisture content versus time for field down-air top-layer data (394°C
[102.9°F], 11.62% relative humidity) and thin-layer laboratory data
(40°C [104°F], 24.3% relative humidity).

 

+7Laboratory —»
+ Field __

 

 

 

 

 

 

 

 

 

 

Morsture Content (%, d b )
N
O

 

 

 

 

Time (h)

Figure 5.8 Moisture content versus time for field down-air top-layer data (41 .3°C
([106.4°F], 16.17% relative humidity) and thin-layer laboratory data
(40°C [104°F], 24.3% relative humidity).

57

5.3 REGRESSION RESULTS
5.3.1 NONLINEAR REGRESSION

The complete set of calibration data (nse(s=127, npoims=1,206) was
imported to a JMP worksheet along with Equation (4.6). Table 5.3 shows an
example of the drying data used for the nonlinear regression. The Nonlinear Fit
Platform (nonlinear regression user interface in JMP) using second derivatives
was employed to solve for the coefficients A, B, C, D, and n. This procedure
used the Newton-Raphson method (JMP Statistics and Graphics Guide, Version

4,2001)

Table 5.3 Example of drying data at 40°C (104°F) and 24.3% relative humidity.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Drying Moisture Initial
Code Time(hr) Ratio M.C. (%) Temp. (K)
1 0 1.0000 45.6 313.0
1 1 0.9855 45.6 313.0
1 2 0.9662 45.6 313.0
1 3 0.9444 45.6 313.0
1 4 0.9154 45.6 313.0
1 5 0.8961 45.6 313.0
1 7 0.8550 45.6 313.0
1 8 0.8405 45.6 313.0
1 22 0.6206 45.6 313.0
1 25 0.5796 45.6 313.0
1 45 0.3403 45.6 313.0
1 53 0.2461 45.6 313.0
1 72 0.1470 45.6 313.0
1 94 0.0673 45.6 313.0

 

 

 

 

 

 

 

Eighty iterations were required by the JMP software to converge to the

following values for the parameters in Equation (4.6):

58

A -> -28.66

B —> 7947

C —> 0.2744

D -> -86.00322

n —> 0.9915

Figure 5.9 shows the JMP output for nonlinear regression to solve for the

parameter values. RMSE is the standard deviation of the residual error when
comparing the model-predicted values to the experimental values; it is also called
the standard error of calibration (SEC). The RMSE will be compared to the
standard error of prediction (SEP) for validation purposes. The SEP is calculated
using the independent validation set in the same manner the RMSE is calculated

for the calibration data set:

 

SEP = RMSE = fix” _ x~")2
(n _ 1) (5.1)

The value of the RMSE for the complete calibration data set is 0.08185.

 

This means that when using the prediction model to determine moisture ratio
values, the average expected error of the model is $008185. With moisture
ratios ranging from one to zero, this is approximately an 8% error. In the case of
Figure 5.9, the SSE is 8.04615. As the RMSE, SSE, and MSE get smaller, the
predictive equation for moisture ratio is more closely modeling the experimental

data.

59

 

 

NonflnearFfi

 

 

Control Panel

 

 

 

Stopped
Converged in the Gradient

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Criterion Current Stop Limit
Iteration 79 1 00
Shortening 0 1 5
Obj Change 7 .1 1 2601 3e-9 0.0000001
Prm Change 00002846137 0.0000001
Gradient S .72432848-8 0.000001
Parameter Current Value Look
.91. -28.65590333 r— SSE 8.0451452?81
5 79468012548 I" N 1205
1: 02743851787 I"
o -86.00322229 l"
n 09915435211 I"
Edit Alpha 0.050
Convergence Criterion 0.05
Goal SSE for CL
Solution
SSE DFE MSE RMSE

8 .0461 462781 1 201 0.0066995 0.081850?r

Parameter Estimate
-28.65590333
7946.801 2548
0 .2743851 787
43600322229
0.991 5435211

I:

DUITICD

ApproxStdErr Lower CL Upper CL
5.131 1 3055
1 604 .66594
0 03791 906
1 1 .8607088
0 .01 379777

Figure 5.9 JMP output for the parameter values of Equation (4.6).

60

 

A plot of the experimental values versus the predicted values (Equation
[46]) for the calibration data set (mats-=127, npomts=1,206) shows the relationship
for the moisture ratio (Figure 5.10). The scatter plot has a high R2 (0.947).
Further analysis on the outliers and their effect on the predictive model will be
discussed later in this section.

After the values for the equation parameters were determined, the
prediction of the k—value was examined. In order for the model to predict
moisture ratio and moisture content properly, the drying parameter (k) must
increase as temperature increases for a particular initial moisture content. Figure
5.11 shows the relationship between the temperature and the k-value at an initial

moisture content 42.9% (d.b) (30%, w.b.).

61

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0%

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62

0.06
0.055

/
/

0.04 //
0.035

0.03 /
0.025

0.02

 

 

 

 

 

k-Value

 

 

 

 

 

 

304 306 308 310 312 314 316 318 320

Temperature (Kelvin)

Figure 5.11 k-value versus temperature for Equation (4.5) at 42.9% (d.b.) initial
moisture content.

The SEP values for the moisture ratio and moisture content were
calculated using the 30 data sets removed for validation (npomts=152). For each
data set, the corresponding drying conditions were used to calculate the k-value
and the equilibrium moisture content. Equation (4.6), with the parameters
estimated from the calibration data set, was used to calculate the predicted
moisture content for each data point in the validation set, and subsequently this
value was compared to the experimental moisture content. The SEP for the
moisture content was 3.8% (d.b.); the SEP for the moisture ratio was 0.1147.

Table 5.4 shows an example of data from the validation set.

63

Table 5.4 Example of the validation set for moisture content and moisture ratio.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temp =110°F 316.3 K
R.H. = 28.44%
IMC (w.b.) = 37.7% d.b=60.6%
EMC = 13.1%
k = 0.047209
Experimental Predicted
Code # Time (h) M.C. (%, d.b.) M.C. (%, d.b.) Difference Squared
135 0 42.9 42.9 0.0 0.0
135 8 34.0 33.7 0.4 0.1
135 16 26.5 27.4 -0.8 0.7
135 21.65 15.3 24.1 -8.9 78.8
Experimental Predicted
Code # Time (h) MRAT MRAT Difference Squared
135 0 1.0000 1.0000 0.0000 0.0000
135 8 0.7028 0.6900 0.0128 0.0002
135 16 0.4509 0.4781 -0.0272 0.0007
135 21.65 0.0724 0.3694 -0.2970 0.0882

 

 

 

 

 

A further robustness check of the thin-layer equation (Equation [46]) is the

ratio of SEP divided by SEC for the moisture ratio:

SEP_ 0.1147 _14
SEC 0.08185 "

The value of 1.4 reflects good robustness of the model against the independent
validation set.

The effect of outliers in the calibration data set was further explored by
using the jackknife technique to eliminate outliers (Netter, 1993). The jackknife
technique calculates the distance of n data points from the multivariate mean.

The distance is calculated using the estimates of the mean, standard deviation,

64

and correlation for n-1 observations. The process is repeated until each data
point has been once excluded from the calculations. In this study, data points
were deemed outliers if the jackknife distance was greater than 2.5 for the
moisture ratio. As a result, 37 data points were removed as outliers and the
nonlinear regression was run on the remaining data. The resulting parameter
values were:

A -> -26.78

B -> 7380

C -> 0.2556

D -> 80205

n -> 0.9783

The SEC for the moisture ratio without the outliers reduced to 0.07773.
The resulting new parameter estimates, calculated using the modified data,
resulted in a SEP of 0.1160 for the moisture ratio and 3.8% (d.b.) for the moisture
content. Thus, the value for the SEP/SEC ratio for moisture ratio is 1.49. This
shows that the outliers do not have an effect on the data set. The complete
validation analysis for the unmodified data and the jackknife-modified data can
be found in Appendix A.

Figures 5.12 and 5.13 show the experimental moisture ratio versus the
predicted moisture ratio, and the experimental moisture content versus the
predicted moisture content, for the unmodified validation data. The R2 value for

the moisture ratio comparison was 0.8491, and for the moisture content data

65

0.9165. Figures 5.14 and 5.15 show the experimental moisture ratio versus the
predicted moisture ratio and the experimental moisture content versus the
predicted moisture content for the model based on the jackknife-modified
calibration data set, respectively. The R2 value for the moisture ratio comparison
was 0.8457, and for the moisture content data 0.9157. For both the moisture
ratio and moisture content, the R2 values are larger for the unmodified data than
for the jackknife-modified data; the unmodified data has a higher correlation.
Using the parameter values calculated with the unmodified data, thin-layer

drying Equations (4.5) and (4.6) become:

AIR/1T = €Xp(—kto'9915) (5.2)

where

k = exp — 28.66(0.2744(Ta,,, )+ —86.0032)M0 + 7—94—7—

abs

(5.3)

Thus, Equations (5.2) and (5.3) are the thin-layer drying rate model for ear
corn. The parameter values have been validated against independent field data.
Subsequently, Equations (5.2) and (5.3) will be incorporated in the deep-bed,
ear-corn drying rate program. In the following section, the newly parameterized

thin-layer model will be compared to the Sharaf-Eldeen (1980) thin-layer model.

66

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70

5.4 EQUATION COMPARISONS
5.4.1 EXPERIMENTAL DATA AND THE SHARAF MODEL

Comparison of the experimental data from this thesis to the model from
Sharaf-Eldeen et al. (1980) indicates poor predictions of moisture ratio and
moisture content at times larger than 40 hours (See Figures 5.16 and 5.17). The

experimental data shows a more rapid drying rate than predicted by the Sharaf

 

 

 

model.
1.0000
—Sharaf
0.9000 « . -
A Experimental
0.8000 -
0.7000

 

0.6000 \\
0.5000 \
0.4000 \
0.3000
\
0.2000

0.1000 1

 

 

 

Moisture Ratio

 

 

 

 

 

 

0.0000 I I I r I I I I I I I I I I I I I T I I I I I I I I I
0 20 40 60 80 100 120 140

Time(h)

Figure 5.16 Moisture ratio versus time for a comparison of the Sharaf model to
experimental data for moisture ratio dried at 40°C and 7% relative
humidity.

