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6/01 cJClRC/DateDuepes-sz

THE DESIGN OF A REGULATED LOW TEMPERATURE ENVIRONMENT FOR
STORING BIOLOGICAL SAMPLES

By

Monica Widjaya

A THESIS

Submitted to
Michigan State University
In partial fulfillment of the requirements
For the degree of

MASTER OF SCIENCE
Department of Mechanical Engineering

2002

ABSTRACT

THE DESIGN OF A REGULATED LOW TEMPERATURE ENVIRONMENT FOR
STORING BIOLOGICAL SAMPLES

By

Monica Widjaya

The purpose of this research is to design, fabricate, and test a thermally controlled
environment (0°C to -10°C) for holding biological samples in a low temperature
incubator. In regards to this design, twelve boxes made with various materials are built
to hold the biological samples and stabilize the temperature. It is important to choose
materials that can provide temperature uniformity within the samples. In addition, a
temperature controller system is used to regulate the temperature of the biological
samples between 0°C to -10°C. During the process of designing the twelve boxes, a
mathematical modeling is used to attempt to improve the design. This mathematical
modeling is used to change the thickness of the walls within the box in order to optimize
the design.

After optimizing the design of the box, the twelve boxes are tested during
conditions of automatic defrost, opening the incubator door, and opening the incubator
door and lid of the box at the same time. The results show that the biological sample in
these twelve boxes are able to maintain a regulated set temperature between 0°C to -10°C
during the automatic defrost condition. In addition, the biological samples are able to
maintain a steady temperature for at least three minutes during the opening incubator
door, and opening the incubator door and lid of the box at the same time. These results

meet the requirements that were requested by the Center of Microbial Ecology.

ACKNOWLEDGMENTS

I would like to give my sincere gratitude to my advisor, Dr. John J. McGrath, for
providing this opportunity as well as his encouragement and understanding. Along with
my advisor,I would like to thank Dr. Craig W. Somerton and Dr. Ahmed Naguib for
serving on my advisory committee. Furthermore, I would like to give my special
appreciation to Theron J. Hicks for building the controller temperature system. Also, I
would like to give my extreme gratitude to the Microbial Ecology Department in
Michigan State University for their support. Finally, I would like to thank my family as

well as my friends for their support.

iii

TABLE OF CONTENTS

LIST OF TABLES .............................................................................. vi

LIST OF FIGURES ............................................................................... vii
Chapter 1

INTRODUCTION ............................................................................... 1

1.1 Literature Search ...................................................................... 1

1.2 Objective ................................................................................ 5

1.3 The Importance of this Research ...................................................... 7

1.3.1 Defining the Problem .......................................................... 7

1.3.2 How to Solve the Problem .................................................... 9

1.3.3 Why this Research is Unique ................................................. 10
Chapter 2

THEORY ........................................................................................ 12

2.1 Definition of Heat Transfer ........................................................... 12

2.2 Natural Convection .................................................................... 13

2.3 Conduction .............................................................................. 15

2.3.1 The Thermophysical Properties of Matter .................................. 16

2.3.2 One-Dimensional Steady State Conduction ................................ 18

2.3.3 One-Dimensional Transient State Conduction ............................. 22

2.4 Capacitor and Resistor Relationship for a Sinusoidal Voltage Source ......... 27
Chapter 3

DESIGN ......................................................................................... 30

3.1 Choosing the Correct Materials ...................................................... 31

3.2 Temperature Controller ................................................................ 34

3.3 Mathematical Modeling ............................................................... 35

3.3.1 Mathematical Modeling with Temperature Controller Disabled ......... 36

3.3.2 Mathematical Modeling with Temperature Controller is Enabled ....... 50

3.3.3 Sensitivity of Design Parameters .............................................. 57

3.4 Design Optimization .................................................................... 62
Chapter 4

FABRICATION AND TESTING PROCEDURE .......................................... 63

4.1 Fabrication Process ..................................................................... 63

4.2 The Testing Procedure for Data Collection ......................................... 72
Chapter 5

RESULTS AND DISCUSSION ............................................................... 75

iv

Chapter 6

CONCLUSION .................................................................................. 85
Chapter 7

SUGGESTIONS FOR FUTURE RESEARCH .............................................. 88
APPENDICES .................................................................................... 9O
BIBLIOGRAPHY ............................................................................. 132

LIST OF TABLES

Table 1 - Typical Values of the Convection Heat Transfer Coefficient

Table 2 - Range of Thermal Conductivity at Normal Temperatures and Pressures
Table 3 - Properties Values for Insulation Materials

Table 4 — Comparison between Power Output vs. Aluminum Bottom Temperature
Table 5 - Dimensions of Each Material of the Box

Table 6 - Instruction Manual for Operating the Temperature Controller

Table 7 - Procedure to Operate the Data Acquisition Software

Table 8 - Set Temperature for Box 1, Box 2, and Box 3 (Petri Dishes)

Table 9 - Set Temperature for Box 4 — Box 12 (Cyro Vials)

Table 10 -Temp Difference between Set and Sample Temperature (Petri Dishes)
Table 11 - Temp Difference between Sample and Set Temperature (Cyro Vials)

Table 12 - Temp Difference between Sample and Set Temperature Using
New Voltage Reference Equation

Table 13 - Temperature Error for the Sample at Different Locations in the Box

Table 14 - The Amount of Time for the Boxes to Maintain Temperature Stability
during Opening the Incubator Door

Table 15 - The Amount of Time for the Boxes to Maintain Temperature Stability
during Opening the Incubator Door and Lid of the Box

vi

14

17

32

56

70

73

74

76

77

78

78

79

81

82

83

LIST OF FIGURES

Figure 1 - Temperature Difference between each Shelf of the Incubator
Figure 2a - Temperature Distribution through Plane Wall

Figure 2b - Equivalent Thermal Circuit for a Plane Wall

Figure 3a - Temperature Distribution for a Series Composite Wall
Figure 3b - Equivalent Thermal Circuit for a Series Composite Wall
Figure 3c - Single-Lump Heat Capacity Analysis

Figure 5 - A Hydraulic First-Order System

Figure 6 - Sinusoidal Voltage

Figure 7 - Sinusoidal Voltage after Reducing Resistor Values

Figure 8 - Sinusoidal Voltage after Reducing Capacitor Values

Figure 9 - Box with Three Coordinate Directions

Figure 10 - Composite Wall for the Box in x-direction

Figure 11 - Electrical Circuit Representation for Composite Wall in x-direction

Figure 12a - Styrofoam Modeling vs. Measurement during Automatic Defrost
Condition (Non Heater — x Direction)

Figure 12b - Aluminum Modeling vs. Measurement during Automatic Defrost
Condition (Non Heater — x Direction)

Figure 12c - Styrofoam Sample Holder Measurement vs. Modeling during
Automatic Defrost (Non Heater — x Direction)

Figure 12d - Water Measurement vs. Modeling during Automatic Defrost (Non
Heater — x Direction)

Figure 12e - Incubator Temperature during Automatic Defrost
(Non Heater — x Direction)

vii

9O

19

20

21

21

23

26

27

28

28

37

38

38

91

92

93

94

95

Figure 13a - Styrofoam Measurement vs. Modeling during Automatic Defrost
(Non Heater - y Direction)

Figure 13b - Aluminum Measurement vs. Modeling during Automatic Defrost
(Non Heater - y Direction)

Figure 13c - Styrofoam Sample Holder Measurement vs. Modeling during
Automatic Defrost (Non Heater — y Direction)

Figure 13d - Sample Measurement vs. Modeling during Automatic Defrost
(Non Heater - y Direction)

Figure 13e - Incubator Temperature during Automatic Defrost
(Non Heater - y Direction)

Figure 14 - Composite Wall for Box in z-direction (1)
Figure 15 - Composite Wall for Box in z-direction (2)
Figure 16 - Electrical Circuit Representation for z-direction

Figure 17a - Styrofoam Measurement vs. Modeling during Automatic Defrost
(Non Heater - z direction)

Figure 17b - Aluminum Measurement vs. Modeling during Automatic Defrost
(Non Heater — z Direction)

Figure 17c - Sample Measurement vs. Modeling during Automatic Defrost
(Non Heater- z Direction)

Figure 17d - Incubator Temperature during Automatic Defrost Measurement
(Non Heater - z Direction)

Figure 183 - Styrofoam Measurement vs. Modeling during Opening Incubator
Door (Non Heater)

Figure 18b - Aluminum Measurement vs. Modeling during Opening Incubator
Door (Non Heater)

Figure 18c - Sample Measurement vs. Modeling during Opening Incubator
Door (Non Heater)

viii

96

97

98

99

100

42

43

101

102

103

104

105

106

107

Figure 18d - Incubator Temperature during Opening Incubator Door
(Non Heater)

Figure 19 - Composite Wall when Top of the Box is opened
Figure 20 - Electrical Circuit when Top of the Box is opened

Figure 21a - Styrofoam Measurement vs. Modeling during Opening Incubator
Door and Top of the Box (Non Heater)

Figure 21b - Aluminum Measurement vs. Modeling during Opening Incubator
Door and Top of the Box (Non Heater)

Figure 210 - Sample Measurement vs. Modeling during Opening Incubator
Door and Top of the Box (Non Heater)

Figure 21d - Incubator Temperature during Opening Incubator
Door and Top of the Box (Non Heater)

Figure 22 - Plane Wall for Temperature Controller System is Enabled
Figure 23 - Electrical Circuit Representation for the Composite Wall

Figure 24a - Styrofoam Measurement vs. Modeling during Automatic Defrost
(Heater is on)

Figure 24b - Aluminum Measurement vs. Modeling during Automatic Defrost
(Heater is on)

Figure 24c - Sample Measurement Vs. Modeling during Automatic Defrost
(Heater is on)

Figure 24d - Temperature Incubator Measurement vs. Modeling during Automatic
Defrost (Heater is on)

Figure 24e - Heat Transfer Rate vs. Time

Figure 25 - Composite Wall

Figure 26 — Equivalent Electrical Circuit fi'om the Composite Wall

Figure 27 - Relationship between Electrical Circuit and Thermal Circuit (1)
Figure 28 —— Relationship between Electrical Circuit and Thermal Circuit (2)

Figure 29 - Styrofoam Sample Holder and Cover

ix

108

47

48

109

110

111

112

52

53

113

114

115

116

117

60

60

61

61

63

Figure 30 - Composite Wall for the Condition when Automatic Defrost Enabled
Figure 31 - Electrical Circuit for Condition when Automatic Defrost is Enabled

Figure 32 - Sample Old Modeling vs. New Modeling during Automatic Defrost
Heater is on)

Figure 33 - Box with Styrofoam Sample Holder for Cyro Vials

Figure 34 - Box with Styrofoam Sample Holder for Petri Dishes

Figure 35 - Styrofoam Sample Holder for Cyro Vials

Figure 36 - Styrofoam Sample Holder for Petri Dishes

Figure 37 - Temperature Controller System

Figure 38 - Plastic Heater Attached to the Aluminum Box

Figure 39 - Twelve Boxes inside the Incubator

Figure 40 - Sample Temperature Performance after Testing for 10 Days

Figure 41 - Automatic Defrost Condition with Set Temperature inside the Box
at -1.1 Deg C (Box 1)

Figure 42 - Automatic Defrost Condition with Set Temperature inside the Box
at -5 Deg C (Box 2)

Figure 43 - Automatic Defrost Condition with Set Temperature inside the Box
at -9.4 Deg C (Box 3)

Figure 44 - Automatic Defrost Condition with Set Temperature inside the Box
at -1.1 Deg C (Box 4)

Figure 45 - Automatic Defrost Condition with Set Temperature inside the Box
at -5 Deg C (Box 5)

Figure 46 - Automatic Defrost Condition with Set Temperature inside the Box
at -9.4 Deg C (Box 6)

Figure 47 - Automatic Defrost Condition with Set Temperature inside the Box
at -3 Deg C (Box 7)

Figure 48 - Automatic Defrost Condition with Set Temperature inside the Box
at -7 Deg C (Box 8)

64

64

118

68

68

69

69

7O

71

72

128

119

120

121

122

123

124

125

126

Figure 49 - Automatic Defrost Condition with Set Temperature inside the Box
at -9 Deg C (Box 9)

Figure 50 - Automatic Defrost Condition with Set Temperature inside the Box
at -4 Deg C (Box 10)

Figure 51 - Automatic Defrost Condition with Set Temperature inside the Box
at -6 Deg C (Box 11)

Figure 52 - Automatic Defrost Condition with Set Temperature inside the Box
at -8 Deg C (Box 12)

Figure 53 - New Voltage Reference Equation

Figure 54 - Automatic Defrost Condition with Set Temperature inside the Box
at -1 Deg C (Box 10)

Figure 55 - Automatic Defrost Condition with Set Temperature inside the Box
at -5 Deg C (Box 11)

Figure 56 - Automatic Defrost Condition with Set Temperature inside the Box
at -9 Deg C (Box 12)

Figure 57 - Opening Incubator Door Condition with Set Temperature inside the
Box at —1.1 Deg C (Box 1)

Figure 58 - Opening Incubator Door Condition with Set Temperature inside the
Box at -5 Deg C (Box 2)

Figure 59 - Opening Incubator Door Condition with Set Temperature inside the
Box at -9.4 Deg C (Box 3)

Figure 60 - Opening Incubator Door Condition with Set Temperature inside the
Box at -1.1 Deg C (Box 4)

Figure 61 - Opening Incubator Door Condition with Set Temperature inside the
Box at -5 Deg C (Box 5)

Figure 62 - Opening Incubator Door Condition with Set Temperature inside the
Box at -9.4 Deg C (Box 6)

Figure 63 - Opening Incubator Door Condition with Set Temperature inside the
Box at -3 Deg C (Box 7)

xi

127

128

129

130

129

130

131

132

133

134

135

136

137

138

139

Figure 64 - Opening Incubator Door Condition with Set Temperature inside the
Box at -7 Deg C (Box 8)

Figure 65 - Opening Incubator Door Condition with Set Temperature inside the
Box at -9 Deg C (Box 9)

Figure 66 - Opening Incubator Door Condition with Set Temperature inside the
Box at -4 Deg C (Box 10)

Figure 67 - Opening Incubator Door Condition with Set Temperature inside the
Box at -6 Deg C (Box 11)

Figure 68 - Opening Incubator Door Condition with Set Temperature inside the
Box at -8 Deg C (Box 12)

Figure 69 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -1.1 Deg C (Box 1)

Figure 70 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -5 Deg C (Box 2)

Figure 71 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -9.4 Deg C (Box 3)

Figure 72 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -1.1 Deg C (Box 4)

Figure 73 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -5 Deg C (Box 5)

Figure 74 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -9.4 Deg C (Box 6)

Figure 75 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -3 Deg C (Box 7)

Figure 76 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -7 Deg C (Box 8)

Figure 77 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -9 Deg C (Box 9)

Figure 78 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -4 Deg C (Box 10)

xii

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

Figure 79 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -6 Deg C (Box 11) 155

Figure 80 - Opening Incubator Door and Lid of the Box with Set Temperature
inside the Box at -8 Deg C (Box 12) 156

xiii

Chapter 1

INTRODUCTION

The purpose of this research is to design, build, and test a thermally controlled
environment (0°C to -10°C) that can maintain a regulated temperature for holding
biological samples in a low temperature incubator. This thermally controlled system
consists of twelve boxes that were built to hold the biological samples and stabilize the
sample temperature. Also, a temperature controller system is used to regulate the
temperature inside the boxes. These twelve boxes are tested during conditions of
automatic defrost, opening the incubator door, and opening the incubator door and lid of
the box at the same time. The results give confidence that for the conditions mentioned
this thermally controlled system can maintain a regulated temperature in the required
amount of time given by the Center of Microbial Ecology. A detailed description of this
system is explained in Chapter 2.