71

 

 

 

 

 

 

 

 

 

 

 

35.0
—Sharaf

3 30-0 2 A “Experimental"
3' :
°\; 25.0 .
E
2 20.0
C
o
o
2 15.0
B
.2
o — fl
2 100 ‘
a A
I!
"J 5.0-

0.0 d I I I I I I I I I I I I I I I I I I I I I I I I I I I

0 20 40 60 80 100 120 140

Time (h)

Figure 5.17 Ear moisture content versus time for a comparison of the Sharaf
model to the experimental data for moisture content dried at 40°C
and 7% relative humidity.

5.4.2 FRIANT AND SHARAF

In this section, the Sharaf model (Sharaf-Eldeen et al., 1980) and the new
model are compared to the experimental values. Table 5.5 shows the data in the
comparison. The drying conditions — drying-air temperature, drying-air relative
humidity, and kernel initial moisture content — are contained in the shaded cells.

The equilibrium moisture content for both the Sharaf model and the new model

was calculated using Equation (4.10). The constants of the new model2 are

labeled “Friant constants”. The constants of the Sharaf Equation are labeled

“Sharaf constants.”

 

2 For ease of comparison, the newly parameterized model is referred to as the Friant model.

72

Table 5.5 Spreadsheet used to calculate predicted moisture content, moisture

”All values for moisture content are dry basis unless otherwise stated.

ratio, and drying time using the Friant and Sharaf equations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Drying air temperature (Deg. F) = 104 = 40.00 Celsius = 313.00 [Kelvin
Drying air relative humidity (%) = 7 = 0.0700 decimal
Initial kernel moisture content (%, Ear M.C.,
w.b.) = 28.6 = 0.514 Decimal, db. EMC (w.b.)
EMC (%, d.b.) = 5.7 = 0.057 decimal, d.b. 5.4
k (Friant) = 0.035836 Sharaf constants
k (Sharaf)= 0.031999 A= 0.8459
Friant Sharaf Ear Moisture Content 8: 0.1278
Time Ear M.C. Moisture Ear M.C. Moisture %, wet basis Friant constants
(h) (%, d.b.) Ratio (%, d.b.) Ratio Friant Sharaf A= -28.6559
0 51.4 1.000 51.4 1.0000 34.0 34.0 8: 7946.80
1 49.8 0.9648 50.2 0.9727 33.2 33.4 C: 0.274385
2 48.3 0.9312 49.0 0.9463 32.6 32.9 D: -86.0032
3 46.8 0.8990 47.8 0.9207 31.9 32.3 n= 0.991544
4 45.4 0.8679 46.6 0.8959 31.2 31.8
5 44.0 0.8380 45.6 0.8718 30.6 31.3
6 42.7 0.8091 44.5 0.8485 29.9 30.8
7 41.4 0.7813 43.5 0.8259 29.3 30.3
8 40.2 0.7545 42.5 0.8040 28.7 29.8
9 39.0 0.7286 41.5 0.7828 28.1 29.3
10 37.9 0.7037 40.5 0.7622 27.5 28.8
20 28.4 0.4972 32.6 0.5880 22.1 24.6
30 21.8 0.3518 26.7 0.4602 17.9 21.1
40 17.1 0.2492 22.4 0.3660 14.6 18.3
50 13.8 0.1767 19.2 0.2964 12.1 16.1
60 11.4 0.1253 16.9 0.2446 10.3 14.4
70 9.8 0.0889 15.1 0.2058 8.9 13.1
80 8.6 0.0631 13.8 0.1765 7.9 12.1
90 7.8 0.0448 12.7 0.1541 7.2 11.3
100 7.2 0.0318 12.0 0.1369 6.7 10.7
110 6.7 0.0226 11.3 0.1233 6.3 10.2
120 6.4 0.0161 10.8 0.1125 6.0 9.8

 

 

 

 

 

 

 

 

 

 

73

 

Figure 5.18 shows a comparison of moisture content (d.b.) versus time for
the experimental data and as calculated by the two models - Sharaf and Friant
for a randomly selected data set. The Friant equation has the faster drying rate —
i.e., has the steepest curve; at 120 hours, the Friant curve is closer to the
equilibrium moisture content than is the model developed by Sharaf-Eldeen et al.
(1980). Figure 5.19 shows a comparison of the moisture ratio versus time for
experimental data and the two models.

Statistically, when comparing the Sharaf model to the validation set, the
SEP for the moisture ratio is 0.2000, which is larger than the SEP for the F riant
model (0.1147). The SEP for the moisture content was 6.7%, d.b., which is
larger than the SEP for the Friant model (3.8%, d.b.). The SEP/SEC ratio for the
Sharaf equation cannot be determined, because there are no calibration statistics
available to the author. Complete calculation of the SEP for the Sharaf model
can be found in Appendix A. The effect of the two models on the deep-bed
model will be discussed in Section 5.7.

Another comparison for the Friant and Sharaf models is to compare the
SEP values during the first half of drying (MRAT20.5) and the SEP values during
the second half of drying (MRAT<0.5) (Table 5.6).

Table 5.6 SEP values for the Friant and Sharaf models during the first half of

drying (MRAT20.5) and the SEP values during the second half of
drying (MRAT<0.5).

 

 

 

 

Friant Sharaf
MRAT M.C. (%, d.b.) MRAT MC. (%, d.b.) MRAT
>=0.5 4.2 0.1108 4.3 0.1170
<05 34 0.1204 9.0 0.2740

 

 

 

 

 

 

 

74

Table 5.6 shows that after the moisture ratio decreases below 0.5, the
Sharaf model becomes very poor at predicting the moisture ratio and moisture
content. When applying the thin-layer model to the deep-bed model, the
prediction of moisture content during the last portion of drying is particularly
important in predicting the total drying time. Table 5.6 shows that the Sharaf
model will not predict as well as the newly parameterized model during the last

portion of drying (MRAT < 0.5).

35.0

 

I Experimental

 

30.0 -

 

25.0 ‘

20.0 : X
\\ / Sharaf model
15.0 I
W

 

 

 

 

Ear Moisture Content (%, w.b.)

 

 

 

 

10.0 ‘ . - ~
1 . /
. Friant model I
5.0 ‘
0.0 ‘ I I I r T r I I I I I I I I I r I I I I I I I I I I I
0 20 40 60 80 100 120 140

Time (h)

Figure 5.18 Moisture content versus time for the two thin-layer models and the
experimental data dried at 40°C (104°F), 7% r.h.

75

1.0

 

 

0.9 - I Experimental —
0.8
0.7

\

0.5 x

0.4 \\

0 3 \\ / Sharaf model
.2 N

 

 

 

 

 

 

Moisture Ratio

 

 

 

 

 

 

0.1 I
0 0 Friant model /' M
O 20 40 60 80 100 120 140
Time (h)

Figure 5.19 Moisture ratio versus time for the two thin-layer models and the
experimental data dried at 40°C (104°F), 7% r.h.

A comparison of the time for the Friant and Sharaf models to predict
moisture contents of 22% (w.b.) and 12.5% (w.b.) is tabulated in Table 5.7. The
drying air temperatures used were 35, 37.8, 40.6, 43.3, and 461°C (95, 100,
105, 110, and 115°F); the initial moisture contents used were 35, 30, and 25%
(w.b.), and the relative humidity was 15%. For the initial ear moisture contents of
35 and 30% (w.b.), the Friant model calculates shorter times to reach the 12.5%
(w.b.) moisture content. The large times for the Sharaf model to reach 12.5%

(w.b.) at 35, 37.8, and 406°C (95, 100, and 105°F) should be noted.

76

Table 5.7 Time (h) for the moisture content in the Friant and Sharaf models to
predict 22 and 12.5% (w.b.) at different temperatures and initial
moisture contents at 15% relative humidity.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Goal Initial Ear Moisture Contents (%, w.b.)
M.C. Temp. 35 30 25
(%, w.b.) Deg. C Friant Sharaf Friant Sharaf Friant Sharaf

22.0 35.0 34 44 20 19 7 6
12.5 35.0 86 150 63 77 45 41
22.0 37.8 29 40 18 17 7 5
12.5 37.8 72 135 57 70 44 37
22.0 40.6 24 36 16 16 7 5
12.5 40.6 59 120 52 63 42 33
22.0 43.3 20 32 14 14 7 4
12.5 43.3 49 108 46 57 41 30
22.0 46.1 16 29 13 13 6 4
12.5 46.1 40 97 41 51 39 28

 

 

 

 

 

 

 

 

5.5 MODEL SENSITIVITY TO VARYING IRYING CONDITIONS

To gain a better understanding of how sensitive the newly parameterized

model is to changing conditions, the effects of the drying conditions were

examined. As the drying conditions vary — i.e., drying-air temperature, drying-air

relative humidity, and initial moisture content — the drying rate of ear corn

changes. The new thin-layer model was run using varying inputs to illustrate

these relative effects. The standard initial inputs were chosen based on a

possible normal range of inputs that may occur in actual drying. The standard

initial inputs were:

Drying-air temperature = 40°C (104°F)

Drying-air relative humidity = 20%

Initial ear-corn moisture content = 35.6% (w.b.)

77

 

To quantify the effects of the drying-air temperature and relative humidity,
the time to reach 10-percentage point moisture content reduction [from 35.6%
(w.b.) to 25.6% (w.b.)] was compared for each input condition.

As the drying-air temperature increases, the time for ear corn to reach the
10-percentage point reduction will decrease. Figure 5.20 shows the effect of the
drying-air temperature on the time to reach 25.6% (w.b.) for three temperatures:
35, 40, and 45° C. The fastest temperature at which the 10-percentage point
reduction is reached is 45°C (13 h); the slowest temperature at which the 10-
percentage point reduction is reached is 35°C (26 h).

Figure 5.21 shows the effects of the relative humidity on the time to reach
25.6% (w.b.) for three relative humidities: 15, 20, and 25%. At the lowest
humidity (15%) it takes 17 h to reach 25.6% moisture content, while at the

highest humidity (25%), it requires 19 h.

78

Ear Moisture Content (%, w.b.)

36.0

 

 

32.0 ‘

30.0 '

:\
34.0 1

\\\¥ 7......
—40 Deg. C

 

28.0 '

\\\/ {—3. D... c
\Kx7

 

i

 

26.0

24.0 ‘

 

\\ \

 

 

0

I T I I I I I I I I I I I I I I I I I I I I I I I I I I

15 20 25
Time (h)

30

Figure 5.20 Moisture content versus time to reach 25.6% ear moisture content

Ear Moisture Content (%, w.b.)

(w.b.) for the new thin-layer model at three temperatures: 35, 40,
and 45°C. Initial ear moisture content = 35.6% (w.b.), relative
humidity = 20%.

 

 

 

 

 

 

 

 

 

 

 

 

37.0
1
J
35.0 \
33.0 ‘ _
- —15% rh
.. _ 0
31.0 / 20 /0 Th _
j // \ 25% rh
N \
25.0 r I I IIIIIIIII I IIIIIIIII I IIIIIIIII
0 5 10 15 20
Time (h)

Figure 5.21 Moisture content versus time to reach 25.6% ear moisture content

(w.b.) for the new thin-layer model at three relative humidities: 15,
20, and 25%. Initial ear moisture content = 35.6% (w.b.),
temperature = 40°C.

79

To illustrate the sensitivity to initial moisture content for the new thin-layer
model, the time for each initial moisture content to reduce 10-percentage points
was analyzed. The initial ear moisture contents were 29.4, 35.6, and 41.4%
(w.b.). The time for the ear moisture content to reach 19.4, 25.6, and 31.4%
(w.b.), for each initial ear moisture content, respectively, was calculated. Figure
5.22 shows the ear moisture content versus the time to reach a 10-percentage
point reduction for each of the initial moisture contents.

In Figure 5.22, the initial moisture content of41.4% (w.b.) requires the
shortest time to reach the 10-percentage point reduction; the initial moisture
content of 29.4% (w.b.) requires the longest time. This demonstrates that higher
initial moisture contents result in a faster drying rates (i.e., it is easier to remove
water from a higher moisture content sample than from a lower moisture content
sample). This can also be seen in a direct comparison of the three drying rates3
(see Figure 5.23). The upper curve is for an initial moisture content of 41 .4%

(w.b.), and the lower curve is the lower initial moisture content of 29.4% (w.b.).

 

3 The drying rate here is defined as average percentage points of moisture (w.b.) lost per hour
[points/hour]. Drying rate will also be addressed in terms of kg of water per metric tonne of grain
perhour

80

45.0

 

40.0 ‘\

/——.29 4% IMC

 

l L

35.0 :

 

/.—35 6% IMC
/——.41 4% IMC

 

 

30.0 :

 

25.0 ‘

 

Ear Moisture Content (%, w.b.)

20.0 :

 

15.0 ‘

 

 

C

Time (h)

Figure 5.22 Ear moisture content versus time for the new thin-layer model at

three initial moisture contents: 29.4, 35.6, and 41.4% (w.b.).
Temperature = 40°C, relative humidity = 20%.

 

0.8

q

0.7 u

 

0 6 i\\ /=—25% IMC

 

 

 

 

 

 

 

 

 

 

 

1: . ,

a; : \\ / —30%lMC

3 0.5j\ //’ 5% IMC

o 0.44

1'6 1

n: :

a, 0.3 .

.5 .

E 0.2: \\
0'1 Z \
0.1 1 I T I I I r r I I I I I I I I I T I I T

0 20 40 60 80 100 120
Time(h)

Figure 5.23 Drying rate vs. time for the new thin-layer model at three initial

moisture contents: 29.4, 35.6, and 41.4% (w.b.). Temperature =
40°C, relative humidity = 20%.

81

The average drying rates are as follows:
41 .4% (w.b.) initial ear moisture content -> 0.26 points/h
35.6% (w.b.) initial ear moisture content -> 0.21 points/h
29.4% (w.b.) initial ear moisture content -9 0.16 points/h
The drying rate increases as the initial moisture content increases.

The difference between the longest time and the shortest time to reach 10-
percentage point moisture reductions across a normal range of drying conditions
can determined by inspecting Figures 5.20, 5.21, 5.22. The resulting differences
are:

Drying-air temperature (45 to 35°C) —) 13 h

Drying-air relative humidity (25 to 15%)-> 2 h

Initial moisture content (35 to 25% [w.b.]) -> 8 h
The greatest effect on time to reach a 10-percentage point moisture content
reduction results from the changing drying-air temperature.

The average amount of water lost per hour to reach the 10-percentage point
moisture content reduction from a one metric tonne (1,000 kg) sample can also
be used to evaluate which initial condition has the greatest effect in the new thin-
layer model. The units chosen for calculating drying rate for this case are
kilograms of water for an initial mass of one tonne (1 ,000-kilograms) of ear corn
per hour (i.e., kg/tonne/h). For ease of calculation, the dry basis moisture
content is used to determine the amount of water removed. Table 5.8 shows the

average drying rate and the difference between the fastest and slowest average

82

drying rate for each initial condition. The standard initial inputs for Table 5.8
were:

Drying-air temperature = 40°C (104°F)

Drying-air relative humidity = 20%

Initial ear-corn moisture content = 55.3% (d.b.)
The average amount of water removed per hour is more sensitive to the initial
moisture content than to the drying-air temperature and relative humidity in the
relevant ranges.

Table 5.8 Drying rate (kg/tonne/h) differences for each initial condition to
determine which initial condition has the greatest effect on drying rate

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(kg/tonne/h).
Temperature Drying rate Largest
(Deg. C) (kg/tonne/h) Drying rate
45 1.954 Difference
40 1.370 0.923
35 1.031
Initial M.C. Drying rate
(%, d.b.) (kg/tonne/h)
69.9 0.867 0.983
55.4 1.370
41.6 1.850
Relative Drying rate
Humidity (%) (kg/tonne/h)
25 1.322 0.126
20 1.370
15 1.447

 

 

 

Table 5.8 suggests that the initial moisture content has the greatest effect on
the predicted water removal rate, while inspection of Figures 5.22, 5.23, and 5.24
suggests that the drying-air temperature has the greatest effect on drying time.

These effects suggest that in the modeling of thin-layer drying, accurate

83

determination of the drying-air temperature and the initial moisture content is
important in predicting the drying time of ear corn. The effect of the drying-air
relative humidity is relatively small compared to the effects of the drying-air
temperature and initial moisture content. This is contrary to deep-bed drying, in
which the relative humidity does have a significant effect on the total drying time
(Islam, 2002, b).
5.6 HYBRID EFFECTS

To determine if there was a bias caused by hybrid type, analysis of variance
(ANOVA, o=0.05) was run on the residuals for the moisture ratio and the
moisture content from the independent validation set. The hybrid information for
the validation data set was designated with a special letter, to protect confidential
genetic information. There were nine hybrids in the validation set, letters A
through I. Table 5.9 shows the hybrids, number of sampling points for each
hybrid, and the bias between the new thin-layer model and the experimental data
for that hybrid.

Table 5.9 Bias of the hybrid effect on the moisture ratio (a) and the moisture
content (b) (NS = not significant at q = 0.05).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Number Bias Number Bias
Hybrid Of Samples (MRAT) Hybrid Of Samples (%, d.b.)

A 18 005056 A 18 NS
8 13 008945 B 13 NS
C 16 0.05392 C 16 2.1143
D 11 NS D 11 NS
E 11 NS E 11 NS
F 38 NS F 38 0.9722
G 12 NS G 12 NS
H 10 NS H 10 NS
l 22 NS I 22 NS

Average = 00287 Average = 1.54

(a) (b)

84

When analyzing the bias for the hybrid effect on the moisture ratio prediction,
hybrids A, B, and C did have a significant bias. When analyzing the hybrid
effects on the moisture content, hybrid C (again) and hybrid F showed a
significant bias from the model. While it should be noted that certain hybrids
might dry slightly faster/slower than average, the bias resulted in only a relatively
small error.

5.7 THIN-LAYER EFFECTS ON THE DEEP-BED MODEL

Use of the new thin-layer model or the Sharaf model in the deep-bed ear-
corn drying model also has an effect on the drying times - air reversal and dryer
shut-off times — and on the final moisture content gradient (i.e., the difference
between the average moisture content at the top and bottom of the deep bed).
Air reversal time is the time at which the airflow is switched from up-air to down-
air (see Figure 1.1 explanation). Dryer shut-off time is the time at which the ear
corn being dried has reached the desired moisture content of 12.5% 10.5%
(w.b.). Table 5.10 shows the drying parameters used to compare the effect of
the new thin-layer and Sharaf thin-layer models on the deep-bed ear-corn drying
model (Islam, 2002, a). The table shows the air reversal times, dryer shut-off

times, and the final moisture content gradient.

85

in the deep-bed ear-corn drying model.

Table 5.10 Comparison of the reversal time, dryer shut-off time, and final
moisture content gradient for the Friant and Sharaf thin-layer models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Air Temp Air Temp
Before After Bed Static Reversal
Reversal Reversal Depth Pressure M.C. Final M.C.
(Deg. F) (Deg. F) (ft) (in H20) (%, w.b.) (%, w.b.)
95 105 9 2 22 12.5
Initial Moisture Contents (%, w.b.)
Ambient Ambient Test # M.C.
Temp. rh 1 35
(Deg. F) (%) 2 30
65 65 3 25
Friant Sharaf
Final M.C. Final M.C.
Drying Gradient Gradient
Test# Stage Time (h) (%, w.b.) Time (h) (%, w.b.)
1 Reversal 51 0.2 53 1.2
Shut-off 93 120
2 Reversal 30 0.8 27 2.9
Shut-off 75 69
3 Reversal 12 1.3 9 4.0
Shut-off 65 41

 

 

 

 

 

 

 

 

This table shows the marked effect that the thin-layer model can have on the
deep-bed ear-corn drying model. In Section 5.4.2, the difference in the SEP for
the new thin-layer and Sharaf thin-layer models was shown to be relatively large.
Table 5.10 shows that the dryer shut-off time and final moisture content gradient
in the deep-bed ear-corn drying model are sensitive to the changes in the thin-

layer model. In comparing the deep-bed results using the two different thin-layer

86

models, differences in the predicted drying times were as large as 1.5x, and

differences in the moisture content gradient were as large as 2.5x.

87

CHAPTER 6

CONCLUSIONS

The thin-layer drying of ear corn was investigated in order to parameterize
a model that accurately predicts the drying rate of the product. To parameterize
the new thin-layer drying model for ear corn, four main steps were taken:

1) Experiments were performed to collect data on thin-layer drying.

2) Psychrometric equations were modified to obtain accurate parameter

values in the moisture equilibrium and drying rate equations.

3) A five parameter, single term thin-layer model was parameterized with
the experimental data and validated against and independent set of
field data.