Before explaining a description of the thermally controlled system, a literature
search is given to explain about the background of the microorganisms. The background
explains the different types of microorganisms. It provides geographic locations where
they are formed, and it gives a definition of how microorganisms are created and how
they survive. In addition, Section 1.1 also describes previous research that has been
completed by biologists. Section 1.2 explains why this research is unique and that
biologists are interested in this research because it provides information to show the
importance of studying the behavior of microorganisms in a low temperature

environment.

1.1 Literature Search

Microorganisms such as microbial, microalgae, cyanobacteria, and microbacteria
have been found viable during a geologically significant time (more than three to four
millions years). These viable microorganisms are found throughout the cold regions of
the earth such as the North Eurasia, North America, and Antarctica [1].

In Antarctica, microorganisms inhabit the ice on land, lakes, and sea. This
microhabitat occurred when water interfaces with land and the cold winter air at
temperatures below the freezing point of water (~30°C). As a result of the temperature
below freezing, it caused a great osmotic stress as ice freezes and leaves microsites of
concentrated salt solutions at temperature well below freezing. As a result, a new
microhabitat is then created. During the winter time, the surface of ice itself on land,
lakes, and sea is lacking water to support a microhabitat. Although, even without water,
it is proven that a viable microorganism is detected and anhydrobiotically preserved deep
within the ice sheet and permafrost [2].

In addition to the ice on land, lakes, and sea, microorganisms can also grow and
survive in the cold deserts of continental Antarctica. The desert surface biota has
endured a long period of dehydration, hypersalinity, transient and daily freeze-thaw
cycles, and prolonged low temperatures during winter. Y et, it is evident that the low
temperature and the limitation of water accessibility help microorganisms to regulate
their survival and grth in this region [2].

In North Eurasia, microorganisms are often found in the permafrost region of

Northeastern Siberia. In this region, freezing conditions have existed here for over three

million years. Not only organic residues, but also large numbers of viable bacteria have
been preserved for three million years in ice [3].

Due to the existence of microorganisms and their capability to survive and grow
in the permafrost regions, biologists have conducted expeditions in North Eurasia to
obtain samples of permafrost soils and sediments. There are several procedures to be
performed before the study of the permafrost soils began. First, permafrost sediments
were detected. After the sediments are detected, the frozen sediments cores were
obtained by using a slow rotary drill so that the sediments cores will not melt. These
cores were immediately placed in frozen storage. This is because these sediments have
been continuously frozen since they were deposited, therefore it is important to keep
them frozen. Afierward, these samples cores were sent to the laboratory for the study of
microbial activities in different ranges of temperatures [4]. The results of this study are
explained in the next paragraph.

Viable microorganisms have been discovered from buried Siberian permafrost
soils and sediments, where their age is ranging from seven thousand to two million years.
These samples were analyzed for viable populations of anaerobic bacteria and their
metabolic end products. The samples were taken from the tundra zone of Kolyma-
Indigirkan Lowland, where permafrost occurs throughout the area to depths of 600-800
meters. Evidence showed that buried permafrost in this region has remained
continuously frozen since its deposition. The current average temperature of the
sediments ranges from -9°C to -12°C. The results of the study showed that anaerobic
bacteria maintain their viability at a temperature range of -7°C to -12°C for very long

periods of time, from several thousand to two million years. These long time survivals

may require some adaptive mechanisms in order to endure these stresses. It is also
concluded that the long-term conservation of authigenic sulfides and the activity of
sulfate-reducing bacteria at 4°C leads to the theory that these minerals as well as methane
were formed within the permafi'ost [4].

Other samples of permafrost soil have also been taken from a different depth (0.5-
3.8 meters) during expeditions to Northern Siberia. These permafrost soil samples were
buried in frozen soil for 2-5 million years where the temperature is around -10°C. Viable
aerobic heterotrophic microorganisms have been found in these permafrost soil samples.
The In orphology and p hysiology o f these microorganisms w ere identified and s tudied.
During this study, the following characteristics were studied: cell shape, motility, ability
to sporulate and form colonies, range of grth temperature, and capacity to grow in
media of different salinity. In order to determine the optimal growth temperature, the
microorganisms were incubated at 0°C, 4°C, 10°C, 15°C, 20°C, 25°C, and 30°C. The
study showed that not all the cells have the same shape. Some cells have a small shape,
some have a shape of a rod, and others have irregular shapes of rods. As for the growth
temperature, all cells are growing in the temperature range of 0-30°C. Their optimum
growth temperature is higher than 15°C, mainly 25°C [5].

Recently in the Siberian permafrost soils, viable microorganisms at a different
depth are studied. These permafrost soils have a temperature range between 9°C to -13°C
and were taken from a depth of 55 meters. Thirty isolates from different permafrost
samples representing aerobic bacteria are being investigated for their cold adaptation.
The results show all cells have a capability to grow at or below 0°C. But, the lowest

growth temperature has not yet been determined. During their growth at low temperature,

the cells developed a very peculiar layer. At temperature growth between 0°C, 10°C, and
20°C, the cells strain showed significant changes in their total fatty acid composition.
These feature changes might be because of adaptations to cold temperatures, which are
currently proposed as part of a unifying adaptation strategy for microorganisms [6].

All these studies mentioned in the previous paragraphs show that Siberian
permafrost microorganisms have a capability to grow at or above 0°C and develop
different strategies to maintain their viability and activity at low temperatures. Moreover,
during the repeated warming/cooling and fieezing/thawing, cells have an ability to
protect themselves by adaptating to this environment. From preliminary studies,
biologists were able to identify and study the microorganism’s activities and adaptations
during temperature grth at or above 0°C. But, the activities and adaptations at
temperature growth below 0°C have not yet studied by biologists [6].

Currently, a proposal is being made to study the Siberian permafrost
microorganism adaptations and activities at grth temperatures between 0°C and -10°C
[6]. As mentioned previously, permafrost soil samples need to be kept frozen. To fulfill
this requirement, samples are kept in a low temperature incubator. In order to study the
microorganism activities at different low temperature growth conditions, not only do the
samples need to be kept in a low temperature incubator, but they also need to be kept in a
thermally controlled environment to regulate the temperature. Therefore, a thermally
controlled environment needs to be designed and fabricated to function inside the

incubator in order to accomplish microorganism studies.

1.2 Why this Research is Unique

This research is unique because by designing and manufacturing the controlled
environment boxes, it would help biologists to conduct a study of the growth activities
and adaptations for the Siberian permafrost samples at temperatures between -0°C and -
10°C. By studying their growth activities and adaptations in a lower temperature
environment, it will help answer these questions: what are the forms of the vital activity
preserved by cells? Are microorganisms able to periodically change from cryoanabiosis
to the inhibited o r retarded state, b ut still h ave a vital activity and p ropagation? W hat
quantitative, morphological and genetic changes are caused by the adaptation of ancient
microbial complexes? In the future, the answers of these questions will help to answer the
keystone problem: How long can life be preserved? Today nobody can solve this basic
question by modeling, experiments or calculations [3].

According to the evidence taken by NASA missions seeking signs of past life on
Mars, it showed that there was once water flowing in Mars, which indicated that Mars
once had a warmer temperature and a thicker atmosphere. These conditions would have
supported the evolution of life at an early time. Since the Mars environment is so similar
to Earth, then viable cells in the Earth permafrost could be considered as an analogue of
potential habitants of Martian frozen progressions. If viable Earth permafrost
microorganisms could live in a Martian environment then the next question is: Could
Earth organic materials survive 3.5 billion years if it were buried and frozen at Martian
temperatures (-70°C)? Even more intriguing, could microorganisms survive? And if they
did not survive, would their cell structure remain intact? By studying the activity and

adaptation of the Siberian biological samples, a conclusion can be made whether there

microorganisms can survive on Mars. If there are activities and adaptations of Siberian
organic material during temperatures growth at 0°C and -10°C, then it may be possible for
the Siberian organic material to survive at Martian temperatures and for a longer period

time [3].

Chapter 2

DESCRIPTION OF THE SYSTEM

This chapter describes and clarifies the main objective of the system that controls
the temperature of the biological samples. Before describing the system, it is important
to first understand the behavior of the incubator and define the problems of the incubator
that can affect the sample temperature. Furthermore, it is important to define the
problems associated with the conditions of automatic defrost, opening the incubator door,
and opening the incubator door at the same time. Then understanding these problems can
help in the design procedure to build a temperature controlled system that can fulfill the
design requirements that are needed. The end of this chapter also provides a brief
description of the test procedure used to acquire the data needed to verify the

fimctionality of the system.

2.1 Objective

The main objective of this research is to keep the biological sample temperature
stable during the conditions of automatic defrost, opening the incubator door, and
opening the incubator door and lid of the box at the same time. Before designing a
temperature controlled environment for holding the biological samples, the specifications
for the environment of the biological samples need to be defined. The temperature of the
samples needs to be controlled and regulated at set temperatures between 0°C and -10°C.
Also, the biological sample temperature needs to be maintained at a constant temperature

for a long period of time during their incubation. Moreover, the temperature of the

biological samples must be the same as the temperature controlled environment. The
maximum temperature error that is allowed is :tl°C.

In the process of designing and building a thermally controlled environment the
first step is to establish the correct living conditions for the biological sample
environment. There are several steps for designing and building the biological sample
environment. First, a low temperature box was built based on the specifications from the
previous paragraph and the incubator characteristics. This box is then tested and studied
in the low temperature incubator to study the performance of the box and determine if the
sample temperature can be regulated. The results of the box were favorable, but did not
yet fully comply with the specifications. In order to optimize the box performance, an
experimental characterization of the system is conducted. Then, the results of the
experimental characterization are modeled with computing software called Mathematica.
Once the m athematical modeling is v erified with respect to the e xperimental d ata, the
modeling will be used to develop optimal designs for the box. After the design of the box
is established, then twelve boxes are built and tested based on the optimized design. The

test procedure is given at the end of this chapter.

2.2 Behavior of the Incubator

Before designing a thermally controlled environment for the biological samples, it
is important to understand the incubator itself. An incubator is designed to keep
conditions favorable for development or testing. In this research, the incubator (Model
Number BOD 50 ABA, manufactured by the General Signal Laboratory Equipment) is a

refiigerator that has 2 temperature ranges, which are an incubator mode (0°C to 60°C) and

a freezer mode (-20°C range). This low temperature incubator has an automatic defrost
feature for removing the excessive ice on the cooling coil. The incubator also consists of
four shelves, where the temperature differences of each shelf during automatic defrost is
between 0.5°C-1°C. The graph of the temperature differences for each shelf can be seen

in Figure l on the next page.

— Fiflh Shelffi'om the Bottom
— Fourth Shelffiom the Bottom
— Third Shelffi‘om the Bottom
— Second Shelffrom the Bottom
— First Shelffiom the Bottom

Temperature (Celsius)

 

0 10000 20000 30000 40000 [50000 60000 70000 80000 90000
Time (Second)

Figure 1 - Temperature Difl'erence between each Shelf ofthe Incubator

As can be seen in Figure 1, the temperature is warmer from the bottom to the top
shelf. This is because the cooling coil is located near the bottom shelf, which makes the

cold air flow from the bottom shelf to the top shelf. Due to the small temperature

10

difference, it can be concluded that the temperature inside the incubator is almost
uniform.

During the freezer mode, the temperature of each shelf inside the incubator is in
the region of -21°C for approximately 5 hours, then the automatic defrost feature turns
on. Once the automatic defrost is on, the temperature of each shelf is heated to
approximately —7°C, thus allowing the ice on the cooling coil to be defrosted. It takes
approximately 15 minutes for the temperature to change from -21°C to the defrost
temperature of -7°C. After the temperature reaches -7°C, then the automatic defrost
feature turns off and the temperature in the incubator is cooled back to its original setting,

which is -21°C.

2.2.] Defining the Problem

After discussing the behavior of the low temperature incubator, the next step is to
define the problem within the incubator that needs to be considered in order to design the
thermally controlled environment for the biological samples. The first problem concerns
keeping the temperature of the biological samples at a constant temperature when the
automatic defrost turns on. During automatic defrost, the temperature in the incubator
warms to approximately -7°C causing the temperature of the biological sample to tend to
warm considerably. Furthermore, the temperature changes to -7°C within approximately
15 minutes, which is a severe change in temperature and could cause harm to the living
biological samples. The second problem concerns regulating the temperature of the
biological samples regardless of what the temperature is inside the incubator. For

example, the temperature 0 f the s amples shall b e able to regulate at a s et temperature

11

between 0°C to -10°C even if the incubator temperature is at -12°C. Other problems
include: regulating the sample temperature inside the box when the incubator door is
opened, or when the incubator door is opened and the lid of the box is opened at the same

time.

2.2.2 How to Solve the Problem

For this research, a box using a temperature controller was already designed to
hold biological samples in the low temperature incubator. But, it was found that the
result of this box did not fulfill the design specification. As a result, a design
optimization was done based on the original design to comply with the design
specification. Using the optimized design, twelve boxes were fabricated based on the
fact that only a total of twelve boxes can fit inside the incubator. Furthermore, the Center
of Microbial Ecology requested that nine of the boxes to be filled with cyro Vials and
three of the boxes to be filled with petri dishes. Figure 2 illustrates the twelve boxes

inside the incubator.

12

examine-emu»; «nu-1' "

 

Figure 2 - Twelve Boxes inside the Incubator

The fabrication process is important because it can affect the performance of the box.
For example, the walls of the box must fit together tightly with a minimum amormt of air
leakage. If there is air coming into the box through the leakage, this can affect the
temperature performance of the sample. Table 1 shows the dimensions of each material
of the box.

13

Table l - Dimensions of Each Material of the Box

Dimensions
Width

.8 cm
cm
cm

 

Because this box is already designed, there are constraints for optimizing the
design of the box. For example, the materials for the box have already been chosen. The
materials used are Styrofoam and aluminum. To optimize the design of the box, the
styrofoarn sample holder is modified. Also, the arrangement of the samples is changed.
The modification to the different sample holders and change in arrangement in the
sample is explained in Chapter 3. Shown below in Figures 3, 4 and 5 are pictures
illustrating the original design and the optimized design of the box using different sample
holders. Figures 6 and 7 also show the sample holder for the petri dishes and the cryo

vials for a new design optimization.