4) The newly developed thin-layer model was inserted and tested in the
MSU deep-bed, ear-corn drying model.

The standard error of calibration (SEC) of the new thin-layer model was
0.08185. Validation of the model against the independent field data showed a
standard error of prediction (SEP) for the moisture ratio of 0.1 147 (equivalent to
3.8% (d.b.). The ratio of the SEP to SEC gave a value of 1.4, showing the new
model to be reasonably robust.

The coefficients of the new thin-layer drying model (Equations [5.2] and
[5.31) for ear corn are:

A = -28.66

B = 7947

88

C = 0.2744
D = -86.0032

n = 0.9915

When comparing this model to the previously published Sharaf model
(Sharaf-Eldeen et al., 1980) the SEP for the new model was 3.8% (d.b.), while
the SEP for the Sharaf model was 6.7% (d.b.). Additionally, when evaluating the
first half (MRAT .2 0.5) and second half (MRAT < 0.5) of drying separately, the
new model had an SEP of 4.2 and 3.4% (d.b.), for each half of drying,
respectively, while the Sharaf model had an SEP of 4.3 and 9.0% (d.b.), for each
half of drying, respectively. This shows that during the second portion of drying
(MRAT < 0.5) the new model predicts the moisture content much more
accurately than the Sharaf model.

When comparing the effects of the new model and the previously
published model of Sharaf-Eldeen (1980) on the deep-bed ear-corn drying
model, a relatively large difference in the SEP resulted in relatively large effects
on the deep-bed model. This suggests that the deep-bed ear-corn drying model
is very sensitive to the thin-layer model.

An illustration of the sensitivity of the new thin-layer model to initial
conditions showed that both the drying-air temperature and initial moisture
content of the ear corn have a marked effect on the drying times and rates.
Conversely, in the deep-bed model, the relative humidity has a significant effect

(Islam, 2002, b).

89

CHAPTER 7

RECOMMENDATIONS FOR FUTURE STUDY

The recommendations for future study are:
1) Test the new thin-layer model with larger temperature, initial moisture
content, and relative humidity ranges.
2) Validate the deep-bed model to see “big picture" impact of the new thin-

layer model.

90

REFERENCES

91

LIST OF REFERENCES

American Society of Agricultural Engineers (a). 2000. ASAE Standards 2000:
Standards, Engineering Practices, Data. Standard S448 DEC99: Thin-
Layer Drying of Grains and Crops. American Society of Agricultural
Engineers, St. Joseph, MI.

American Society of Agricultural Engineers (b). 2000. ASAE Standards 2000:
Standards, Engineering Practices, Data. Standard S3522 Dec97:
Moisture Measurement — Unground Grain and Seeds. American Society
of Agricultural Engineers, St. Joseph, MI.

American Society of Agricultural Engineers (c). 2000. ASAE Standards 2000:
Standards, Engineering Practices, Data. Data: Psychrometric Data.
American Society of Agricultural Engineers, St. Joseph, MI.

American Society of Heating, Refrigerating, and Air-Conditioning Engineers.
1992. ASHRAE Psychrometric Chart No. 1 (SI units). American Society
of Heating, Refrigerating, and Air-Conditioning Engineers, Atlanta, GA.

Bakker-Arkema, F.W., L.E. Lerew, S.F. De Boer, M.G. Roth. Research Report
from the Michgan State University Agricultural Experiment Station: Grain
Dryer Simulation. Michigan State University Experimentation Station, East
Lansing, MI.

Barre, H.J., G.R. Baughman, M.Y. Hamdy. 1971. Application ofa Logarithmic
Model to Deep-Bed Drying of Grain. Transactions of the ASAE 14(6):
1061-1064.

Baughman, G.R., M.Y. Hamby, H.J. Barre. 1970. Analog Computer Simulation
of Deep-Bed Drying of Grain. Paper No. 70-326. ASAE St. Joseph, MI.

Biotechnology and Development Monitor. 2001. Hybrids: The Techniques.
Online Publication.
http://www.biotech-monitor.nI/1902.htm

Brooker, D.B., F.W. Bakker—Arkema, C.W. Hall. 1992. Drying and Storage of
Grains and Oilseeds. Van Nostrand Reinhold, New York, New York.

Cabrera, E. 2001. Personal communication. Pioneer Hi-Bred International, Inc.
Johnston, IA.

Chu, S., A. Hustrulid. 1968. General Characteristics of Variable Diffusivity
Process and the Dynamic Equilibrium Moisture Content. Transactions of
the ASAE 11(5): 709-710, 715.

92

CIGR — The International Commission of Agricultural Engineering. 1999. CIGR
Handbook of Agricultural Engineering, Vol. 4: Agro Processing
Engineering. American Society of Agricultural Engineers, St. Joseph, MI.

Copeland, L.O., and MB. McDonald. 2001 .Principles of Seed Science and Seed
Technology, Fourth Edition. Kluwer Academic Publishers, Norwell, MA.

Council for Biotechnology Information. 2000. Online Publication
www.whybiotech.com

Hamdy, M.Y., H.J. Barre. 1969. Theoretical Analysis and Simulation of Deep-
bed Drying of Grain. Paper No. 69-328. ASAE St. Joseph, MI.

Heiniger, R.W., J.F. Spears, D.T. Bowman, E.J. Dunphy. 2002. “Crop
Management.” Online Publication.
http://plymouth.ces.state.nc/cropsci/cornguide/Chapter2.html

Henderson, J.M., and SM. Henderson. 1968. A Computational Procedure for
Deep-Bed Drying Analysis. Journal of Agricultural Engineering Research
13(2): 1968.

Holman, JP. 1997. Heat Transfer 8th Edition. McGraw-Hill, New York, New
York.

Hunter, J. 2002. Personal Communication. Pioneer Hi-Bred International, Inc.
Johnston, IA.

Islam, Md. T. (a). 2002. Personal Communication. Michigan State University,
East Lansing, MI.

Islam, Md. T. (b). 2002. “The Drying Rate of Ear Corn in Deep-Beds.”
Dissertation, to be published. Michigan State University, 2002.

Lauer, J. 2001. “Corn Breeding: A Brief History of Com Breeding in the USA." 4
May Online Publication.
httpzllcorn.agronomy.wisc.edu/FlSC/Corn/ Corn.htm

Laws, N and J.L. Parry. 1983. Mathematical Modeling of Heat and Mass
Transfer in Agricultural Grain Drying. Proceeding of the Royal Society of
London. Series A, Mathematical and Physical Sciences. Volume 385,
Issue 1788 (Jan. 8, 1983), 167-187.

Lerew, L.E. “A FORTRAN Psychrometric Model.” Master’s Thesis. Michigan
State University, 1972.

93

Lewis, W.K. 1921. The Rate of Drying Solid Materials. Journal of Industrial
Engineering 13(5): 427-432.

Li, H., and V. Morey. 1984. Thin-Layer Drying of Yellow Dent Corn.
Transactions of the ASAE: 581-858.

Monsanto Company. 2001. Biotech Basics. Online Publication.
www.biotechbasics.com

Mourad, M., M. Hemati, and C. Laguerie. 1996. A New Correlation for the
Estimation of Moisture Diffusivity in Corn Kernels from Drying Kinetics.
Drying Technology 14 (3&4), 873-894.

Netter, J., W. Wasserman, G.A. Whitmore. 1993. Applied Statistics, Fourth
Edition. Allyn and Bacon, Boston, MA.

Page, C. “Factors Influencing the Maximum Rate of Drying Shelled Corn in
Layers.” Master’s Thesis. Purdue University. 1949.

Parti, M, and l. Dugmanics. 1990. Diffusion Coefficient for Corn Drying.
Transactions of the ASAE 33(5): 1652-1656.

SAS Institute Inc. 2001. JMP® Statistics and Graphics Guide, Version 4. SAS
Institute Inc. Cary, NC.

Schmidt, J.L. 1948. How to Reduce Ear Corn to Bushels of Shelled Corn.
Agricultural Engineering July 1948: 294 — 296.

Sharaaf—Eldeen, Y.L., J.L. Blaisdell, M.Y. Hamdy. 1980. A Model for Ear Corn
Drying. Transactions of the ASAE 23(5): 1261-1265, 1271 .

Thompson, T.L., R.M. Peart, and G.H. Foster. 1968. Mathematical Simulation of
Com Drying - A New Model. Transactions of the ASAE 11: 582-586.

Tolaba, M.P., R.J. Aguerre, and C. Suarez. 1997. Modeling Cereal Grain Drying
with Variable Diffusivity. Cereal Chemistry 74(6): 842-845.

University of Wisconsin. 2001. Grain Crops Production and Management: Corn
Breeding. Online Publication.
http://corn.agronomy.wisc.edu/FISC/Corn/CropBreedingBiotechnology.htm

USDA: Economic Research Service. 2000. Farm Income and Costs: Farm

Income Estimates. Online Publication.
www.ers.usda.gov/Briefing/Farmlncome/FIUS_txt.htm

94

APPENDICES

APPENDIX A Experimental Data and Validation Tables

APPENDIX B FORTRAN Code

APPENDIX C Equipment Specifications

95

APPENDIX A

Experimental Data and Validation Tables

96

Data Tables for MSU Postharvest Laboratory thin-layer data

Data sets 1-21: Dried at 40 Deg. C, 24.3% rh

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 2
Time M.C. M.C. M.C.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 31.3 1.0000 26.8 1.0000 28.7 1.0000
1 31.1 0.9835 26.4 0.9725 28.6 0.9924
2 30.7 0.9615 26.0 0.9451 28.3 0.9723
3 30.3 0.9368 25.5 0.9066 28.0 0.9471
4 29.8 0.9038 25.0 0.8682 27.5 0.9168
5 29.4 0.8818 24.4 0.8297 27.1 0.8916
7 28.6 0.8350 23.8 0.7858 26.6 0.8563
8 28.3 0.8185 23.3 0.7528 26.2 0.8337
22 23.7 0.5683 18.7 0.4507 22.3 0.5892
25 22.8 0.5216 17.9 0.4013 21.4 0.5413
45 16.9 0.2494 12.6 0.1047 15.9 0.2464
53 14.3 0.1422 11.3 0.0333 14.1 0.1582
72 11.4 0.0295 8.8 -0.0931 10.4 -0.0082
94 9.0 -0.0613 7.4 -0.1590 8.3 -0.1014
4 5
Time M.C. M.C. M.C.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 31.6 1.0000 27.8 1.0000 26.4 1.0000
1 31.4 0.9874 27.6 0.9852 26.2 0.9888
2 31.1 0.9655 27.3 0.9615 25.9 0.9664
3 30.7 0.9404 26.9 0.9348 25.6 0.9440
4 30.1 0.9090 26.4 0.9022 25.2 0.9104
5 29.8 0.8870 26.0 0.8725 24.8 0.8805
7 29.1 0.8462 25.4 0.8340 24.1 0.8319
8 28.7 0.8274 25.1 0.8132 23.8 0.8095
22 24.4 0.5921 21.1 0.5554 19.8 0.5331
25 23.5 0.5481 20.3 0.5109 19.1 0.4883
45 17.5 0.2689 15.5 0.2411 14.4 0.2044
53 15.6 0.1904 14.0 0.1641 12.9 0.1222
72 11.5 0.0335 10.6 -0.0019 10.0 -0.0347
94 9.1 -0.0543 8.5 -0.0998 8.3 -0.1206