 

Figure 3 - The Box with the Original Design

 

Figure 5 - Optimized Box Design with Petri Dishes

 

F‘igure7-StyrofoanSampleHolderforPetriDishee

Theboxthathasaheadybeendesignedmustkeepdresampletempemtmesteady

dmingmfiomaficdefiosteondiflomopeningflremcubatordoor,mrdopeningdre

16

incubator door and top of the box at the same time. During the automatic defrost
condition, the warmest incubator temperature is at -7°C. The box made with styrofoam
and aluminum materials is built to damp this temperature as it is warming during the
automatic defrost conditioning. Obviously, if the samples are placed inside the incubator
without using this box, the sample temperature will have the same approximate
temperature as the incubator. By placing the sample inside the box that is made from
styrofoam and aluminum materials, the sample temperature would not be influenced by
the warm incubator temperature (-7°C). This is because the materials damp the outside
temperature and keep the sample temperature colder than -7°C. Therefore, building a box
with styrofoam and aluminum materials can help to solve this problem.

During opening of the incubator door condition, the biological samples
temperature needs to be kept steady at least 3 minutes for petri dishes and at least 5
minutes for the cyro vials. This is because the biologists only need 3 minutes for the petri
dishes and 5 minutes for the cyro vials to open the incubator door and top of the box for
adding chemical solution to the samples. More time is needed for the cyro vials because
each box has a total twelve cyro vials compared to eight petri dishes. Furthermore, the
cyro vials are more difficult to remove from the box compared to the petri dishes. These
same circumstances are required for the condition of opening the incubator door and top
of the box at the same time.

Even though the box damps the incubator temperature, the problem is not
completely 5 olved. T his is b ecause the sample temperature is still not regulated e ven

though the sample temperature stays colder than -7°C. Looking at Figure 8, the warmest

17

the sample temperature can reach during an auto defrost condition is -12°C, but the

temperature still needs to be regulated.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-5
7 A —— Styrofoam Bottom

- — Aluminum Bottom
4!? _9 d _ Curve Fit
.3
é — Sarrple
:41 q —Styrofi)amTop
t-
3 — Aluminum Top
g -13 ~
a.
E
E" -15 - A

— 17 i i i i i
0 5000 10000 15000 20000 25000

Time (Second)
Figure 8. Original Design Box Temperature and Sample Temperature

To solve this issue, a temperature controller is used to regulate the sample
temperature. For example, the temperature controller could regulate the sample
temperature at -9°C instead of its previous warmest temperature of -12°C during the
automatic defrost condition. The temperature controller would still be enabled to
regulate the sample temperature at -9°C even though the incubator temperature goes
down to -6°C. This is because the warmest sample temperature during the automatic
defrost condition is -12°C, meaning the temperature controller would need to be enabled
in order to regulate the sample temperature down to -9°C. This controller can be used to

regulate the biological sample temperature at a different set temperature, which is also a

18

solution of the second problem mentioned in the previous section. For example, if the
incubator temperature is -25°C and the biological samples need to be set to a temperature
of -5°C, then the temperature controller will turn on and generate enough heat for the
sample to reach -5°C. This condition is known as the transient state. Once -5°C is
reached, the temperature controller will enter a steady state condition and will regulate
the temperature at -5°C.

The temperature controller system consists of a closed-loop electrical control
circuit, plastic heater, and thermocouples within the aluminum box that senses the
temperature of the samples and provides feedback to the electronic controller. The
electronic controller was built by Theron Hicks. Figure 9 shows the picture of the

temperature controller system.

 

Figure 9 - Temperature Controller System

As can be seen in Figure 9, the labels on the temperature controller consist of a reference
voltage (RV), the potentiometer (RA), the temperature voltage (TV), the sensor
temperature (S), and the voltage to the plastic heater (H). There are a total of twelve
channels in the temperature controller system because there are a total of twelve boxes
that were built to fit inside the incubator. Figure 10 shows the plastic heater attached to
the bottom side of the aluminum box. The heater output (H) from the temperature
controller system provides a voltage across the two wires that are attached to the plastic

heater shown in Figure 10.

 

Figure 10 - Plastic Heater Attached to the Aluminum Box

This plastic heater consists of resistance on both sides. One side has infinite resistance

and the other side has a finite resistance value. The plastic heater is connected to the

regulated output voltage of the temperature controller. When supplying a voltage

20

through the resistance of the plastic heater, the resistance becomes heated, thus
generating h eat for biological s amples. In 0 rder to h ave good h eat g eneration for the
biological samples, the plastic heater is placed underneath the aluminum box. The
voltage regulator also has a reference voltage, which can be adjusted by the user for
changing the temperature at the plastic heater. After the user sets the desired voltage, the
temperature sensor gives the feedback to the voltage regulator. The temperature sensor
needs to be placed in a location where the temperature needs to be monitored and
regulated. The perfect location for this sensor is inside one of the cyro vials. But, the
sensor cannot be placed inside a cyro vial because the microorganisms will be
contaminated. Therefore, it was decided to locate the temperature sensor inside the
aluminum box. The voltage regulator then compares the temperature voltage inside the
aluminum box to the desired voltage (set reference voltage). If the temperature voltage
inside the aluminum box is less than the desired voltage, the voltage regulator then
supplies voltage to the plastic heater until the temperature voltage inside the box is equal
to the set reference voltage. When the temperature voltage inside the aluminum box is
equal to the set reference voltage, the voltage regulator will stop supplying voltage to the

plastic heater.

2.3 The Testing Procedure for Data Collection

The temperature performance of all twelve boxes is tested in different conditions,
such as automatic defrost condition, opening the incubator door, and opening the
incubator door and lid of the box at the same time. First, the boxes are filled with the

samples. Then, the boxes are placed inside the incubator for 1 day, so that the

21

temperature inside the incubator becomes steady. After the temperature is uniform
everywhere inside the box, the box is tested for the conditions that were mentioned. The
boxes are tested with the temperature controller enabled to determine the performance of
the box. The test results for the twelve boxes and the conditions mentioned are shown in
Chapter 5. The tables showing the procedures for operating the temperature controller

and operating the Data Acquisition software can be seen in the Appendix.

22

Chapter 3

DESIGN

After understanding the theory of heat transfer, the next step is to design a box
that can provide the most efficient performance for controlling the low temperature
environment. The objective of the box is to maintain a constant temperature inside the
box even though the temperature outside the box is varying. In order to comply with this
objective, the styrofoam and aluminum materials are used to meet the requirements
needed in a low temperature environment. The explanation about the types of materials
used and the reason why these materials are used can be found in Section 3.1. Once the
box is fabricated with the styrofoam and aluminum materials, the next objective in the
design process is attempting to enhance the performance for the box. This can be done
by generating a model from the experimental test results of the box. The model can be
achieved using two methods, which are using a finite element method or mathematical
modeling method. The finite element method analysis uses commercial software called
F LUENT to perform a numerical analysis to find the temperature distribution inside the
box. The mathematical modeling uses an analytical solution for finding the temperature
distribution inside the box. In this research, the finite method analysis only models the
steady state condition for determining the temperature distribution inside the box. Due to
lack of knowledge in C programming, the boundary conditions of the box during the
transient state of the incubator can not be defined. As a result, the finite method analysis
was not considered in this research because the transient state of the incubator causes the

most harm to the biological sample. Section 3.2 explains the finite analysis in more

23

detail. Section 3.3 explains the mathematical modeling. The design optimization of the

box can be found in Section 3.4.

3.1 Explanation of the Styrofoam and Aluminum Materials

The first step of designing a thermally controlled low temperature environment is
finding the correct materials for the box used for storing the biological samples. This is
because it can help stabilize the incubator temperature even during automatic defrosting
conditions. It is important that the m aterial u sed c an e reate an insulated environment
inside the box and damp the incubator temperature during automatic defrost conditions so
that the temperature of the biological samples can be steady at a uniform temperature.
According to the heat transfer theory, the best material used for insulation systems is a
material that has a low thermal conductivity, a high heat capacity, and a low density. The
ratio of a low thermal conductivity and a high heat capacity will provide a low thermal
diffusivity. This low thermal diffusivity is beneficial for damping the incubator
temperature during automatic defrost conditions. The next paragraph explains more
detail about insulation materials.

As mentioned in heat transfer theory, insulation materials are composed of a
multilayer of small hollow spaces. These hollow spaces are designed to restrict the
motion of air and to trap the air. As a result, the restriction of air motion in the void
space will reduce the effective thermal conductivity of the system material. If the
performance of the insulation material is enhanced, then there is less thermal conductivity
in the material. The insulation materials also have a high heat capacity and a low thermal

diffusivity. According to the heat transfer theory, a material that has a low heat capacity

24

is not an acceptable material to store a thermal energy. As for thermal diffusivity, a
material that has a small thermal diffusivity (or) will respond longer to reach a new
equilibrium condition compare to a large thermal diffusivity. These properties match the
characteristics of insulation materials. According to Chapter 1, a box was designed using
styrofoam and aluminum materials. Styrofoam was used as the first layer of the box
because it has a low thermal diffusivity, which helps to damp the incubator temperature
during an automatic defrost condition. The thermal diffusivity of styrofoam and

aluminum is described as following,

a_ k _ 0.029W/m~K
pCp 50kg/m3*1000J/kg-K

 

 

=5.8E—7m2/s (1)

Moreover, styrofoam is easily available, simple to manufacture, and inexpensive
compared to the other insulation materials.

Since the biological samples are put in the box, it is important that the box has a
uniform temperature distribution. This will ensure a uniform temperature within the
biological samples. In order to have a uniform temperature, the material needs to have a
Biot number less than 0.1. When a Biot number of the material is less than 0.1, then the
conduction resistance within the solid material is much less than the convection
resistance across the fluid boundary layer. Therefore, the major temperature gradient
occurs through the fluid layer at the boundary, assuring that the temperature gradient in
the material is small. As a result, there exists a uniform temperature distribution in the

solid material when the Biot number is less than 0.1.

25

Next, it is necessary to determine the Biot number for styrofoam. Equation (2)

shows the Biot number for styrofoam.
Bi=—=-——-———-—2.>7 0.1 (2)

According to the Equation (2), the Biot number for the styforoam is greater than 0 .1,
which means that the styrofoam is not a good material to have a uniform temperature
distribution. To solve this problem, the box needs to have another layer of material,
which has a Biot number less than 0.1. From Chapter 1, the second material that was
used was aluminum. The Biot number of aluminum is shown below:

4:
Bi:-’-’£=-3—-9—99§-5-=625— 5> 0.1 (3)
k 170

By having a Biot number less than 0.1, the aluminum can improve the uniform
temperature distribution for the box. Besides having a uniform temperature distribution,
aluminum also has another advantage. Aluminum has a large thermal conductivity, so
aluminum is a good conductor. As mentioned in Chapter 1, a heater will be placed
underneath the aluminum layer of the box for heating the biological samples when the
temperature becomes too cold. Since aluminum is a good conductor, the heat will easily
diffuse through the aluminum layer of the box and heat the biological samples. Using the

temperature controller that was explained in Chapter 1, the heat can be regulated.

26

3.2 Finite Element Method Modeling

Using a software package named FLUENT, a numerical method analysis is used
to model the temperature distribution inside the box when the temperature controller is
enabled and disabled during the steady state condition. A s mentioned previously, the
transient state cannot be defined due to lack of knowledge in C programming. The
software package FLUENT 5.2 is a commercial program that is used to solve and
compute fluid flow and heat transfer in a complex 2D or 3D geometry. For this
modeling, the box is modeled in 2D geometry and only half of the box is modeled due to
symmetry of the box. Only 2D geometry is used because of lack of knowledge using
FLUENT in 3D applications. During the transient state, the boundary condition for the
box is the incubator temperature dependant upon time. As for a steady state condition,
the boundary condition of the box does not depend upon time because the incubator
temperature is not changing.

The modeling is able to illustrate the temperature distribution inside the box when
the temperature controller is enabled and disabled during the steady state. The results of
this modeling are then compared with the experimental results. The result shows that the
temperature difference between the experimental and the finite element method are close,

which is below 1°C.

3.2.1 Finite Element Method Modeling with Temperature Controller Disabled

Figure 11a shows the comparison between the experimental and the finite element

method results during the steady state condition for styrofoam bottom.

27

 

 

 

-13'5 —Styrofoam Bottom

— Incubator Terrperatme
— Modeling (Styrofiiam Bottom)

 

 

 

 

Temperature (Cehrus)

 

 

'15 I I I ' I I T I I

O 200 400 600 800 1000 1200 1400 1600 1800

Time (Second)
Figure 11a - Comparison between Measurement and Modeling for

Styrofoam (Terrperature Controller Disabled)

 

For the styrofoam bottom, the temperature difference between the modeling and

experimental result is about 01°C. Figure 11b is the comparison between the modeling

and the experimental result for the aluminum bottom.

 

 

 

 

 

 

- 13.5
a — Aluminum Bottom
.2 — Incubator Terrperature
% —Modeling(Aluminmn Bottom)
9 -14
2 WWW—W
i
g: 14.5 ‘
.3.
h .

- 15 i i i . i i i i i

 

 

 

O 200 400 600 800 1000 1200 1400 1600 1800

Time (Second)
Figure 11b - Comparison between Measurement and Modeling for
Aluminum (Temperature Controller Disabled)

28

The temperature difference between the experimental and modeling result for the
aluminum bottom is about 02°C. Figure 11c is the comparison between experimental

and modeling results for the sample.

 

-13.5

 

— Sarrple
— Incubator Terrperature

— Modeling (Sanple)

 

 

 

 

-14 7

 

-14.5 - ‘

Temperature (Celsrus)

 

 

 

- 1 5 r V I I
O 500 1000 l 500 2000

Time (Second)

Figure 11c - Comparison between Measurement and Modeling for
Sanple (Tenurerature Controller Disabled)

From Figure 11c it can be seen that the temperature difference between the modeling and
experimental result is about 01°C.

Looking at Figures 11a, 11b, and 11c for the styrofoam bottom, aluminum
bottom, and samples, the results for the two cases are very close, which is a temperature

difference below 1°C. This temperature difference is acceptable.

29

3.2.2 Finite Element Method Modeling with Temperature Controller Enabled

Figure 12a shows the comparison between the experiment and modeling when

temperature controller enabled at -6.7°C for styrofoam.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-5
— Terrperature Incubator
A -7 Modeling (Styrofoam)
a — Measmement (Styrofoam)
% -9
B
0 WW
5 ’11 I '
E
a -13
:11
MW
-15 -
-17 I I I I I I l I
0 500 1000 1500 2000 2500 3000 3500 4000 4500

Time (Second)

Figure 12a - Comparison between Measurement and Modeling for
Styrofoam (Temperature Controller Enabled)

Looking at Figure 12a, the temperature difference between the measurement and
modeling for styrofoam is about 4°C. Figure 12b is the comparison between the
measurement and modeling for aluminum bottom. The temperature difference between

the measurement and modeling is about 01°C.