 

 

 

 

 

 

 

97

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 8 9
Time M.C. M.C. MC.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 27.6 1.0000 25.0 1.0000 25.3 1.0000
1 27.5 0.9907 24.7 0.9804 25.1 0.9795
2 27.3 0.9721 24.4 0.9489 24.8 0.9557
3 26.9 0.9473 23.9 0.9136 24.4 0.9250
4 26.5 0.9164 23.5 0.8782 23.9 0.8909
5 26.0 0.8854 23.0 0.8428 23.6 0.8602
7 25.4 0.8420 22.4 0.7957 23.0 0.8159
8 25.1 0.8204 22.2 0.7760 22.7 0.7920

22 21.1 0.5664 18.4 0.4971 18.9 0.5192

25 20.4 0.5199 17.7 0.4460 18.2 0.4714

45 15.6 0.2505 13.1 0.1513 13.8 0.1850
53 13.9 0.1637 11.9 0.0767 12.4 0.1032
72 10.5 -0.0066 9.4 -0.0687 9.7 -0.0503
94 8.0 -0.1212 7.9 -0.1552 8.1 -0.1389

10 11 12
Time MC. MC. M.C.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 24.3 1.0000 28.3 1.0000 26.8 1.0000
1 24.1 0.9786 28.2 0.9878 26.4 0.9751
2 23.7 0.9486 27.8 0.9603 25.8 0.9252
3 23.4 0.9186 27.4 0.9327 25.6 0.9128
4 22.9 0.8801 26.9 0.8991 25.1 0.8754
5 22.5 0.8459 26.5 0.8747 24.6 0.8422
7 21.9 0.7988 25.9 0.8349 24.0 0.7965
8 21.7 0.7816 25.6 0.8135 23.6 0.7674

22 18.0 0.4990 21.4 0.5567 18.9 0.4641

25 17.3 0.4477 20.6 0.5109 18.0 0.4101

45 13.1 0.1565 15.7 0.2418 12.8 0.1111
53 11.8 0.0752 14.0 0.1593 11.3 0.0363
72 9.4 -0.0747 10.8 0.0064 8.9 -0.0883
94 8.0 -0.1603 8.4 -0.0975 7.4 -0.1589

 

 

 

 

 

 

 

98

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

13 14 15
Time M.C. ‘ M.C. M.C.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 29.3 1.0000 34.0 1.0000 28.7 1.0000
1 29.0 0.9834 33.7 0.9871 28.3 0.9770
2 28.6 0.9570 33.4 0.9661 27.8 0.9397
3 28.2 0.9272 32.9 0.9418 27.2 0.9024
4 27.8 0.8907 32.4 0.9127 26.6 0.8622
5 27.1 0.8809 32.0 0.8901 28.1 0.8249
7 26.4 0.8146 31.3 0.8529 25.3 0.7790
8 26.0 0.7914 31.0 0.8335 24.9 0.7532

22 21.0 0.5000 26.1 0.5944 19.9 0.4604

25 20.2 0.4537 25.2 0.5523 19.1 0.4116

45 14.7 0.1822 18.9 0.2873 13.8 0.1446
53 13.1 0.1080 16.9 0.2146 12.2 0.0700
72 17.4 0.3113 12.7 0.0875 9.2 -0.0620
94 15.8 0.2352 9.5 00359 7.5 -0.1338

18 17 18
Time MC. MC. M.C.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 31.7 1.0000 32.8 1.0000 28.3 1.0000
1 30.9 0.9500 32.3 0.9790 28.0 0.9748
2 30.7 0.9351 31.8 0.9496 27.5 0.9433
3 30.0 0.8978 31.3 0.9223 27.0 0.9086
4 29.4 0.8578 30.7 0.8886 28.5 0.8739
5 28.8 0.8251 30.2 0.8613 28.0 0.8393
7 28.0 0.7802 29.6 0.8235 25.3 0.7951
8 27.5 0.7527 29.2 0.8048 24.9 0.7668
22 21.7 0.4579 24.5 0.5830 20.0 0.4768
25 20.6 0.4080 23.6 0.5188 19.1 0.4284
45 14.4 0.1432 17.4 0.2520 13.8 0.1490
53 12.6 0.0732 15.5 0.1764 12.2 0.0702
72 9.5 -0.0417 11.4 0.0251 9.2 -0.0653
94 7.7 -01041 8.4 -00737 7.3 01441

 

 

 

 

99

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

19 20 21
Time M.C. MC. M.C.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 25.8 1.0000 31.5 1.0000 30.5 1.0000
1 25.4 0.9674 31.0 0.9714 30.1 0.9721
2 24.9 0.9282 30.5 0.9381 29.5 0.9380
3 24.4 0.8890 29.9 0.9024 28.9 0.9009
4 23.8 0.8466 29.3 0.8887 28.3 0.8637
5 23.2 0.8042 28.7 0.8334 27.7 0.8265
7 22.6 0.7585 28.0 0.7906 28.9 0.7801
8 22.2 0.7259 27.6 0.7891 26.4 0.7522

22 17.4 0.4028 22.3 0.4930 21.2 0.4872

25 18.5 0.3440 21.3 0.4431 20.2 0.4176

45 11.5 0.0471 15.3 0.1813 14.8 0.1605
53 10.1 -0.0280 13.5 0.1099 12.9 0.0923
72 8.0 0.1422 10.1 -0.0187 9.6 0.0409
94 6.7 -02075 8.0 -0.0925 7.4 01214

 

 

 

 

 

 

 

100

 

Data sets 22-28: Dried at 40 Deg. C, 7% rh

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

22 23 24 25
Time M.C. Moisture M.C. Moisture M.C. Moisture M.C. Moisture
(h) (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio
0 27.7 1.0000 27.0 1.0000 25.5 1.0000 26.6 1.0000
1 27.4 0.9803 26.5 0.9683 25.0 0.9728 26.1 0.9704
2 26.9 0.9541 25.9 0.9321 24.5 0.9417 25.4 0.9310
3 26.5 0.9278 25.5 0.9094 24.0 0.9107 24.8 0.8966
4 25.9 0.8983 24.9 0.8778 23.5 0.8796 24.3 0.8670
5 25.6 0.8786 24.4 0.8461 22.9 0.8446 23.8 0.8375
6 24.8 0.8359 24.0 0.8234 22.5 0.8213 23.3 0.8079
7 24.6 0.8228 23.5 0.7963 22.0 0.7941 22.8 0.7833
8 24.2 0.8031 23.1 0.7782 21.4 0.7591 22.4 0.7587
22 19.1 0.5472 17.9 0.5156 16.4 0.4911 17.2 0.4927
51 11.6 0.2256 10.7 0.1986 10.3 0.2036 10.2 0.1873
70 9.5 0.1469 9.3 0.1443 9.2 0.1570 8.8 0.1282
94 7.9 0.0878 7.9 0.0900 7.7 0.0948 7.4 0.0741
118 6.9 0.0517 7.0 0.0583 7.0 0.0638 6.6 0.0445
140 5.8 0.0156 5.9 0.0175 6.5 0.0443 5.9 0.0199
162 5.7 0.0091 5.8 0.0130 5.8 0.0172 5.5 0.0051
Final 0.0 0.0 0.0 0.0
28 2'7 28
Time MC. Moisture M.C. Moisture Time M.C. Moisture
(h) (%, w.b.) Ratio (%, w.b.) Ratio (h) (%, w.b.) Ratio
0 34.0 1.0000 37.7 1.0000 0 24.8 1
1 33.3 0.9653 37.4 0.9839 2.5 23.2 0.893916
2 33.1 0.9560 36.7 0.9553 22 16.2 0.494335
3 32.5 0.9283 36.1 0.9285 27 14.6 0.416541
4 31.9 0.8982 35.5 0.9000 46 10.4 0.211446
5 31.2 0.8658 34.9 0.8732 73 8.1 0.108898
6 30.7 0.8427 34.4 0.8517 94 7.4 0.080609
7 30.1 0.8172 33.9 0.8321 99 7.2 0.073537
8 29.9 0.8057 33.6 0.8178 117.5 6.5 0.041712
22 23.9 0.5604 27.6 0.5909 123 6.4 0.038176
51 15.2 0.2666 17.6 0.2855 141 6.0 0.020495
70 12.5 0.1880 14.6 0.2087 147.5 5.9 0.016959
94 9.1 0.0931 8.9 0.0747
118 7.7 0.0584 7.5 0.0443
140 6.7 0.0330 6.5 0.0229
162 6.1 0.0168 6.1 0.0139
Final 0.0 0.0

 

 

 

 

 

 

101

 