30

 

 

 

 

 

' V

-9 — Temperature Incubator

— Modeling (Ahrminum Bottom)
— Measurement (Almninum Bottom)

 

 

 

 

 

 

 

 

 

Temeprature (Celsius)

 

 

 

'17 I I I I I I I I
O 500 1000 1500 2000 2500 3000 3500 4000 4500

Time (Second)
Figure 12b - Comparison between Measurement and Modeling for
Aluminum (Temperature Controller Enabled)

Figure 12c shows the comparison between the modeling and measurement for the

sample. As it can be seen in the graph, the temperature difference is about 16°C.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-5 __

E -7

a -9 ' . ,r"~
8

2 _11 — Temperature Incubator

g ——Modeling(Sample)

9 _13 — Measurement (Sample)

3

MW
-15

 

 

 

 

' 1 7 T I I I I I I I
O 500 1000 1500 2000 2500 3000 3500 4000 4500
Time (Second)

Figure 12c - Comparison between Measurement and Modeling for
Sample (Temperature Controller Enabled)

31

Since the temperature difference between measurement and modeling for the styrofoam
bottom and sample is above 1°C, therefore these modeling results are not acceptable.
This error may occur because the natural convection coefficient (h) that was used in
FLUENT is not correct, or the error may occur because 2D analysis was used instead of
3D analysis. In addition, the error may be caused due to lack of knowledge using the

FLUENT software package.

3.3 Mathematical Modeling

Even though the box is three—dimensional, it was determined that one-dimensional
analysis was acceptable to help improve the design of the box. This means that the x, y,
or the z-axis needs to be used for this analysis. For this analysis, mathematical modeling
is used to solve and plot first order differential equations using the theory of transient
conduction and plane wall steady state conduction analysis. The first order differential
equation used in this analysis represents the temperature distribution through each
material of the box. This first order differential equation is represents the equivalent
thermal circuit for the composite wall of the box. The resistance of each material is
divided by two since the thermocouple measurement of the temperature is in the middle
of each material. After plotting the mathematical results of the temperature distribution
through the x, y, and z-axis, they need to be matched with the experimental results. The
plots show that the z-axis best matches the experimental results, meaning that heat
transfers through the z-axis faster than the x or y axis. Therefore, the z-axis is used in the

mathematical modeling for optimizing the design. The next sections explain the

32

modeling of the system without the temperature controller and with the temperature

controller.

3.3.1 Mathematical Modeling with Temperature Controller Disabled

It is useful to first analyze the temperature characteristics of the box with the
electronic temperature controller disabled. This is because the results provide a
benchmark describing a passive system. The first condition that needs to be modeled is
the changes in the internal temperature of the box during an automatic defrost condition.
The second condition to be modeled analyzes the change in the internal temperature of
the box when opening the refrigerator door. The last condition modeled is analyzing the
internal temperature of the box when opening the refiigerator door and opening the top of
the box at the same time.

As shown in Figure 13, the box is three-dimensional meaning that temperature
gradients may exist along all three coordinates. To simplify the heat transfer analysis, the
modeling deals with one—dimensional heat transfer through the box. To understand a
more accurate flow of heat transfer through the box, a three-dimensional analysis should
be considered in future research. The coordinate direction used in the modeling is
explained in the next paragraphs. Note that in Figure 13 the box is drawn only half its
original size. This is because the compositions of materials within the box are easier to

visualize.

33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r ---Styrofoam
. 394/ l Sample Holder
' ' " Water
I . - < - -- - ,v‘”Aluminmn Plate
Styrofoam—4..

Figure 13 - Box with Three Coordinate Directions

First, heat transfer in the x-direction is considered. Figure 14 illustrates the heat
transfer in the x—direction of the composite wall of the box. It can be seen from Figure 14
that heat transfers through each material of the box. An electrical circuit can be
generated to represent the composite wall in the x-direction. This representation is shown

in Figure 15.

34

I' Cold Air} _—;

,l-- I ___-

K I
\ _. )
i ’2’" I F. %

 

ax
A G
B=F:
C=E
D
L

 

ELF

 

Lo

 

LA I .
A B C D ' E

 

: Styrofoam

Aluminum

 

: Styrofoam Sample Holder
: Sample
: Thickness

 

Figure 14 - Composite Wall for the Box in x-direction

Air I Styrofoam
|
I

R] R2 R3

V0.1:Cll

Figure 15 - Electrical Circuit Representation for Composite Wall in x-direction

Aluminum I Styrofoam I Sample I
Sam le I I
I Ho] er I I
| I l
R4 R5 R6 R7 R8 R9

I|e———gJ N

T...

Cold Air

I

Aluminum I Styrofoam I Styrofoam I Air

Sam 1e I
Hol er I

R10

|
R11 R12

1

|
R13

I
I
C6|
I

R14 R15

1”

I
R16

It is important to define the area and thickness of each material in order to optimize the

design of the box. It can be seen from Figure 15 that the area and thickness of each

35

material of the box can be represented as resistance and capacitance parameters. Using

node voltage analysis, equations can be generated from the electrical circuit.

Equations (4) — (10) are shown below,

Where,

 

V—V V—V

0 1 = Vl'Cl + l 2
R1+R2 R3 +R4
W’Q 5‘5

——=VéC2+——
R3+R4 R5+R6

= 4C4+

R7+R R +R10
V —V V —V

4 5 _V5'C5+ 6
R +&O R11+R12
V -V V —V

5 6 =VoCo+ 6 7
R11+R12 R13 ”14
V —V V -V

6 7 =P3C7+ 7 ‘8
R13 +R14 R15 +R16

V() = V3 = Voltage source = Forcing function

V1 = V5 = Styrofoam temperature/voltage

V2 = V6 = Aluminum temperature/voltage

V3 = V7 = Styrofoam sample holder temperature/voltage

36

(4)

(5)

(6)

(7)

(8)

(9)

(10)

The

V4 = Sample temperature/voltage

C1 = C5 = p*Cp*A*L =Styrofoam capacitance

C2 = C6 = Aluminum capacitance

C3 = C7 = Styrofoam sample holder capacitance

C4 = Sample capacitance

R1 = R16 = 1/(h’I‘A) =Air resistance

R2 = R3 = R10 = R11 = L/(2*K*A)=Styrofoam resistance
R4 = R5 = R12 = R13 = Aluminum resistance

R6 = R7 = R14 = R15 = Styrofoam sample holder resistance

R3 = R9 = Water resistance

Equations (4) - (10) that are generated contain a voltage at each node of the
electrical circuit. Each node voltage represents temperature in each material. Adjusting
the resistance and capacitance values in the equations corresponds to adjusting the area
and the thickness of the box. Adjusting the resistance and capacitance values would
change the voltage or temperature at each node of the circuit. If the changes in values
benefit the design of the box, then changes can be implemented in adjusting the area and
thickness of the wall of the box. After calculating the temperature in each material, the
modeling results are then compared with the experimental results. The next paragraph
explains how the supply voltage, V0, is generated for the modeling.

In order to find the voltage or temperature in the equations, the supply voltage,
V0, must be calculated. This voltage is the voltage source representing the temperature

outside the box. Furthermore, V0 is the temperature of any shelf in the incubator at a

37

given period of time. The voltage source, V0, can be obtained by finding the equation of
the temperature incubator graph during the automatic defrost condition. This equation is
found by entering the graph of the automatic defrost response into the software
Tablecurve 2D using curve fitting method. Once the equation for V0 is found, Equations
(4) — (10) are then implemented in Mathematica software to find the voltage of each node
for each material. In the heat transfer analogy, the node voltage for each material is equal
to the temperature in each material.

Figures 16a, 16b, 16c, and 16d show the comparison between the mathematical
modeling results and the temperature measurement results for the x-direction. For the
incubator temperature, V0, the result of the curve fit during automatic defi'ost conditions
can be seen in Figure l6e. These figures referred to the plane wall composite in Figure

14.

38

Temperature (Celsius)

Temperature (Celsius)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-115 I] —Modeling(Wa11A)
— Measurement
'12 -—Modeling(Wa G)
- 12.5 — Measurement (Wall G)
' l 3 I | T T I
0 2000 4000 6000 8000 10000 12000
Time (Second)

Figure 16a - Styrofoam Modeling vs. Measurement during Automatic
Defrost Condition (Non Heater- x Direction)

 

 

 

 
 

 

 

     

 

 

 

 

 

 

 

-9
-9.5
- 10 ~—— 7 —
- 10.5 -
-1 l
_1 1 5 _ j — Measurement (Wall B)
' I — Modeling (Wall B)
_12 , ,, . ,,,,, 7 I — Measurement (Wall F) —_
L — Modeling (Wall F)
-12.5 , 7 , ,_L_ ”—fi” l l
0 2000 4000 6000 8000 10000 12000
Time (Second)

Figure 16b - Aluminum Modeling vs. Measurement during
Automatic Defrost Condition (Non Heater - x Direction)

39

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-9.5
“WWII-sill.“ ..
-10 new
8 H
E -1 1 “f ”II-If
E (IV //
3-1 1.5 ,z'”
E if ,/’
E- M/ / — Measurement (Wall C)
-12 ‘ _ Modeling (Wall C)
W — Measurement (Wall E)
-—1 I 11' I!!! 11 E3
' 12.5 I I I I I
O 2000 4000 6000 8000 10000 12000
Time (Second)
Figure 16c - Styrofoam Sample Holder Measurement vs. Modeling
during Automatic Defrost (Non Heater - x Direction)
-9
A .95 — Modeling (Wall D)
g _ 10 — Measurement (Wall D)
8 W
5
g -11.5
E— '12 fi/
-12.5 l l n l t
0 2000 4000 6000 8000 10000 12000

Time (Second)
Figure 16d - Water Measurement vs. Modeling During Automatic
Defrost (Non Heater - x Direction)

40

Temperature (Celsius)

 

-13

O 2000 4000 6000 8000 10000 12000
Time (Second)

Figure l6e - Incubator Temperature during Automatic Defrost (Non
Heater - x Direction)

Figures 16a and 16b show that the temperature measurement results and the
mathematical modeling results for the styrofoam and aluminum boxes in the x-direction
are similar. But, the temperature of the measurement results and the mathematical
modeling results are not similar for the sample and styrofoam sample holder. Since these
two results are not close, then it was decided that the x-direction shall not be used for the

mathematical modeling.

41

Next, heat transfer in the y—direction is analyzed. The composite wall shown in
Figure 14 for heat transfer flow and the equivalent electrical circuit shown in Figure 15
are the same for the y-direction as in x-direction. As a result, the same mathematical
modeling procedure in the x-direction is now performed in the y-direction. Then the
mathematical modeling results for each material in the y—direction are compared to the
experimental results in the y-direction. This comparison can be seen in Figures 173, 17b,

17c, and 17d. These figures referred to the plane wall composite in Figure 14.

 

 

  
 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-10
—Measurement (WallA)
’5 'II “ —Mode1ing(WallA) —
'5 —Measurement (WallG)
9°, '12 —Modeling (Wall G) T
g -13 -
2
a -14 —
5
I- -15 '
-16 I ’ I f r
0 5000 10000 15000 20000 25000

Time (Second)

Figure 17a - Styrofoam Measurement vs. Modeling during Automatic
Defrost (N on Heater- y Direction)

42

Temperature (Celsius)

Temperature (Celsius)

 

 

— Measurement Wall B)

 

— Modeling (Wa B) ~—
— Measurement Wall F)

 

 

 

 

  

A — Modehgg‘ (Wa F) _

 

 

 

 

 

I I I I

5000 l 0000 1 5000 20000 25000
Time (Second)

Figure 17b - Aluminum Measurement vs. Modeling during Automatic

Defrost (Non Heater - y Direction)

 

 

 

- 10
— Measurement (Wall C)

-11 —-—- Measurement (Wall E) m
— Modeling (Wall C)

- 12 — Modeling (Wall E) I—

 

 

 

 

 

 

 

 

 

 

I I I I

5000 10000 15000 20000 25000
Time (Second)

Figure 17c - Styrofoam Sample Holder Measurement vs. Modeling
during Automatic Defrost (Non Heater - y Direction)

43

Temperature (Celsius)

Temperature (Cebius)

 

L.
o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'1 1 — Measurement (Wall D)
_12 -— Modeling (wall D)
_ 13 f V k A w“.
-14 / A
- 15 ~
-16 T I l I
0 5 000 l 0000 1 5000 20000 25000
Time (Second)
Figure 17d - Sample Measurement vs. Modeling during Automatic
Defrost (Non Heater - y Direction)
-4
-6
-3 —— fi———— — --— Measurement
— Curve Fit
-10 l
- 12 l
- 14
-16 T . l l T

0 5000

Figure l7e - Incubator Temperature during Automatic Defrost (Non

1 0000

1 5000 20000

Tinre (Second)

Heater- y Direction)

44

 

25000

Just like the results in the x-direction, the temperature measurement results and
mathematical modeling results are not similar. As a result, heat transfer direction in the
y-direction is not used. Finally, heat transfer in the z-direction is analyzed. Figure 18

illustrates the composite wall for the box in the z-direction.

 

 

Air

A = E: Styrofoam

B = D: Aluminum

C1 : Sample

C2 : Styrofoam Sample Holder

Figure 18 - Composite Wall for Box in z—direction (1)

Looking at Figure 18, the heat is first transferred through the styrofoam (walls A

and E) and secondly through the aluminum (walls B and D). The heat reaches the

45

styrofoam sample holder (wall C2) and the sample (C 1) at the same time. Keep in mind,
heat is also transferred from the styrofoam sample holder (C2) to the sample (C1) due to
the heat transfer in x-direction. But this condition is ignored because heat first reaches
the sarnple in the z-direction even before it is transferred from the sample holder through
the x-direction. The reason why is because in the z-direction there is less thermal
resistance compared to the x-direction due to the styrofoam sample holder. The new

composite wall for the box in the z—direction is depicted in Figure 19.

 

 

 

 

I LC C
fierrrr
Lb D ‘
I .. I
E
v _L _ *ATA— _. __ * L.
.— Clx , .
I Air
A = E: S rofoam
B = D: A uminum
C : Sample
L : Thickness

Figure 19 - Composite Wall for Box in z-direction (2)

46

Based on Figure 19, the electrical circuit for the plane wall is shown in Figure 20.

Air I Styrofoam AluminumI Styrofoam

| |
I l l
| I I I I
l I |
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11

Aluminum I Sample

I l
we I I
| I

 

Air

.%

 

l r 3
[C1 [c2 [c3
l 7 l T l T l '" l T

Figure 20 - Electrical Circuit Representation for z-direction

The equations of this electrical circuit are described as the following:

 

V —V V -V

R1+R2 R3+R4
Vl'Vz _ . Vz‘Vs
R3+R4 R5+R6

—=V3'C3 +———
R5+R6 R7+R8

V —V V -V
R7+R8 129+R10
R9+R10 R +R12

47

(11)

(12)

(13)

(14)

(15)

Where,

Vo = V6 = Voltage source = Forcing function
V1 = V5 = Styrofoam temperature/voltage
V2 = V4 = Aluminum temperature/voltage
V3 = Sample temperature/voltage

C1 = C5 = Styrofoam capacitance

C2 = C4 = Aluminum capacitance

C3 = Sample capacitance

R1 = R12 = Air resistance

R2 = R3 = R10 = Rn = Styrofoam resistance
R; = R5 = R9 = R3 = Aluminum resistance

R6 = R7 = Water resistance

The comparison of the modeling results and the temperature measurement results
are depicted in Figures 21a, 21b, and 21c located. Figures 21a, 21b, 21c, and 21d show
that the modeling results and measurement results are similar. These figures referred to

the plane wall composite in Figure 19.

48

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A -9
a _10 \\ —Measm‘ement (WallA)
E -12 I - -——Measm'ernent(WallE)
a _13 ' —— Modeling (Wall E)
E
8. -14 \
.‘i -15 _
I- 16 -
-17 l e . l - I T;
0 5000 10000 15000 20000 25000 30000
Tirrre (Second)

Figure 21a - Styrofoam Measurement vs. Modeling during
Automtic Defrost (Non Heater - z Direction)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-10
— Measurement (Wall B)

,3, -1 1 — Modeling (Wall B)
2% _12 _ —Measrn'ement(WallD)
6 — Modeling (Wall D)
E -13 -
g -14 -
i- -15
13

-16

-17 r r l l I

O 5000 10000 15000 20000 25000 30000
Time (Second)

Figure 21b - Aluminum Measurement vs. Modeling during Automatic
Defrost (Non Heater - z Direction)

49

Temperature (Celsius)

Temperature (Celsius)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-1 l
- 12
13 — Measurement (Wall C)
- // —— Modeling (Wall C)
- 14 V
\-
-15 \
-16
-17 I I I I I
0 5000 1 0000 1 5000 20000 25000 30000
Time (Second)
Figure 21c - Sample Measurement vs. Modeling during Automatic
Defrost (Non Heater- z Direction)
-5

 

 

 

-ll
// \ — Measurement
-13

 

 

 

 

 

 

 

 

 

 

— Cm've Fit
-15
-17
- 19 I r i T m
0 5000 1 0000 1 5000 20000 25000 30000

Time (Second)

Figure 21d - Incubator Temperature during Automatic Defrost
Measurerneut (Non Heater- z Direction)

50

Figure 2 la 3 hows that the temperature difference for the s tyrofoarn b etween m odeling
results and measurement results are around 3°C at 1980 seconds and the temperature
difference is become smaller as time is increasing. The temperature difference for
aluminum is about 1.43°C at 4200 seconds and similar to the styrofoam, the temperature
difference becomes less as time increases. As for the sample, its temperature difference
is about 016°C at t = 500 second and the temperature difference decreases as time
increases. Since the temperature difference for each material is relatively small and the
line graph between the modeling results and the measurement results for each material
are similar, this mathematical modeling can be used to model the box in the z-direction.
The second condition to be modeled is analyzing the change in the internal
temperature of the box when opening the incubator door. The same procedure for
modeling the automatic defrost condition can be used in this condition also. The only
difference is the supply voltage, V0. This supply voltage is solved using the same
procedure explained for the x-direction analysis. Once the supply voltage V0 is found,
then the voltages at each node of the material are determined. These node voltages
represent the temperature of each material. Since the only difference is the supply
voltage (V0) or in another words, the incubator temperature, then the same composite
wall and electrical circuit analogy from Figures 19 and 20 are used for the condition
when the incubator door is opened. Figures 22a, 22b, and 22c show the temperature
difference between the measurement and mathematical modeling results for styrofoam,
aluminum, and the sample during opening the incubator door. These figures referred to

the plane wall composite in Figure 19.

51

Temperature (Celsius)

Temperature (Celsius)

 

 

 

 

   
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 

 

 

 

 

0 _
— Measurement (Wall A)
‘5 i — Modeling (Wall A)
- 10 , — Measurement (Wall E)
_ 1 5 — Modeling (Wall E)
-20 I I I I I
0 1000 2000 3000 4000 5000 6000
Time (Second)
Figure 22a - Styrofoam Measurement vs. Modeling during Opening
Door Incubator (Non He ate r)
10
5 #4
0
-5 -
— Measurement (Wall B)
-10 - — Modeling (Wall B) _.
— Measurement (Wall D)
'15 “ ' — Modeling (Wall D)
'20 I I I I I
0 1 000 2000 3000 4000 5000 6000

Time (Second)
Figure 22b - Aluminum Measurement vs. Modeling during
Opening Incubator Door (Non Heater)

52

— Measurement (Wall C)
— (Wall C)

Temperature (Celsius)

 

O 1000 2000 3000 4000 5000 6000
Time (Second)

Figure 22c - Sample Measurement vs. Modeling during Opening
Incubator Door (Non Heater)

In Figures 223, 22b, and 22c the temperature difference for styrofoam, aluminum, and
the sample becomes smaller as time increases. But, for this research, the temperature of
the sample needs to be steady for at least 3 minutes for petri dishes and at last 5 minutes
for the cyro vials when the incubator door is opened and when the incubator door and the
top of the box are opened at the same time. For the styrofoam, the maximum temperature
difference is about 12°C for 600 second. The maximum temperature difference for
aluminum shows that the aluminum bottom is around 04°C and the aluminum top is
around 1.5°C. As for the sample, the temperature difference is about 1°C. Looking at
Figures 18b and 18c the temperature difference for the aluminum and the sample are
acceptable and the graphs between the measurement and modeling results for the
aluminum and the sample are similar. But, Figure 22a shows that the temperature
difference between the measurement and modeling result is not acceptable for the

styrofoam. It was determined that the temperature difference is large because the

53

placement of the thermocouple while conducting the experiment is not precisely in the
middle of the styrofoam wall.

The final condition is opening the incubator door and the lid of the box at the
same time. Since the lid of the box is opened, therefore the layer of aluminum and the
layer of styrofoam are eliminated from the electrical circuit and composite wall. Figures
23 and 24 show the composite wall and electrical circuit for this model with the layer of

aluminum and styrofoam removed.

 

 

 

I
0 LC
B LB
I
A LA

 

 

 

 

A: Styrofoam L: Thickness
BI Aluminum C; Sample

Figure 23 - Composite Wall when Top of the Box is Opened

54

Air I Styrofoam Aluminum I Sample

   

 

I”

Figure 24 - Electrical Circuit when Top of the Box is Opened

 

The equations are described as follows:

 

V —V . V —V

0 I =V1C1+———1 2 (16)
R1+R2 R3+R4

V —V V -V
———I 2 =VéC2+———2 3 (17)
R3+R4 R5+R6

V —V

2 3:%g on
R5+R6

Where,

Vo = V4 = Voltage source = Forcing function
= Styrofoam temperature/voltage

V2 = Aluminum temperature/voltage

V3 = Sample temperature/voltage

C1 = Styrofoam capacitance

C2 = Aluminum capacitance

C3 = Sample capacitance

55

R1 = R3 = Air resistance
R2 = R3 = Styrofoam resistance
R4 = R5 = Aluminum resistance

R, = R7 = Water resistance

The comparison between mathematical modeling results and temperature
measurement results are shown in Figures 25a, 25b, and 25c during the opening incubator
door and top of the box at the same time. These figures referred to the plane wall

composite in Figure 23.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16

A 14 -

m

.E 12 - -———

1'3 10

B

e 8 /

E 6 // /

E 2 K / Measm'ement (Wall A) ~
0 / Modeling (Wall A) ~
-2 T i l

O 500 1 000 l 500 2000

Time (Second)

Figure 25a - Styrofoam Measurement vs. Modeling during Opening
Incubator Door and Top of the Box (Non Heater)

56

Temperature (Celsius)

Temeprature (Celsius)

-10

-12

-14

 

/

 

//

 

//

 

///

 

//

 

 

 

— Measurement (Wall B)

 

 

 

 

— Modeling (Wall B)

 

 

 

 

I I

F

I I I I I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Time (Second)

Figure 25c - Sample Measurement vs. Modeling during Opening
Incubator Door and Top of the Box (Non He ate r)

57

O 200 400 600 800 1000 1200 1400 1600 1800
Time (Second)
figure 25b - Aluminum Measurement vs. Modeling during Opening
Incubator Door and Top of the Box (Non Heater)
// -— Measm‘ement (Wall C)
// — Modeling (Wall C)
W
0 500 1 000 1500 2000

As can be seen, the graph for the styrofoam bottom and sample are not similar for the
mathematical modeling results and measurement results. As for the aluminum bottom,
the graph for the mathematical results and measurement results are similar. Looking at
Figures 25a and 25b, the styrofoam and aluminum temperature difference is larger as the
time increases.

The temperature difference when the automatic defi'ost is enabled and when the
incubator door is opened may occur because the mathematical modeling describes one-
dimensional heat transfer analysis instead of the three-dimensional heat transfer analysis.
This means the heat transfer in the x and y-direction may affect the performance of the
box but is not taken in to account since the modeling is one-dimensional using the z-
direction. In addition, the error may be caused because of the location of the
thermocouples in each material. The thermocouples may not be placed in the exact
middle position of each material as specified by the mathematical modeling. As a result,
this may cause an error in the temperature measurement results for each material. The
software code of the mathematical modeling in the heat transfer in x, y, and z-direction
with the conditions explained can be seen in the Appendix. The next section explains the

heat transfer analogy when the temperature controller is enabled.

3.3.2 Mathematical Modeling with Temperature Controller is Enabled

This section explains the modeling and performance of the box while the
temperature controller is enabled. As mentioned in Section 3.2, the temperature
controller regulates the temperature inside the box and keeps the temperature of the

samples steady. The modeling of the box with the temperature controller enabled uses

58

the same assumptions as mentioned in the previous modeling explained in Section 3.3.1.
This means the z-direction of the box is used for modeling the heat transfer analogy.
While using the temperature controller, heat is generated inside the box to warm up the
samples. The heater inside the box only works when the temperature of the box is colder
than the set temperature. When the temperature inside the box has not yet reached the set
temperature, the heater will generate the heat until the temperature reaches the set
temperature. After the set temperature is reached, then the heater will turn off and stop
generating heat. When the temperature inside the box is below the set temperature, the
heater will turn on and generate the heat again. Thus, this temperature controller system
functions as a regulated system known as “bang-bang” controller.

While modeling this temperature controller system, one issue is how to model the
box when the heat is generated inside the box. In order to solve this problem, the heat
transfer rate produced by the heater needs to be found and analyzed. The heat transfer
rate can be found by calculating the output power of the heater. Looking at Equation
(19), the value of the voltage and resistance can be found by measuring the output voltage
and resistance of the controller system. The calculation of heat transfer rate is described

as following:

2 2
P=K—=-2—4—-=10.87 Watts (19)
R 53

After finding the heat transfer rate, a logic statement is imbedded in the
mathematical modeling corresponding to how the heater works. Using an arbitrary set
temperature between 0°C and -10°C, the logic statement is described as following:

Q/ : Q[Y_/;Y < —6.7] = 10.87;

Q/ : Q[Y _/;Y 2 —6.7] = o (20)

59

Where,

Y = set temperature in the aluminum

Equation (20) states that if the aluminum temperature is less than -6.7°C, then the heater
will turn on and generate heat with the amount of 10.87 Watts to the inside the box. On
the other hand, if the sensor temperature is greater than -6.7°C, then the heater will turn
off and discontinue generating the heat. The sensor temperature monitors the
temperature of the aluminum box. The next paragraph will explain the mathematical
modeling when the temperature controller heater is regulating the temperature inside the

box during the automatic defrost condition.

60

 

 

r‘

{Tl

 

{—1
U

 

.

.__ _T.

l
- I
I I
ll r‘
,.
U |
I
I l
'i
't
l

_ _,,_._‘

 

 

Heater

I" .
I O
-——>--< - 44—,— <.____,_. — A ——-N ——v
is i
: 1
O

.. .—_. 3,1
_.
,,
I
I

 

A = E: Styrofoam L: Thickness
B = D: Aluminum C: Sample

Figure 26 - Plane Wall when Temperature Controller System is Enabled
Figure 26 illustrates the composite wall for the box when the temperature

controller is enabled. Figure 27 shows representation of electrical circuit for this

composite wall.

61

 

- l
l
O |
R1 R2 R3 R4 R5 R6

I 3
l
|
l

R7

I”

Aluminum I
I

R8 R9

Styrofoam

I
R10 R11

Figure 27 - Electrical Circuit Representation for the Composite Wall

From Figure 27, the heater acts as a current source instead of a voltage source

since the heater generates heat through the box. In addition, the current source is put in

the voltage node, V2. This is because the plastic heater is placed underneath the

aluminum. The node voltage equations for this circuit are described as:

 

V -V . V —V
0 1=V1C1+ 1 2
R1+R2 R3+R4
V —V V —V
2 ' 2 3
V +——= +
QIZ) R+R 7-2 R5+R
V —V . V —V
= 3C3+ 3 4
R +R R +R
V —V V —V
_3___4_=V4C4+__4___5_
R7+R8 R9+R10
R9+R10 R 1+R12

62

(21)

(22)

(23)

(24)

(25)

Where,

Vo = V6 = Voltage source = Forcing function
V; = V5 = Styrofoam temperature/voltage
V2 = V4 = Aluminum temperature/voltage
V3 = Sample temperature/voltage

Ci = C5 = Styrofoam capacitance

C2 = C4 = Aluminum capacitance

C3 = Sample capacitance

R. = R12 = Air resistance

R2 = R3 = R10 = Rn = Styrofoam resistance
R4 = R5 = R9 = R3 = Aluminum resistance

R6 = R7 = Water resistance

These equations and their logic statements for the automatic defi'ost condition are
imbedded in the Mathematica software and are executed in order to obtain the
temperature performance for each material. The comparison between the experimental
results and the modeling results are shown in Figures 28a, 28b, and 28c. These figures

referred to the plane wall composite in Figure 26.

63

l
A

 

 

 

 

 

 

— Measurement (Wall A)

-6 — Modeling (Wall A) _.
— Measurement (Wall E)

-8I —Modeling (Wall E) F

 

 

 

 

 

: e

I

(I;

Iii
,i' »

I I

(I

W I

II

 

Temperature (Celsius)
S

 

 

 

I
y—a
O\
—(

 

0 5000 10000 15000 20000 25000 30000
Time (Second)

Figure 28a - Styrofoam Measurement vs. Modeling during
Automatic Defrost (Heater is On)

Looking at Figure 28a, the maximum temperature difference for the styrofoam top
and styrofoam bottom is approximately 15°C. This large temperature difference may be
caused by resistance values used for each material. The calculated resistance values of
the styrofoam bottom and top may be smaller or larger than the actual resistance of the

material. Also, the temperature difference for the styrofoam bottom and top is larger as

time increases.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E
.2
O
B
0
‘5
E
8. - 12
E ,
[2 — Measmement (Wall B) \
- l4 ~~ — Modeling (Wall B) a
— Measurement (Wall D)
— Modeling (Wall D)
' 1 6 l l l l I
0 5000 l 0000 l 5000 20000 25000 30000

Time (Second)

Figure 28b - Aluminum Measurement vs. Modeling during
Automatic Defrost (He ater is On)

The modeling results and measurement results for aluminum bottom are
represented in Figure 28b, showing that there is a small temperature difference about
03°C. Even though there is temperature difference for the aluminum bottom, this
temperature difference is still acceptable since the temperature error is below 1°C. On
the other hand, Figure 28b shows the temperature of the aluminum top between
measurement results and modeling results are not similar and has a large error
approximately 1.6°C. Furthermore, the longer the time, the larger the temperatue
difference is. Also in Figure 28b, the error in the aluminum top may be caused by the

capacitance value.