Data sets 29-37: Dried at 35 Deg. C, 11.4% rh

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

29 30 31
fime MC. Moisture MC. Moisture MC. Moisture MC. Moisture
(h) (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio
0 27.8 1.0000 27.8 1.0000 28.0 1.0000 24.1 1.0000
1 27.0 0.9498 27.0 0.9536 27.1 0.9412 23.4 0.9464
2 26.3 0.9087 26.4 0.9179 26.4 0.8993 22.8 0.9062
3 25.6 0.8677 25.8 0.8821 25.7 0.8615 22.2 0.8659
4 25.1 0.8357 25.4 0.8571 25.1 0.8279 21.8 0.8347
5 24.5 0.8038 24.8 0.8250 24.5 0.7943 21.2 0.7989
6 23.9 0.7718 24.4 0.8000 24.1 0.7691 20.9 0.7766
7 23.4 0.7399 24.0 0.7750 23.5 0.7398 20.5 0.7497
24.5 15.5 0.3474 17.0 0.4178 15.9 0.3620 14.4 0.3788
27.5 14.6 0.3063 16.2 0.3821 15.0 0.3200 13.6 0.3386
32 13.2 0.2470 14.9 0.3214 13.5 0.2571 12.6 0.2805
48 9.9 0.1101 11.4 0.1714 10.4 0.1269 10.0 0.1465
53 9.2 0.0827 10.6 0.1393 9.7 0.1017 9.6 0.1241
55.3 8.9 0.0690 10.3 0.1250 9.4 0.0892 9.3 0.1107
72 7.7 0.0233 8.9 0.0714 8.2 0.0430 8.2 0.0571
76.5 7.4 0.0142 8.7 0.0607 8.0 0.0346 8.0 0.0437
79.5 7.2 0.0051 8.6 0.0571 7.9 0.0304 7.8 0.0347
97.5 6.6 -0.0177 7.8 0.0285 7.2 0.0052 7.1 0.0035
103 6.3 -0.0269 7.6 0.0214 7.1 0.0010 6.9 -0.0055
Final 0.0 0.0 0.0 0.0
33 34 35 36
Time MC. Moisture MC. Moisture MC. Moisture MC. Moisture
(h) (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio
0 28.0 1.0000 27.1 1.0000 27.8 1.0000 25.5 1.0000
1 27.2 0.9515 26.3 0.9491 27.1 0.9540 24.7 0.9484
2 26.6 0.9175 25.8 0.9151 26.5 0.9195 24.2 0.9122
3 26.1 0.8835 25.1 0.8769 25.9 0.8812 23.6 0.8761
4 25.6 0.8544 24.6 0.8472 25.4 0.8544 23.1 0.8451
5 25.1 0.8252 24.1 0.8175 24.9 0.8238 22.6 0.8141
6 24.6 0.8010 23.7 0.7920 24.4 0.7969 22.2 0.7883
7 24.2 0.7767 23.3 0.7665 23.9 0.7701 21.8 0.7625
24.5 17.3 0.4272 16.4 0.4057 16.9 0.4100 15.7 0.4165
27.5 16.4 0.3835 15.6 0.3675 16.0 0.3678 15.0 0.3752
32 15.2 0.3301 14.3 0.3081 14.6 0.3065 13.8 0.3184
48 11.7 0.1796 10.9 0.1553 10.9 0.1495 11.0 0.1790
53 11.0 0.1505 10.3 0.1298 10.1 0.1188 10.5 0.1532
55.3 10.6 0.1359 9.9 0.1128 9.9 0.1073 10.1 0.1377
72 9.1 0.0776 8.5 0.0576 8.4 0.0498 9.0 0.0861
76.5 8.9 0.0679 8.3 0.0492 8.2 0.0422 8.8 0.0758
79.5 8.7 0.0631 8.1 0.0402 8.0 0.0345 8.7 0.0706
97.5 7.8 0.0291 7.3 0.0110 7.2 0.0039 8.0 0.0396
103 7.7 0.0242 7.1 0.0025 7.1 0.0000 7.8 0.0344
Final 0.0 0.0 0.0 0.0

 

102

 

 

 

37

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time MC. Moisture
(h) (%, w.b.) Ratio
0 24.3 1.0000
1 23.6 0.9467
2 23.0 0.9111
3 22.5 0.8755
4 22.0 0.8400
5 21.6 0.8103
6 21.2 0.7860
7 20.7 0.7570
24.5 14.7 0.3954
27.5 14.1 0.3599
32 13.0 0.3006
48 10.4 0.1643
53 9.8 0.1346
55.3 9.6 0.1228
72 8.4 0.0635
76.5 8.3 0.0576
79.5 8.0 0.0457
97.5 7.4 0.0161
103 7.2 0.0042
Final 0.0

 

 

 

 

103

Data Sets 38-46: Dried at 45 Deg. C, 6.98% rh

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

38 39 40 41
Time MC. Moisture MC. Moisture MC. Moisture MC. Moisture
(h) (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio
0 27.2 1.0000 23.5 1.0000 25.8 1.0000 25.9 1.0000
1 26.3 0.9491 22.3 0.9208 24.9 0.9402 25.0 0.9435
2 25.4 0.8983 21.3 0.8528 23.8 0.8761 24.1 0.8905
3 24.4 0.8378 20.0 0.7736 22.6 0.8078 23.1 0.8304
4 23.4 0.7870 18.9 0.7057 21.6 0.7523 22.2 0.7810
5 22.8 0.7520 18.3 0.6661 20.9 0.7139 21.6 0.7456
6 22.1 0.7170 17.5 0.6208 20.1 0.6711 20.8 0.7033
7 21.5 0.6852 16.9 0.5868 19.6 0.6412 20.3 0.6750
24.5 13.5 0.3164 9.9 0.2133 11.6 0.2569 12.8 0.3076
47.5 8.2 0.1065 7.3 0.0888 7.4 0.0818 8.1 0.1098
50 7.8 0.0906 7.0 0.0775 7.2 0.0732 7.8 0.0956
72.5 6.2 0.0302 6.1 0.0379 6.0 0.0262 6.3 0.0391
78.5 6.0 0.0239 5.9 0.0265 5.8 0.0177 6.1 0.0320
96 5.4 0.0048 5.5 0.0096 5.3 0.0006 5.6 0.0109
98.5 5.3 0.0016 5.4 0.0039 5.3 0.0006 5.6 0.0109
104 5.3 -0.0016 5.3 -0.0018 5.2 -0.0037 5.4 0.0038
126.5 4.8 -0.0175 5.3 -0.0018 4.8 -0.0207 5.0 -0.0103
150 4.5 -0.0270 4.9 -0.0187 4.5 -0.0293 4.7 -0.0245
168 4.3 -0.0366 4.9 -0.0187 4.3 -0.0378 4.5 -0.0315
Final 0.0 0.0 0.0 0.0
42 43 44 45
Time MC. Moisture MC. Moisture MC. Moisture MC. Moisture
(h) (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio (%, w.b.) Ratio
0 27.4 1.0000 26.4 1.0000 25.5 1.0000 26.5 1.0000
1 26.6 0.9551 25.5 0.9457 24.7 0.9484 25.7 0.9516
2 25.8 0.9069 24.6 0.8915 23.9 0.9007 24.9 0.9069
3 24.7 0.8492 23.5 0.8281 22.9 0.8412 23.9 0.8474
4 23.9 0.8043 22.5 0.7739 22.0 0.7895 23.0 0.7990
5 23.3 0.7722 21.8 0.7332 21.5 0.7578 22.4 0.7617
6 22.6 0.7369 20.9 0.6880 20.8 0.7181 21.7 0.7245
7 22.1 0.7080 20.3 0.6563 20.3 0.6903 21.2 0.6984
24.5 14.4 0.3518 11.7 0.2538 13.0 0.3249 13.4 0.3262
47.5 9.1 0.1368 7.6 0.0865 8.3 0.1185 8.7 0.1288
50 8.7 0.1207 7.4 0.0774 7.9 0.1026 8.4 0.1177
72.5 7.0 0.0598 6.2 0.0322 6.3 0.0390 7.0 0.0618
78.5 6.7 0.0501 5.9 0.0232 6.1 0.0311 6.7 0.0507
96 6.2 0.0309 5.4 0.0051 5.6 0.0112 6.2 0.0320
98.5 6.1 0.0277 5.4 0.0051 5.5 0.0073 6.2 0.0320
104 6.0 0.0245 5.3 0.0005 5.4 0.0033 6.0 0.0246
126.5 5.5 0.0084 4.9 -0.0135 5.0 -0.0126 5.6 0.0097
150 5.2 -0.0044 4.6 -0.0266 4.7 -0.0245 5.4 0.0023
168 5.0 -0.0108 4.5 -0.0311 4.4 -0.0364 5.1 -0.0089
Final 0.0 0.0 0.0 0.0

 

 

 

 

 

104

 

 

46

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time MC. Moisture
(h) (%, w.b.) Ratio
0 27.2 1.0000
1 26.3 0.9498
2 25.4 0.8960
3 24.3 0.8385
4 23.4 0.7883
5 22.8 0.7560
6 22.1 0.7198
7 21.6 0.6914
24.5 13.5 0.3147
47.5 8.4 0.1138
50 8.0 0.0995
72.5 6.5 0.0420
78.5 6.2 0.0313
96 5.7 0.0133
98.5 5.7 0.0133
104 5.5 0.0062
126.5 5.1 -0.0082
150 4.8 -0.0189
168 4.6 -0.0261
Final 0.0

 

 

 

 

105

Data sets 47-65: Dried at 40 Deg. C, 12.1% rh

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

47 48 49 so
Time MC. MC. MC. MC.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 23.9 1.0000 25.2 1.0000 22.2 1.0000 24.8 1.0000
1 22.8 0.9209 24.7 0.9709 21.6 0.9485 24.3 0.9679
2 23.3 0.9548 24.2 0.9345 20.7 0.8840 23.7 0.9295
3 22.8 0.9209 23.5 0.8908 20.2 0.8454 23.4 0.9038
4 22.1 0.8757 23.0 0.8543 19.5 0.7938 22.9 0.8718
5 21.5 0.8304 22.5 0.8252 18.8 0.7423 22.2 0.8289
8 21.0 0.7965 21.7 0.7742 18.4 0.7185 21.9 0.8077
7 20.6 0.7739 21.3 0.7524 16.5 0.5877 21.4 0.7756
8 20.1 0.7400 21.1 0.7378 18.3 0.5748 21.0 0.7500

51 52 53 54
Time MC. MC. MC. MC.