65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-7
-7 5 -‘—f

’3
E -8 r/ W
3 8 5 A
f; V \
E -9
E l -— Measurement (Wall C)
E- '9'5 — Modeling (Wall C)
g -10 \

-10.5 i;

'1 1 T l r l I
0 5000 10000 15000 20000 25000 30000

Time (Second)

Figure 28c - Sample Measurement Vs. Modeling During Automatic
Defrost (Heater is On)

For the sample temperature shown in Figure 28c, the graph between experimental
results and modeling results are similar, but they still have a temperature difference
approximately 15°C. Also, the temperature error is getting larger as the time becomes
longer. This error may be caused by the resistance of the sample. Since the temperature
difference for styrofoam bottom and top, aluminum top, and sample is above 1°C, this
modeling is not acceptable.

The condition when opening the incubator door while the temperature controller
enabled is not explained. Also, the condition for the opening incubator door and the top
of the box is not explained. The reason these two conditions were not attempted is
because the modeling results were not acceptable during the condition of automatic

defiost condition while the temperature controller is enabled. These results are not

66

acceptable due to the temperature difference between the modeling and the experimental

results for styrofoam bottom and top, aluminum top, and sample are above 1°C.

3.3.3 Sensitivity of Design Parameters

The design parameters of the box consist of thermophysical properties of the
materials, the h eat transfer c oefficients, the thickness 0 f m aterials, and the area 0 f the
materials. Each of the parameters can play an important role in designing the box.
Changing the values of the parameters will change the temperature performance of the
box, thus affecting the temperature of the biological samples.

As for thermophysical properties, the values are different for each material. The
thennOphysical properties for a material are density (p), thermal conductivity (k), and
specific heat capacity (Cp). These thermophysical properties cannot be changed to
optimize the box. Since in this research, it has already been decided to use aluminum and
styrofoam for the material of the box. Therefore, the therm0physica1 properties have a
constant value and can be looked up in “Introduction to Heat Transfer (Appendix A) by
Frank P. Incropera.” Note that these thermophysical properties could be changed for
more general optimization purpose.

A p roportionality c onstant in N ewton’s C ooling Law e quation is k nown as the
heat transfer coefficient (h). This heat transfer coefficient (h) is influenced by the surface
geometry and the nature of the fluid motion. Having a different surface geometry and
different kind of the fluid motion nature will affect how heat diffuses in the object. From
the mathematical modeling in Section 3.3.1, the value of the heat transfer coefficient (h)

is not the same for each condition. For the condition when the auto defrost is enabled and

67

when the door is opened, the heat transfer coefficient (h) is equal to 3 W/mZ-K. When the
door and the lid of the box are opened, the heat transfer coefficient (h) is equal to 25
W/mZ-K. These show that the heat transfer coefficient affects the temperature
performance of the box.

Other properties that have the ability to change the temperature performance of
the box are adjusting the thickness and area of the materials. As shown in Figures 29 and
30, the thickness and area of the material from the composite wall can be associated with

an equivalent resistor and capacitor electrical circuit.

Figure 29 - Composite Wall

r—A‘m *‘ — r—E rm“ o—"mu D~r

E ._ E E
, . e- ____A AA

E ER' ER2\E R2R3ER3ER4V3R4E

EVO E ‘7“ .1 E

E ; E C1 E EC2 E EC3 E

E E ,A _A. A A A _A. A E A AE

E l E

EAA-A L 1A 1 E

 

 

Figure 30 — Equivalent Electrical Circuit from the Composite Wall

From Figures 29 and 30 it can be seen that adjusting the thickness and area in a material

would change the resistance and capacitance within the material. These resistance and

68

capacitance values are used for the mathematical modeling. Within the mathematical
modeling, adjusting the resistance and capacitance can help to improve the performance
of the box. The paragraphs that follow show the relationship between the composite wall
for the materials in the box and the electrical circuit showing the resistor and capacitor
network for the materials in the box. Furthermore, a relationship between the electrical
circuit and an equivalent thermal circuit is explained to show how heat is transferred to
the sample.

For this analysis, the thickness and area of the cyro vials and petri dishes cannot
be adjusted because they are obtained from the manufacturer. Furthermore, the
aluminum is purchased from a manufacturer because the material is more expensive to
manufacture individually. This means the thickness and area of the aluminum cannot be
changed. As a result, the only change that can be made is the thickness and area of the
sytorofoam or optimizing the design of the box. The changes of the thickness and area of
the styrofoam would affect the styrofoam values of resistance and capacitance that are
used in the mathematical modeling for this research. Figures 29 and 30 shows the
composite w all for each m aterial and h ow it c an b e s hown a s an equivalent electrical
circuit for the mathematical modeling.

Compared to Figure 26 only half the circuit is shown for the styrofoam,
aluminum, and sample. This is because the heat transferring through the other half of the
circuit behaves the same due to symmetry of the box. In Figure 30, the voltage at each
node represents the temperature in each material. This voltage is solved in Mathematica

to determine the temperature in each material.

69

An easy way to understand the functionality in the electrical circuit is to explain it

in terms of an equivalent thermal circuit shown in Figure 31.

 

Figure 31 — Relationship between Electrical Circuit and Thermal Circuit (1)

The flow of water in Figure 31 represents the current flowing in the electrical circuit of
Figure 30. The size of the pipes in the thermal circuit represents the resistance in the
electrical circuit. Likewise, the size of the containers in the thermal circuit represents the
capacitance in then electrical circuit. Adjusting the size of the thermal circuit affects the
flow of water just like RC values affect the current in the electrical circuit. Figure 32

shows the result of adjusting the parameters of the styrofoam.

7O

Figure 32 — Relationship between Electrical Circuit and Thermal Circuit (2)

Where,
A=Ah
B = Styrofoam

C = Aluminum

D = Sample

R1= Air Resistance = Pipe A Diameter

R2: Styrofoam Resistance = Pipe B Diameter
R3= Aluminum Resistance =Pipe C Diameter
R4 = Sample Resistance = Pipe D Diameter
Cl: Styrofoam Capacitance = Water Tank B
C2 = Aluminum Capacitance = Water Tank C
C3 = Sample Capacitance = Water Tank D
Vo = Voltage Source = Water Supply

V1 = Voltage Source = Water level B

V2 = Voltage Source = Water level C

71

V3 = Voltage Source = Water level D

Figure 32 shows the thickness of the styrofoam was made larger. Enlarging the thickness
of styrofoam means the resistance and capacitance in the material is increased. If the
resistance is increased, then the diameter of the pipes for the styrofoam in Figure 28 are
decreased. This means there is more resistance in the flow of the water and it will take
more time for the styrofoam container to be filled with water. Likewise, if the
capacitance is increased then the volume of the container is increased so that it can store
more water. As a result, Figure 32 shows the effect on the sample when increasing the
thickness of the styrofoam. It shows that it takes more time for the water to reach the
sample. This same analogy represents the heat transfer to the sample. By increasing the

thickness of the styrofoam, the heat is diffused by the time it reaches the sample.

3.4 Design Optimization

As mentioned in Section 3.3.3, the design parameters that can affect the design of
the box are the area and the thickness of each material. The area and the thickness of the
aluminum box will be kept the same because it is custom made. As for the styrofoam
box, the area and the thickness of the styrofoam are also kept the same. The reason is
because of the limitation in the incubator space. There are twelve boxes that need to fit
inside the incubator. Making the area and thickness of the styrofoam larger would mean
the boxes may not fit inside the incubator. The position of the cyro vials inside the box
can be changed to improve the temperature inside the box. According to heat transfer

theory, the larger the area of the material, the more efficient the heat is transferred

72

through the material. Due to using the z-direction for the heat transfer analogy, the cyro
vials are inserted horizontally inside the box. By inserting the vials horizontally in the
box, the vials will have a larger area for heat to transfer, meaning the heat from the
plastic heater would diffuse faster through sample.

Adding a styrofoam lid to the samples is another way to improve the temperature
performance inside the box. This is because cold air is flowing into the top and the
bottom of the box (z-direction). By having a styrofoam cover on top of the samples, then
the samples are insulated from the cold air moving into the top of the box. The cold air
moving into the bottom of the box can be neglected since there is a plastic heater below
the samples. Figure 33 shows the design of the box with the samples, styrofoam sample

holder and styrofoam cover.

 

E” If; _if ”i . _ :1 if: V E Styrofoam Sample Holder
Figure 33 - Styrofoam Sample Holder and Cover

After the design of the styrofoam cover is finished, it is then modeled using the
automatic defrost condition while the temperature controller is enabled. As can be seen

in Figure 34, the sytrofoam cover is added to the composite wall.

73

1 Air
_ "49:
4 ‘1
A F_ EL. '
E E
B La E

 

Heater E- A_ ... _ _ E_
E. E A.
EXZLZIJ:.B:::C:\':CZC:ZIITCIC-II‘ZICILingIBZXZImVZZA

 

: Styrofoam Cover
: Thickness

Figure 34 - Composite Wall for the Condition when Automatic Defrost Enabled

74

The electrical circuit for Figure 34 is depicted as:

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 Rll R12 R13 R14

. 5 V6 .
VoQ E0 E cs E C6 .y7

Figure 35 - Electrical Circuit for Condition when Automatic Defrost is Enabled

 

 

'I‘H—N) N
m—d

The equation for this electrical circuit is described as:

 

 

 

 

V —V V —V
0 1=V1'C1+ 1 2 (26)
R +R2 R3+R4
V -V V —V
2_ 2 3
V +——— 27
Q( 2) R +R 2 2 R +R ( )
5 6
V —V V —V
__2__3_=V3'C3+ 3 4 (28)
R +R R7+R

3 4 ' 4 5
——=V C +—— (29)
4 4

R7+R R +R10

V4—V5 _ -5'C5+_§_—V_6 (30)
R9+R10 R11+R12

V5 — V6 Vacs V6 —V7 (31)
R11+R12 R13+R14

75

Where,
V0 = V7 = Voltage source = Forcing function
V, = V6 = Styrofoam temperature/voltage
V2 = V5 = Aluminum temperature/voltage
V3 = Sample temperature/voltage
V4 = Styrofoam cover temperature/voltage
C1 = C6 = Styrofoam capacitance
C2 = C5 = Aluminum capacitance
C3 = Sample capacitance
C4 = Styrofoam cover capacitance
R1 = R14 = Air resistance
R2 = R3 = R12 = R13 = Styrofoam resistance
R; = R5 = R10 = R” = Aluminum resistance
R6 = R7 = Water resistance
R8 = R9 = Styrofoam cover resistance
Figure 36 shows the comparison between the sample temperature using the
modeling results from the old box and the new optimized box. As mentioned in the
opening paragraph of Section 3.4, the old box did not use a lid for the styrofoam sample

holder and the samples were inserted vertically inside the old box.

76

 

-6.5
”i -7
g -7.5
8 -8
g -8.5
{E -9 - — Sample (Original Design)
a -9.5 — Sample (Optimized Design)
§ -10
l" -105
-1 1
0 5000 1 0000 15000 20000 25000 30000

Time (Second)

Figure 36 - Sample Modeling using Original Box vs. Modeling using
Optimized Design during Automatic Defrost (Temperature Controller
Enabled)

From this comparison, the new design provides an improved temperature regulation
compared to the old design. But, the modeling is still not accurate for the automatic
defrost condition. Since the modeling of the auto defrost condition is still not accurate,
the optimization for the condition when the incubator door is opened is not considered.
Also, the optimization when the incubator door and lid of the box is opened is not
considered. Even though the mathematical modeling cannot be used as a tool to optimize
the design of the box, this modeling is still useful for studying how heat is flowing inside

the box. This study can be used as a foundation to achieve a better design for the box.

77

Chapter 4

RESULTS AND DISCUSSION

Twelve boxes were fabricated for the purpose of mantaining biological samples in
a regulated low temperature environment. These boxes were tested during an automatic
defrost condition, opening the incubator door, and opening the incubator door and lid of
the box at the same time. The results for the twelve boxes are given to show that the
boxes can fulfill the temperature requirements during these conditions. These
temperature requirements are explained in Chapter 2. The results are given in the next
paragraphs.

The first requirement defined by the Center for Microbial Ecology is that the
sample shall be regulated with a set temperature between 0°C to -10°C. The Center for
Microbial Ecology requested that the boxes 1-3 be tested with the petri dishes and boxes
4-12 be tested with the cyro vials. Tables 2 and 3 show the set temperature the boxes 1-

12 are tested.

Table 2 - Set Temperature for Box 1, Box 2, and Box 3 (Petri Dishes)

 

 

 

 

 

 

# of the Box Set Temperature
(Celsius)
Box 1 -1.1
Box 2 -5
Box 3 -9.4

 

 

78

Table 3 - Set Temperature for Box 4 - Box 12 (Cyro Vials)

 

 

 

 

 

 

 

 

 

 

# of the Box Set Temperature
(Celsius)
Box 4 -1.1
Box 5 -5
Box 6 -9.4
Box 7 -3
Box 8 -7
Box 9 -9
Box 10 —4
Box 11 -6
Box 12 -8

 

 

 

 

The results of the set temperature can be compared with the sample temperature to verify
the temperature regulation within the box. If the sample temperature is not within 11°C,
then a new calibration equation is generated. The comparison results between the sample
temperature and set temperature are shown in Figures 37 — 48. The sample temperature
was taken using thermocouples to measure the temperature in the left corner, middle, and
right comer of the boxes. Figures 37-39 show the comparison results between the sample
temperature and set temperature within the petri dishes for boxes 1-3 during an automatic

defrost condition.