(11) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 25.9 1.0000 25.0 1.0000 27.4 1.0000 28.2 1.0000
1 25.7 0.9847 24.7 0.9791 28.9 0.9646 27.9 0.9819
2 25.2 0.9541 24.2 0.9457 26.2 0.9222 27.4 0.9528
3 24.8 0.9234 23.7 0.9122 25.4 0.8798 28.7 0.9093
4 24.4 0.8979 23.2 0.8830 24.8 0.8444 26.3 0.8911
5 23.8 0.8822 22.8 0.8537 24.2 0.8091 25.8 0.8585
8 23.5 0.8417 22.4 0.8287 23.7 0.7808 25.3 0.8331
7 23.0 0.8111 22.0 0.8038 23.2 0.7525 24.9 0.8113
8 22.6 0.7907 21.6 0.7785 22.8 0.7313 24.5 0.7895

55 56 57 58
Time MC. MC. MC. MC.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 29.3 1.0000 24.4 1.0000 30.1 1.0000 29.3 1.0000
1 28.9 0.9792 24.0 0.9742 30.0 0.9898 28.9 0.9807
2 28.4 0.9515 23.6 0.9433 29.4 0.9590 28.4 0.9498
3 27.9 0.9238 23.1 0.9072 28.9 0.9317 27.6 0.9073
4 27.4 0.8926 22.6 0.8762 28.4 0.9044 27.3 0.8880
5 28.8 0.8614 22.1 0.8401 27.9 0.8771 26.7 0.8533
8 28.4 0.8372 21.6 0.8092 27.5 0.8532 25.9 0.8108
7 25.9 0.8129 21.2 0.7834 27.0 0.8293 25.7 0.8031
8 25.5 0.7887 20.9 0.7627 26.6 0.8088 25.2 0.7780

 

 

 

 

 

106

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time MC. MC. MC. MC.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 29.7 1.0000 30.5 1.0000 23.8 1.0000 24.7 1.0000
1 29.2 0.9703 29.9 0.9673 22.8 0.9319 24.2 0.9625
2 28.4 0.9259 29.2 0.9313 21.8 0.8637 23.4 0.9099
3 27.7 0.8873 28.5 0.8920 20.9 0.8041 22.6 0.8574
4 27.0 0.8487 28.0 0.8625 20.4 0.7700 21.9 0.8124
5 26.5 0.8221 27.3 0.8265 19.5 0.7104 21.2 0.7673
6 25.9 0.7924 26.8 0.8003 18.8 0.6678 20.8 0.7448
7 25.2 0.7568 26.2 0.7708 18.2 0.6252 20.2 0.7073
8 24.9 0.7390 25.7 0.7479 17.6 0.5912 19.8 0.6847

Time MC. MC. MC.

(h) (%, w.b.) MRAT (%, w.b.) MRAT (%, w.b.) MRAT
0 26.2 1.0000 24.9 1.0000 24.5 1.0000
1 25.7 0.9667 24.5 0.9734 24.1 0.9677
2 24.8 0.9085 23.8 0.9309 23.4 0.9246
3 23.8 0.8502 23.1 0.8831 22.8 0.8815
4 21.4 0.7088 22.6 0.8512 22.3 0.8492
5 22.2 0.7504 21.9 0.8034 21.6 0.8062
6 21.6 0.7171 21.5 0.7769 21.2 0.7792
7 21.0 0.6838 21.0 0.7503 20.7 0.7469
8 20.4 0.6505 20.6 0.7237 20.3 0.7200

 

 

 

 

 

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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141

APPENDIX B

FORTRAN Code

142

program MOISTURECONTENT

!********Ear Corn Equilibrium Moisture Content Calculator******
IDeveloped by Nick Friant 11/19/01

!This program was developed to calculate the equilibrium moisture
lcontent of ear corn given the drying air temperature and relative

Ehumidity.
Write(*,*)'******Equilibrium Moisture Content Calculator******'
WRITE(*,*)

69 WRITE(*,*)
WRITE(*,*)'ENTER THE DRYING AIR TEMPERATURE (DEG. F)‘
READ (*-*) TF
WRITE(*,*)
WRITE(*,*)'ENTER THE DRYING AIR RELATIVE HUMIDITY (%)'
READ (*-*) RH
WRITE(*-*)
RH=RH/lOO
TK=((S.O/9.0)*(TF-32))+273
EMC=5.69*((—(LOG(1-RH))/TK))**O.55

900

EMC=EMC*lOO
WBEMC=(lOO*EMC)/(lOO+EMC)

WRITE(*,*)

WRITE(*,*)'THE EQUILIBRIUM MOISTURE CONTENT IS (%, d.b.)', EMC
WRITE(*,*)

WRITE(*,*)'THE EQUILIBRIUM MOISTURE CONTENT IS (%, W.B.)', WBEMC

WRITE(*,*)'RUN AGAIN? (Y/N)‘

READ 900, REPLY

IF (REPLY.EQ.'Y'.OR.REPLY.EQ.'y') GOTO 69
FORMAT (A)

END

143

program emc
!********** Equilibrium Moisture Content of Bar Corn **********

EDeveloped spring 2000 by Nick Friant revised 10/18/01

lThis program will determine the equilbrium moisture content (EMC)
!of ear corn based on varying the drying air temperature or the
ldrying air relative humidity. This program provides the data to
ldevelop a curve for the EMC when one of the two variables is held
!constant and the other is varied by the given step size.

WRITE(*,
WRITE(*, '*******EMC CALCULATOR FOR VARYING INPUTS*******'
WRITE(*
96 WRITE(*, 'ENTER THE DRYING-AIR TEMPERATURE (DEG. F)‘
READ <* T
WRITE(*
WRITE(*
READ (
WRITE(*
WRITE(* 'ENTER THE PARAMETER TO BE VARIED (T/RH)
READ 900, REPLY
WRITE(* *)
WRITE(* *)
READ (*, *)x
WRITE(* *)
T=(5.0/9.0))*(T-32)+273.1
RH=RH/lOO
IF(REPLY.EQ.'T'.OR.REPLY.EQ.'t') THEN
GOTO 38
ELSE
GOTO 40
ENDIF
38 DO 69, T=273,T,X
EMCDB=5.69*((-(LOG( 1- RH) /T)) **O.55
EMCWB=(100*(EMCDB*100))/(lOO+(EMCDB*lOO))
WRITE(*,*)'THE EMC IS (%,W.B.)', EMCWB
WRITE(*-*)'AT (KELVIN) ', T
PAUSE
69 CONTINUE

40 DO 41, RH=O,RH,X

'ENTER THE DRYING-AIR RELATIVE HUMIDITY (%)'
RH

*
*
*
Vk
*
*
'k
*

*

)
)
)
)
)
)
)
)
*)
*)

'ENTER THE STEP SIZE (DECIMAL OF PERCENTAGE FOR RH)‘

EMCDB=S.69*((-(LOG(l—RH))/T))**O.55
EMCWB=(100*(EMCDB*100))/(100+(EMCDB*100))
WRITE(*-*)'THE EMC IS (%,W.B.)', EMCWB
WRITE(*,*)'AT (KELVIN) ', T
PAUSE

41 CONTINUE
WRITE<*,*)

WRITE(*,*) 'RUN AGAIN? (Y/N)

READ 900, REPLY

IF(REPLY.EQ.'Y'.OR.REPLY.EQ.'y') GOTO 96
900 FORMAT (A)

END

144

PROGRAM DRYPARAM
!**********Drying Parameter, k, Calculator**********
lRevised 2/12/02 By Nick Friant

!This program uses the temperature and initial moisture content to
lcalculate the drying parameter k.

REAL k, MC

WRITE(*,*)

WRITE(*,*)'**********DRYING PARAMTER k CALCULATOR**********'
WRITE(*-*)

WRITE(*,*)'ENTER THE TEMPERATURE (DEGREES F)‘

READ (*,*) Y

WRITE(*,*)

WRITE(*,*)'ENTER THE INITIAL MOISTURE CONTENT (%, W.B.)'
READ (*,*) Z

WRITE(*,*)

A=—28.65590333

B=7946.8012548

C=O.2743851787

D=-86.0032229

T=((5.0/9.0)*(Y-32.0))+273

MC=((100*Z)/(lOO-Z))/lOO

k=EXP(A+(C*T+D)*MC+(B/T))

WRITE(*,*)'DRYING PARAMTER k=', k

END

145

520

program AIRPROPS

**************** Air properties ***************

Development started 4/25/01 by Nick Friant

This program will calculate the properties of air.

It will initially be used to determine the density of air

at different temperatures and relative humidities.

Other properties may be added.

Calculation of relative humidity given wet—bulb and dry-bulb
temperatures added 6/19/01. Code follows SI code developed by
Bakker et al. Advances in Cereal Chemistry and Technology
Volume II, 1978. MSU TS2120.A3, pp.1-90.

'*************** AIR pROpERTIES ***************|

'WHAT TWO VALUES ARE KNOWN?‘
WRITE(*,* '
WRITE(*,*
WRITE(*,*
READ 900, REPLY

IF(REPLY.EQ.'1') THEN

GOTO 52

ELSE

GOTO 96

ENDIF

THIS PORTION OF THE PROGRAM CALCULATES THE

RELATIVE HUMIDTY OF AIR GIVEN THE DRY- AND

WET-BULB TEMPERATURES. EONS WERE DEVELOPED FROM

ASAE STANDARDS, L.E.LEREw AND BAKKER-ARKEMA ET AL.

WRITE(*,*)

WRITE(*-*)'ENTER THE DRY-BULB TEMPERATURE (DEG F)‘

READ(*,*) TDB

WRITE(*,*)

WRITE(*,*)'ENTER THE WET-BULB TEMPERATURE (DEG F)’

READ(*,*) TWB

WRITE(*,*)

CONVERT DEG F TO KELVIN

TDBK= (5.0/9 O)*(TDB-32.0)+273.l6

TWBK= (5.0/9.0)*(TWB-32.0)+273.l6

CALCULATE H"fg BASED ON EON IN ASAE STANDARDS USING WET—BULB TEMP
HFG=2502535.259-2385.76424*(TWBK—273.l6)

CALCULATE SATURATION VAPOR PRESSURE USING WET—BULB, BASED ON
PSYCHROMETRIC PROGRAM DEV. BY BAKKER—ARKEMA ET AL.

EON FROM ASAE STANDARDS

FOR DRY-BULB AND WET—BULB TEMPERATURE'

)
)
)
)
)
)
) 1
)‘2 FOR DRY-BULB TEMPERATURE AND RELATIVE HUMIDITY'
)

DATA R, A, B, C, D, E, F, G/.2210584739E08, -.274055258361E05,&
.9754129373E02, -.l462440044, .l255753189E-03, —.4850171032E-O7,&
.43490287800E01, .3938107141E-02/
PVSWB=R*EXP((A+TWBK*(B+TWBK*(C+TWBK*(D+TWBK*E))))&

/(TWBK*(F-G*TWBK)))

CALCUALTE SATURATION VAPOR PRESSURE USING DRY-BULB,
SAME REF. AS ABOVE.