79

Temperature (Celsius)

Temperature (Celsius)

LI
'5).—

-1.4

l
._.-
O\

-1.8

I
N

-2.2
-2.4
-2.6
-2.8

-4.2
-4.4
-4.6
-4.8

-5.2
-5.4
-5.6
-5.8

— Sanple - Middle (Deg C)
— Sample - Left Corner (Deg C)
— Sampb - Right Comer (Deg C)

—SetT

 

0 5000 10000 1 5000 20000 25000 30000
Time (Second)
Figure 37 - Automatic Defrost Condition with Set Temperature
inside the Box at -l.l Deg C (Box 1)

— Sample - Right Corner (Deg C)
— Sample - Lefi Corner (Deg C)
— Sarrple - Middle (Deg C)

— T Controller

    

fi——T

0 5000 1 0000 1 5000 20000 25000 3 0000

Time (Second)

Figure 38 - Automatic Defmst Condition with Set Temperature
inside the Box at -5 Deg C (Box 2)

80

-5

 

 

 

 

 

 

— Sample - Left Comer (Deg C)
-6 — Sample - Right Corner (Deg C) —
— Sample - Middle (Deg C)
7 — Set Temperature
-8

 

 

 

 

Temperature (Celsius)

 

 

 

 

 

' 1 1 l l T l
0 5000 10000 15000 20000 25000

Tirrre (Second)
Figure 39 - Automatic Defrost Condition with Set Temperature
inside the Box at -9.4 Deg C (Box 3)

Figures 40-48 illustrate the sample temperature performance in the cyro vials for boxes 4-

12 during an auto defrost condition of the samples in the left comer, middle, and right

comer of the box.

81

Temperature (Celsius)
a.

L.
o

-12

 

 

 

 

 

 

—— Sample - Right Corner (Deg C) —
— Sample - Lefi Corner (Deg C)

 

— Sanpb - Middle (Deg C) fl
— Set Terrperature

 

 

 

 

 

 

 

l l l l l l l ‘

0 5000 10000 15000 20000 25000 30000 35000 40000 45000
Time (Second)

Figure 40 - Autonntic Defrost Condition with Set Temperature
inside the Box at -1.1 Deg C (Box 4)

-4.2 — Sample- Right Corner (Deg C)

Temperature (Celsius)

-4.8 r:

-4.4 — Sample - Middle (Deg C)

— Sample - Lefi Corner (Deg C)
7 Set T

    

0 10000 20000 30000 40000 50000
Time (Second)
Figure 41 - Automatic Defrost Condition with Set Temperature
inside the Box at -5 Deg C (Box 5)

 

 

— Sample - Right Comer (Deg C)

 

 

 

-6 _. Sample - Left Comer (Deg C)
‘7 _ Sample - Middle Corner (Deg C)
— Set Temperature

 

 

 

 

Temperature (Celsius)
do

 

 

 

 

 

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

Time (Second)
Figure 42 - Automatic Defrost Condition with Set Temperature
inside the Box at -9.4 Deg C (Box 6)

-2
_2 2 — Sample - Right Corner (Deg C)
' —— San‘ple - Left Corner (Deg C)
-2.4 — Sarmle - Middle (Deg C)

--Set T
-2.6

-2.8

-3.2
-3.4
-3.6

Temperature (Celsius)

 

0 5000 10000 15000 20000 25000 30000 35000 40000

Tirrre (Second)
Figure 43 - Automatic Defrost Condition with Set Temperature inside
the Box at -3 Deg C (Box 7)

83

Temperature (Cebius)

Temperature (Celsius)

 

 

 

 

 

 

 

 

-5.5 — Sample - Left Comer (Deg C) H
— Sample - Middle (Deg C)
-6 — Sample - Rigrt Corner (Deg C) _
-— Set Temperatm'e
-6.5

 

 

 

 

 

 

-8I I I f I I l l

0 5000 10000 15000 20000 25000 30000 35000 40000
Time (Second)

Figure 44 - Automatic Defrost Condition with Set Temperature
inside the Box at -7 Deg C (Box 8)

 

 

 

 

 

 

 

 

-8
-8.2 '
_ Sample - Middle (Deg C)
8 4 _ Sample - Right Comer (Deg C)_
- , _ 32mph - Lefi Comer (Deg C)
-85 _ — Set Temperature A
-8.8 -

       

-9 WW I lE‘““t-ém-n-L

We .1

if

 

 

 

 

‘9.4 H7 l T T l l l

0 5000 10000 15000 20000 25000 30000 35000 40000
Time (Second)

Figure 45 - Automatic Defrost Condition with Set Temperature inside
the Box at -9 Deg C (Box 9)

84

Temperature (Cekius)

Tern peratue (Celsius)

-3.2
-3.4
-3.6
-3.8

-4.2
-4.4
-4.6
-4.8

 

- Rigrtb Corner (geg C)
:Mld Left Comer (DCTDCegree C)

Set

 

 

 

0 5000 10000 15000 20000 25000 30000 35000 40000
Time (Second)
Figure 46 - Automatic Defrost Condition with Set Temperature inside the
Box at -4 Deg C (Box 10)

— Sample- Left Corner (Deg C)

— _Sarrple- Middle (Deg gClge
:8“??- Rigrt Comer( g C) —
Set enperatm'e

 

 

 

 

 

 

 

 

 

0

5000 10000 15000 20000

25000 30000 35000 40000

Time (Second)

Figure 47 - Automatic Defrost Condition with Set Temperatrne imide
the Box at -6 Deg C (Box 11)

85

 

I
\l

 

I
."
(It

 

 

I
00

 

 

-— Sarrple - Lefl Corner (Deg C)

 

 

Temperature (Celsius)
6o
M

 

 

 

 

 

 

 

-9 —Sarrp1e - Middle (Deg C)
— Sarrple - Rigrt Corner (Deg C)
_95 —Set Terrperature
'10 l l l l l T l

 

0 5000 10000 15000 20000 25000 30000 35000 40000

Time (Second)
Figure 48 - Automatic Defrost Condition with Set Temperature
inside the Box at -8 Deg C (Box 12)

Looking at Figures 37 — 48, the temperature difference between the sample temperature
and the set temperature for some of the boxes is greater than 1°C. This temperature
difference does not meet the requirements of 11°C temperature difference explained in
Chapter 2. As a result, a new calibration equation was generated to obtain a closer result
between the sample temperature and set temperature. Tables 4 and 5 show which boxes
did not meet the requirement for the 11°C temperature difference between the sample and

set temperature.

86

Table 4 — Temp Difference between Set and Sample Temperature (Petri Dishes)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Actual
Sample Temperature (Celsius)
# of Box Set
Temperature Left Temp Temp right Temp
(Celsius) corner diff middle Diff corner Diff
Box 1 -1.1 -2.63 1.53 -2.52 1.42 -2.66 1.56
Box 2 -5 -5.38 0.38 -5.67 0.67 -5.54 0.54
Box 3 -9.4 -10.24 0.84 -10.32 0.92 -10.31 0.91
Table 5 - Temp Difference between Sample and Set Temperature (Cyro Vials)
Set Actual Sample Temperature (Celsius)
# of Box Temp
(Celsius) left Temp Temp right Temp
corner Diff middle Diff corner Diff
Box 4 -1.1 -1.74 0.64 -2.22 1.12 -2.08 0.98
Box 5 -5 -5.82 0.82 -5.54 0.54 -5.72 0.72
Box 6 -9.4 -10.56 1.16 -10.60 1.20 -10.49 1.09
Box 7 -3 -2.79 0.21 -3.22 0.22 -3.09 0.09
Box 8 -7 -7.37 0.37 -7.40 0.40 -7.42 0.42
Box 9 -9 -9.05 0.05 -8.98 0.02 -9.00 0.00
Box 10 -4 -3.87 0.13 -3.51 0.49 -3.78 0.22
Box 11 -6 -5.55 0.45 -5.64 0.36 -5.69 0.31
Box 12 -8 -7.84 0.16 -8.04 0.04 -8.09 0.09

 

 

 

 

 

 

 

 

 

Tables 4 and 5 show that the highest temperature difference is more than 1.56°C.

This temperature difference occurs because the voltage sensor providing feedback to the

temperature controller was placed on the bottom of aluminum box instead of inside the

sample. A s a result, a new c alibration e quation n eeds to b e o btained in o rder for the

sample temperature to be close to the set temperature within 1°C. In order to reduce this

temperature difference, the sample temperature in Table 4 and Table 5 is plotted versus

87

 

 

the reference voltage. From this plot, the new calibration equation is determined. This

new calibration equation can be seen in Figure 49.

Vref = 0.2815*Tc + 8.9226

Reference Voltage (Volt)
0 '— N w & Ur ON \) 00 \O

 

- 12 -10 -8 -6 -4 -2 0
Temperature (Celsius)

Figure 49 - New Voltage Reference Equation

Then this new calibration equation is used to reduce the temperature difference
between the sample temperature and set temperature. The new calibration equation is
tested on boxes 10-12 during the automatic defrost condition. Due to time constraints,
the other nine boxes could not be tested. Figures 50 — 52 show the sample temperature

and set temperature is below 1°C using the calibration equation.

88

Temperature (Celsius)

Temperature (Celsius)

oz
-0 4

-0.6

I
.o
00

I
_l

-l.2

 

- l .4
0 5000 10000 15000 20000 25000 30000
Time (Second)

Figure 50- Automatic Defrost Condition with Set Temperature inside
the Box at -1 Deg C (Box 10)

 

 

 

 

 

 

 

-4
_42 E —Sanple- Left Corner(DegC)
° — Sarrple - Middle (Deg C)
— Sarrple - Rigit Corner (Deg C)
-4.4 ——
— Set Terrperature
-4.6 - 7 ¥ 7

 

    

 

Mammary MI),

 

 

 

'5.2 l I . I f A

0 5000 1 0000 1 5000 20000 25000 30000
Time (Second)

Figure 51 - Automatic Defrost Condition with Set Temperature
inside the Box at -5 Deg C (Box 11)

89

 

 

— Sample - Middle (Deg C)

-— Sample - Rigit Comer (Deg C)
— Sample - Left Comer (Deg C)
— Set Temperature

 

 

 

 

 

 

Temperature (Celsius)

 

 

 

 

 

' 1 0 I l l l l
0 5000 l 0000 l 5000 20000 25000

Time (Second)

Figure 52 - Automatic Defrost Condition with Set Temperature inside
the Box at -9 Deg C (Box 12)

30000

Table 6 shows the temperature difference between the sample temperature and the

set temperature for boxes 10-12 using the new calibration equation. Looking at Table 6,

the new calibration equation is able to reduce the temperature difference between the

sample temperature and the set temperature below 1°C.

Table 6 - Temp Difference between Sample and Set Temperature Using New

Calibration Equation

 

 

 

 

 

 

 

 

 

 

 

 

 

Actual
Sample Temperature (Celsius)
# of Box Set

Temperature left Temp Temp right Temp

(Celsius) corner diff middle Diff corner Diff

Box 10 -1 -l.19 0.19 -0.79 0.21 -1.13 0.13
Box 11 -5 -4.84 0.16 -4.91 0.09 -4.99 0.01
Box 12 -9 -9 0 -9.04 0.04 -8.81 0.19

 

90

 

Next, the unifomnity of sample temperature of each box is observed. Figures 37,
38, and 39 illustrate the sample temperature in the petri dishes for the right corner of the
box, left corner of the box, and middle of the box. Also, Figures 40, 41, 42, 43, 44, 45,
46, 47, and 48 shows the uniformity for the sample temperature in cyro vials for the right
corner of the box, left comer of the box, and middle of the box are close within each
other. Table 7 shows the temperature difference between the samples at different

positions of the box.

Table 7 - Temperature Error for the Sample at Different Locations in the Box

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Petri Dishes
Actual Temperature Temperature Difference
Left Right Left- Left- Middle -
# of BOX Corner Middle Corner fight Middle ML
Box 1 -2.63 -2.52 -2.66 0.04 0.11 0.15
Box 2 -5.38 -5.67 -5.54 0.17 0.3 0.13
Box 3 -10.24 -10.32 -10.31 0.08 0.08 0.01
Cyro Vials
Actual Temperature Temperature Difference
Left Right Left- Left- Middle -
# of BOX Corner Middle Corner fight Middle L
Box 4 -1.74 -2.22 -2.08 0.34 0.48 0.14
Box 5 ~5.82 -5.54 -5.72 0.1 0.28 0.18
Box 6 -10.56 -10.6 -10.49 0.07 0.04 0.11
Box 7 -2.79 -3.22 -3.09 0.3 0.43 0.13
Box 8 -7.37 -7.4 -7.42 0.05 0.03 0.02
Box 9 -9.05 -8.98 -9 0.05 0.07 0.01
Box 10 -3.87 -3.51 -3.78 0.09 0.36 0.27
Box 11 -5.55 -5.64 -5.69 0.15 0.1 0.05
Box 12 -7.84 -8.04 -8.09 0.25 0.2 0.05

 

 

 

 

 

 

 

 

91

Look

very

ing at Table 7, the maximum temperature difference is less than 0.48°C, which is

small. As a result, it can be concluded that the temperature of sample is uniform

throughout the box.

After observing the uniformity of the sample temperature in the box, the stability

of the sample temperature when the incubator door is opened is observed. Figures 53-55

show

Temperature (Celsius)

the sample temperature in the petri dishes when the incubator door is opened.

 

0.5

 

O
E
;

 

— Sample - Right Comer (Deg C) 2%.,
— Sample - Left Comer (Deg C) mm”;

— Sample - Middle (Deg C) W

 

.0
(I!
l
E

 

 

 

 

I
._r

 

p—ur
kl!

 

I
N

 

 

2.5 *

 

 

 

 

- 3 l l l l l l l
0 200 400 600 800 1000 1 200 1400 1600

Time (Second)

Figure 53 - Opening Incubator Door Condition with Set Temperature
inside the Box at -1.1 Deg C (Box 1)

92

Temperature (Cebius)

Temperature (Celsius)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0
'1 —Sample- Rig'rtCorner (DegC)
-2 — Sample - Left Corner (Deg C) -
— Sample - Middle (Deg C) fl
-4 /
'5 W
'7 l l T l l l l
0 200 400 600 800 1000 1200 1400 1600
Tinre (Second)
Figure 54 - Opening Incubator Door Condition with Set Temperature
inside the Box at -5 Deg C (Box 2)
-4
-5 Sample - Left Comer (Deg C)
—— Sarrple - Riglt Comer (Deg C)
-6 -— Sample - Middle (Deg C) /,.r
-7 I/I/"d/
-8 W
-9 /
-10 4M7
-1 1 f r I I I I I

 

 

0 200 400 600 800 1000 1200 1400 1600
Time (Second)

Figure 55 - Opening Incubator Door Condition with Set Temperature
inside the Box at -9.4 Deg C (Box 3)

93

 

Figures 56—64 show the sample temperature in the cyro vials when incubator door is

 

 

 

 

opened.
0
-— Sample - Riglt Corner (Deg C)
-0.5 W — Sample - Left Comer (Deg C)
— Sample - Middle (Deg C)

 

 

 

 

 

Temperature (CelsIus)
232

 

 

 

 

0 200 400 600 800 1000 1200 1400 1600
Time (Second)

Figure 56 - Opening Incubator Door Condition with Set Temperature
inside the Box at -l.1 Deg C (Box 4)

I
p—a

 

 

  
    

-— Sample - Riglt Corner (Deg C)
— Sample - Left Corner (Deg C)
— Sample - Middle (Deg C)

I
N

 

 

I
b)

 

 

 

 

 

 

 

 

I
U!