NECESSARY TO CALCULATE THE RELATIVE HUMIDITY

146

PVSDB=R*EXP((A+TDBK*(B+TDBK*(C+TDBK*(D+TDBK*E))))&
/(TDBK*(F—G*TDBK)))

CALCULATE VAPOR PRESSURE USING DRY- AND WET—BULB.
SAME REP. AS ABOVE.

PATM=IOI325 Pa

X=PVSWB

Y=O.62194*HFG*101325
Z=IOO6.9254*(X-101325)*(TWBK—TDBK)
PV=(X*Y—Z*101325)/(Y+O.ISS77*Z)

CALCULATE RELATIVE HUMIDY PROM ASAE STANDARDS
RH=(PV/PVSDB)*IOO

CALCULATE AIR HUMIDITY RATIO BASED ON ASAE STANDARDS
W=(.622*PV)/(101325—PV)

WRITE(*-*)

WRITE(*,*)'LATENT HEAT OF VAPORIZATION, H"fg (J/KG)’, HFG
WRITE(*,*)'WET-BULB SATURATION VAPOR PRESSURE (Pa) ', PVSWB
WRITE(*,*)'DRY-BULB SATURATION VAPOR PRESSURE (Pa) ', PVSDB
WRITE(*,*)'VAPOR PRESSURE (Pa) ’, PV
WRITE(*,*)'RELATIVE HUMIDITY (%) ', RH
WRITE(*,*)'HUMIDITY RATIO ', W
PAUSE

GOTO 722

THIS PORTION OP THE PROGRAM CALCULATES THE DENTSITY OP AIR GIVEN
THE TEMPERATURE AND RELATIVE HUMIDITY.

EONS ARE ADAPTED PROM ASAE

STANDARDS, L E.LEREw (1972) AND BROOKER et al. (1992)
'DRYING & STORAGE OP GRAINS AND OILSEEDS'

WRITE(*,*)

WRITE(*,*)'ENTER THE TEMPERATURE (DEG F)‘

READ(*,*) TF

WRITE(*,*)

WRITE(*,*) 'ENTER THE RELETIVE HUMIDITY (%)'

READ(*,*) RH

WRITE(*,*)

WRITE(*,*)

CONVERT TEMPERATURE FROM DEG P TO KELVIN
TK=(5.0/9.0)*(TF-32.0)+273.16

CONVERT RH TO DECIMAL

RH=RH/IOO

CALCULATE SATURATION PRESSURE BASED ON

ASAE STANDARDS AND L.E.LEREw (1972)

USES SAME R, A, B, C, D, E, P, G, AS ABOVE.
PS=(R*EXP((A+TK*(B+TK*(C+TK*(D+TK*E))))/(TK*(F—G*TK))))/IOOO
CALCULATE AIR HUMIDITY RATIO BASED ON ASAE STANDARDS
W=.622*(RH*PS/(lOl.325—RH*PS))

CALCULATE SPECIFIC VOLUME OP AIR BASED ON SASE STANDARDS
V=((287.09*TK)/(IOI.325-(RH*PS)))/IOOO

CALCULATE AIR DENSITY

RHOA=1/V

WRITE(*,*) 'TEMPERATURE (K) ', TK
WRITE(*,*) 'SATURATION PRESSURE (KPA) ', PS
WRITE(*,*) 'HUMIDITY RATIO (KG/KG) ', W

147

WRITE(*,*) ‘SPECIFIC VOLUME (M‘3/KG) ' V
WRITE(*,*) ’AIR DENSITY (KG/M‘3) ', RHOA
PAUSE
69 CONTINUE
WRITE(*,*)
722 WRITE(*,*) ‘ENTER NEw DATA? Y/N'
READ 900, REPLY
IF<REPLY.EQ.'Y'.OR.REPLY.EQ.'y') GOTO 520
900 PORMAT(A)
END

148

program dryr8

!**********Thin-layer Drying of Bar Corn**********

!Developed by Nicholas R. Friant 2/27/02 Revised 3/25/02

lThis is a main program with subfuctions to determine the average
lmoisture content of ear corn at any time during thin—layer drying.
IEar M.C. is entered in % wet basis, converted to dry basis for
lcalculation and converted back to wet basis for output.

!1.The main program of dryr8 give the average moisture content of
lear corn at any given time during thin—layer drying.

REAL MC, MCWB
REAL MAVG, MRAT

REAL K, N

WRITE(*, *)

WRITE(*, *)'*******THIN- LAYER EAR CORN MOISTURE CALCULATOR*******'
96 WRITE(*, *)

WRITE(* *)'ENTER THE DRYING TIME (HOURS)'

READ (*-*)TI

WRITE(*, *)

WRITE(* *)'ENTER THE TIME STEP (HOURS)'

READ (*,*)X

WRITE(*, *)

WRITE( *)'ENTER THE INITIAL MOISTURE CONTENT (%, w.B.)'

READ (* *) MCWB

WRITE( ,*)

WRITE( *) ENTER THE DRYING- AIR RELATIVE HUMIDITY (%)'

READ (* *)RH

WRITE(*,*)

WRITE(*,*)'ENTER THE DRYING-AIR TEMPERATURE (DEG. F)‘

READ (*-*)TF

WRITE( *)

lConstants for Friant's Equation
A=-28.65590333
B=7946.8012548
C=O.2743851787
D=-86.00322229
N=O.9915435211

lConversion of input to the correct form
RH=RH/IOO
MC=(100*MCWB)/(lOO-MCWB)
TC=(TF-32)*(5.0/9.0)
TK=TC+273

lCalculation of the equilibrium moisture content
EMC=5.69*((~(LOG(I-RH))/TK))**0.55
EMC=EMC*IOO
EMCWB=(IOO*EMC)/(IOO+EMC)

lClaculation of the drying parameter K
K=EXP(A+(C*TK+D)*(MC/lOO)+(B/TK))

149

me

lCalculation of the average moisture content at any given time
DO 69, TI=O,TI,X
MAVG=(EXP(-K*(TI**N))*((MC/100)—(EMC/100))+(EMC/lOO))*lOO
WBMAVG=(lOO*MAVG)/(IOO+MAVG)
MRAT=(MAVG—EMC)/(MC-EMC)

WRITE(* *)
WRITE(*, *)'THE INITIAL EAR MOISTURE CONTENT IS ',MC
WRITE(*, *)'THE DRYING PARAMTER K IS ‘,K
WRITE(*, *)'THE EMC DRY BASIS IS ',EMC
WRITE(*, *)'THE EMC WET BASIS IS ',EMCWB
WRITE(*, *)'THE AVERAGE EAR MOISTURE CONTENT DRY BASIS IS',MAVG
WRITE(* *)’THE AVERAGE EAR MOISTURE CONTENT WET BASIS IS',WBMAVG
WRITE(* ,*)'THE MOISTURE RATIO IS ',MRAT
PAUSE

69 CONTINUE
WRITE(*,*)

WRITE(*,*)'RUN AGAIN WITH NEW INPUTS? (Y/N)

READ 900, REPLY

IF(REPLY.EO.'Y'.OR.REPLY.EQ.'y') GOTO 96
900 FORMAT (A)

END

lGlossary

EA,B,C,D,N —> Constants in the Friant Equation

lTI —>Total drying time in hours

EX —>Time step taken during the drying cycle

1MCWB —>Inital moisture content, percent wet basis

ERH —>Drying air relative humidity, percent

lTF ->Drying air temperature, degrees Fahrenheit

EMC —>Initial ear moisture content converted to dry basis

ITC —>Drying air temperature converted to degrees Celcius

lTK ->Drying air temperature converted to Kelvin

EEMC —>Equilibrium moisture content, determined as a decimal,
! converted to a percent for use in Friant Equation
EEMCWB —>Equilibrium moisture content converted to wet basis
1 for ease of understanding output

1K ->Drying paramter

IMAVG —>Average ear moisture content, dry basis,of ear corn at any ti

EWBMAVG —> Average ear moisture content, wet basis, of ear corn

! at any time
!MRAT ->Moisture ratio at any time during the drying cycle

150

APPENDIX C

Equipment Specifications

151

Equipment Specifications

PQ-100 Single Kernel Moisture Meter
(Seedburo Equipment Company, Chicago, Illinois)

Application: Corn

Measuring principal: DC resistance

Display: LED display

Temperature sensor: Thermistor

Data output: Printer hardcopy

Number of kernels settable: 11 to 599 kernels (1 kernel increments)

Measuring range: 9 to 40% (wet basis) at 20° C

Operating temperature: 5°C to 40°C

Measuring speed: 100 kernels per minute

Power supply: AC 120 Volts, 60 Hz

Dimensions: Main body V 240 x 330 x 380 mm,
Controller -> 120 x 245 x 55mm

Weight: Main body -) 18kg

Controller -> 6509

Yamato DX-400 Gravity Drying Oven
(Yamato Scientific American, Incorporated, Orangeburg, New Jersey)

Operating temperature range: 40°C to 300°C
Temperature adjustment accuracy: 110°C (at 260°C)
Temperature distribution accuracy: 18° C at 300°C
Time to reach maximum temperature: 60 min.

Temperature control system: PlD controlled by microcomputer

152

. Temperature setting system: Digital setting system by A and V keys
. Operation mode: Fixed temperature operation

. Additional functions: temperature preset function

. Heater: Iron — chrome wire heater

. System capacity: 1.36kW

. Control of heater circuit: TRlAC zero cross system

0 Sensor: Platinum resistance bulb (Pt 100(2)

. Interior lining: Stainless Steel SUS304

. Safety systems: Self-diagnostic functions, circuit breaker, alarm buzzer
. Internal dimensions: 17.7 x 16.1 x 15.7” (449.6 x 408.9 x 398.8 mm)
. External dimensions: 21.6 x 21.6 x 28.7" (548.6 x 548.6 x 729 mm)

. Internal capacity: 2.6 ft3 (0.7362 m3)

. Shelf/ Shelf brackets: 2 sets

. Electrical capacity: 115VAC, 2A

. Weight: 84 lbs. (38.1 kg)

Grain Analysis Computer, Model GACZOOO

(DICKEY-John Corporation, Auburn, Illinois)
. Supply Voltage: 85VAC to 264VAC, 48-62Hz at 0.4A maximum
. Operating temperature: 5°C to 45°C (41°F to 113°F)
. Grain temperature limits: 0°C to 50°C (32°F to 122°F)

. Weight: 11.8 kg (26lbs.)

153