 

Temperature (Celsius)
4';

I
0‘

 

 

 

I
\I

 

T T T T T

0 500 1000 1500 2000 2500 3000
Time (Second)

Figure 57 - Opening Incubator Door Condition with Set
Temperature inside the Box at -5 Deg C (Box 5)

94

-4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

er -§me-Re§°mereegg> *
A — amp - Le omer (Deg ) /
g _6 _ —Sample — Middle (Deg C) j
22 J
E -7 /

i! -8 "
0
a /
E -9
E-

-10 -

'11 T l l T T

0 500 1000 1500 2000 2500 3000

Tinre (Second)

Figure 58 - Opening Incubator Door Condition with Set Temperatrne
inside the Box at -9.4 Deg C (Box 6)

— SampES RTgECoderTT
— Sample - Middle (Deg C)
— Sample - Left Comer C)

Temperature (Celsius)

 

0 500 l 000 l 500 2000 2500 3000

Time (Second)

Figure 59 - Opening Incubator Door Condition with Set Temperature
inside the Box at -3 Deg C (Box 7)

95

 

Temperature (Celsius)

Temperature (Celsius)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-1 A — Sample - Left Corner (Deg C)

-2 e# — Sample - Middle (Deg C)

_3 _ —- Sample - Riglt Corner (Deg C)

-4

-5 Ada-$5“;

-6 f

_7 ___ - W M

-8 I I I I I

0 500 1000 1500 2000 2500 3000

Time (Second)

Figure 60 - Opening Incubator Door Condition with Set Temperature
inside the Box at -7 Deg C (Box 8)

—- Sample - Middle (Deg C)
— Sample - Right Comer (Deg
— - Left Comer C)

 

500 1000 1500 2000 2500 3000
Time (Second)

Figure 61 - Opening Incubator Door Condition with Set Temperature
inside the Box at -9 Deg C (Box 9)

96

Temperature (Cebius)

Temperature (Celsius)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0
'0'5 " — Sample - Riglt Corner (Deg C) j
'1 “— —Sample - Middle (Deg C) fix/I
— 1.5 ~~ — Sample Lefl - Comer (Deg C) WI,
-2
-3
-3.5 —
-4 ..
'4,5 l l T I
0 500 1000 1500 2000 2500
Time (Second)
Figure 62 - Opening Incubator Door Condition with Set Temperature
inside the Box at -4 Deg C (Box 10)
-1
-1.5
2 — Sample - Left Comer (Deg C)
2'5 — Sample - Middle (Deg C)
- ' — - Comrer
-3
-3.5
-4
-4.5
-5
-5.5
-6

0 500 1000 1 500 2000 2500

Time (Second)

Figure 63 - Opening Incubator Door Condition with Set Temperature
inside the Box at -6 Deg C (Box 11)

97

 

 

 

 

— Sample - Left Comer (Deg C)
— Sarrple - Middle (deg C)
-4 —— Sample - Riglt Corner (Deg C)

 

 

 

 

 

 

 

 

 

 

Temperature (Celsius)

 

 

 

 

 

 

-9 I I I I
O 500 1000 1500 2000 2500

Tinre (Second)

Figure 64 - Opening Incubator Door Condition with Set
Temperature inside the Box at -8 Deg C (Box 12)

 

Based on the Figures 53 — 64, Table 8 shows the sample maintains temperature stability
in the petri dishes and cyro vials for at least more than three and half minutes.
Furthermore, it can be seen in Figure 8 that the amount of time the sample remains steady
is different between the petri dishes and cryo vials. This is because the area of the petri
dishes is larger than the area of the cryo vials meaning the warm airwill diffuse at a
faster rate in the petri dishes compared to the cryo vials. Likewise, using heat transfer
theory, the heat transfer rate is proportional to the area of the media. This means that
when the area of the media is increased, then the heat transfer rate will also be increased.
As a result, the sample temperature in the petri dishes will become warmer faster

compared to the sample temperature in the cyro vials.

98

Table 8 - The Amount of Time for the Boxes to Maintain Temperature Stability

during Opening the Incubator Door

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Petri Dishes
Steady
# of Box Time
(Minutes)
Box 1 3.5
Box 2 5.4
Box 3 3.5
Cyro Vials
Steady
# of Box Time
(Minutes)

Box 4 9

Box 5 7.6
Box 6 7.5
Box 7 9.3
Box 8 6.1
Box 9 7.3
Box 10 9.2
Box 11 6.9
Box 12 6.8

 

 

 

 

Table 8 shows that each box maintains the temperature about 3.5-9.0 minutes
with a tolerance between 0. 1°C 02°C. According to the requirements defined by Center
of Microbial Ecology, it is important to have sample temperature to be steady at a
minimum of 3 minutes for the petri dishes and at a minimum of 5 minutes for the cyro
vials with approximately 1°C temperature tolerance. Table 8 shows the boxes fulfill the
requirements defined by Center of Microbial Ecology.

Finally, the sample temperature results are examined during opening the incubator

door and the lid of the box at the same time. Figures 65-67 show the sample temperature

99

in the petri dishes when the incubator door and the lid of the box are opened at the same

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

time.
0.2
A _ __ — Sample - Corner Riglt (Deg C) .W
E 0'3 — Sample - Corner Left (Deg C) W
% -0.8 a— —sample - Middle (Deg C)
9; -1.3 fl
5 1 8 add/I,
E _ e
g- -2.3 /
I3 -2.8 J
.3.3 l l l l
O 200 400 600 800 1000
Time (Second)
Figure 65. Opening Incubator Door and Lid of the Box with Set
Temperature inside the Box at -1.1 Deg C (Box 1)
0
a -1 A!
= /
E
g -2 /
g —3
§_4 _ -A —Sample-ComerRigrt(DegC) A
E 5 4_ —Sample-ComerLefl(DegC) L
"' ' -— Sample - Middle (Deg C)
'6 l l I l l
0 200 400 600 800 1000 1200

Time (Second)
Figure 66 - Opening Incubator Door and Lid of the Box with Set
Temperature inside the Box at -5 Deg C (Box 2)

100

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

A -5
B
E -6
8
‘; -7
‘5
E -8
8. — Sanple - Iefi Comer (Deg C)
E '9 —Sarrple-RightComer(DegC)”‘
'1 l I l I I l
O 200 400 600 800 1000 1200

Time (Second)

Figure 67 - Opening Incubator Door and Lid of the Box with Set
Temerature inside the Box at -9.4 Deg C (Box 3)

Figures 68-76 show the sample temperature in the cyro vials during opening the

incubator door and lid of the box at the same time.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O
3‘ — Sarrple - Right Corner (Deg C)
:5 -O.5 — Sarrple - Left Corner (Deg C) ‘
Q —Sample - Middle (Deg C) fl M
2 -1 W
E
a '1.5 WV
0
G- JAM/WW
E '2 “W:
’2.5 I T T T I l
O 100 200 300 400 500 600 700
Time (Second)

Figure 68 - Opening Incubator Door and Lid of the Box with Set
Temperature inside the Box art-1.1 Deg C (Box 4)

101

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-2.5
g -3.5 v j
:1 _4 ff
5 4 5 y
a - o
i -5 fl .
g 55 W —Sarmle-RnglnComer(DegC) _
E" ' ° W —Sarrple-LeflComer(DegC)
-6 —Sample - Middle (Deg C)
’6.5 I T T I I
O 200 400 600 800 1000 1200
Time (Second)
Figure 69 - Opening Incubator Door and Lid of the Box with Set
Tenperature inside the Box at -5 Deg C (Box 5)
-5
9.55 J/A/i
E -6 ‘
a _6.5 w
8 -7 W
0
in
a -7.5
e -8 J
§-8.5 — Sarrple - Right Corner (Deg C)
; -9 Sample - Middle (Deg C)
_9.5 — San'ple - Lefl Corner (Deg C)
-10 T T I f I
O 200 400 600 800 1000 1200

Time (Second)

Figure 70 - Opening Incubator Door and Lid of the Box with Set
Tenperature inside the Box at -9.4 Deg C (Box 6)

102

Temperature (Celsius)
. 2'0 . :'— . 9':
u Ur N Ur ._.. Ur O

I
S”
Kit

I
&

 

 

 

 

 

— Sanple - Right Corner (Deg C)
— Sample - Middle (Deg C)
— Sample - Left Corner (Deg C)

 

x23:

 

 

 

M

 

 

 

 

 

 

 

400 600
Time (Second)

800

Figure 71 - Opening Incubator Door and Lid of the Box with Set
Temperature inside the Box at -3 Deg C (Box 7)

1 000

 

 

 

I
.‘e
M

 

Celsius)
M M

 

-— Sanple - Left Comer (Deg C)
-— Sample - Middle (Deg C)
—- Sample - Right Corner (Deg C)

/

 

 

 

/

 

I
O\

-/

 

I
9‘
UI

 

I
\I

 

Temperature (

I
>1
UI

 

 

 

 

I
00

 

I

0 200

I I I

400 600 800
Time (Second)

Figure 72 - Opening Incubator Door and Lid of the Box with Set
Temperature inside the Box at -7 Deg C (Box 8)

103

 

l 000

Temperature (Celsius)

Temperature (Celsius)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

O
-1 —
_2 — Sarrple - Left Corner (Deg C)

— Sanple - Middle (Deg C)
’3 — Sanple - Right Corner (Deg C)
-4
-5
-6 I
_7 Ire-”£2:—
-8 ”fl/
-9 e —
10 I I I I
O 200 400 600 800 1000
Time (Second)
Figure 73 - Opening Incubator Door and lid of the Box with Set
Tenperature inside the Box at -9 Deg C (Box 9)
0
If”.
'1 JT — Sanple - Right Comer (Deg C)
— Sample - Middle (Deg C) /
-2 AH — Sanpie - Lefi Corner (Deg C) flw
-3 -/
-4
-5 l l l T I I
O 200 400 600 800 1000 1200 1400

Time (Second)

Figure 74 - Opening Incubator Door and Lid of the Box with Set
Temperature inside the Box at -4 Deg C (Box 10)

104

 

Temperature (Celsius)

Tern perature (Celsius)

O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

-1 —
— Sanple - Lefl Comer (Deg C)
_2 afl — Sample - Middle (Deg C)
— Sample - Right Comer Deg C) /
-3 f
-4 M
-5 — f
'6 l I I I I I
0 200 400 600 800 l 000 1200 1400
Time (Second)
Figure 75 - Opening Incubator Door and Lid of the Box with Set
Temperature inside the Box at -6 Deg C (Box 11)
-4
-4-5 - —— Sample - Middle (Deg C)
J:
'5 “ — Sample - Right Corner (Deg C) j
‘5'5 _ —Samp1e - Lefi Comer (Deg C)
-6
-6.5
-7
-7.5 -
-8 —
'8.5 l l l l l

 

 

 

0 200 400 600 800 1000 1200 1400
Time (Second)

Figure 76 - Opening Incubator Door and Lid of the Box with Set
Temperature inside the Box at -8 Deg C (Box 12)

105

Based on the Figures 65 — 76, Table 9 shows the sample maintains temperature stability
in the petri dishes and cyro vials for at least more than 4.4 minutes. Similar as Table 8,
the amount of time the sample remains steady is different between the petri dishes and

cryo vials. The same argument used for Table 8 can be used for Table 9.

Table 9 - The Amount of Time for the Boxes to Maintain Temperature Stability

during Opening the Incubator Door and Lid of the Box

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Petri Dishes
# of Steady
Box Time
(Minutes)
Box 1 5.8
Box 2 4.9
Box 3 4.4
Cyro Vials
# of Steady
Box Time
(Minutes)
Box 4 9
Box 5 9.5
Box 6 6.1
Box 7 9.1
Box 8 6.3
Box 9 7.5
Box 10 9
Box 11 7.8
Box 12 8.4

 

 

 

It can be seen that each box is able to maintain the temperature approximately
4.4-9.1 minutes with a tolerance temperature about il°C. According to the design

specification, the sample temperature needs to be steady at a minimum of 3 minutes for

106

the petri dishes and at a minimum 5 minutes for the cyro vials and the maximum
temperature tolerance that can be allowed is 11°C. Table 15 shows the boxes fulfill the
requirement by Center of Microbial Ecology. Note that images in this thesis are
presented in color.

Finally, one box is tested for 10 days in the incubator to see if the sample can
maintain its temperature for a long period of time. This testing also shows the reliability
of the temperature controller that is regulating the temperature of sample. Figure 77
shows the sample temperature is able to maintain its temperature for 10 days. This means
the performance of the controller system is reliable and can regulate the temperature of

the box for a long period of time.

-3.1
-3.2

I
S»
b)

-3. 4
-3. 5
-3.6
-3.7
-3.8

Temperature (Celsius)

F tComer C)
'3-9 "WA; A' ‘ :SampleE Middle (Deg

-4 fi fi 7 a V : ~7—
0 2000 4000 6000 8000 10000 12000 14000 16000
Time (Minutes)

Figure 77 - Sample Temperature Perfonmnce after Testing for 10
Days

 

107

Chapter 5

CONCLUSION

The purpose of this research is to design, build, and test a thermally controlled
environment (0°C to -10°C) that can maintain a regulated temperature for holding
biological samples in a low temperature incubator. While in the process of designing the
box, it was also important to attempt to improve the design of the box using mathematical
modeling. This mathematical modeling was done when the controller system is disabled
and w hen the c ontroller system is e nabled. T he results 8 howed that the m athematical
modeling when the temperature controller system is enabled during the automatic defrost
condition were not consistent with the experimental results. Because of this, the
conditions for opening the incubator door, and opening the incubator door and the lid of
the door at the same time were not modeled. Even though the mathematical modeling
showed that the results are not consistent with the experimental results, the modeling was
still used to optimize the design of the box. This is because the mathematical modeling
helps to understand the flow of heat transfer within the box. Based on this understanding,
the twelve boxes were built and tested. These results were tabulated during the
conditions of automatic defrost, opening the incubator door, and opening the incubator
door and the lid of the box at the same time. During these conditions, several
investigations were conducted to see if the sample in the box fulfills the requirements
defined by Center of Microbial Ecology. These investigations during the automatic
defrost condition include the sample temperature stability, the longest time for the sample

to maintain the stability, the comparison between the accuracy of the sample temperature

108

 

and the set temperature, and the uniformity of the sample inside the box. As for testing
the amount of time the sample is able to maintain the temperature stability, the results
showed the sample was able to maintain its temperature stability for 10 days. The results
for these investigations showed that there was temperature difference more than 1°C
between the sample temperature compared to the set temperature. But, this temperature
difference was corrected by defining a new calibration equation that is used to adjust the
set temperature inside the box. Using this new calibration equation, the temperature
difference between the sample temperatures and the set temperature was minimized. As
for the temperature uniformity of the samples inside the box, the results showed that the
sample temperature is uniform to within O.48°C. This is because the sample temperature
difference between the location of the left corner, middle corner, and right corner of the
box was less than 11°C, meeting the requirements defined by Center of Microbial
Ecology. During the condition of opening door, and the condition of opening the door
and lid of the box at the same time, the amount of time for sample temperature to be
steady was investigated. The results showed that the samples were able to maintain the
temperature stability between 3-7 minutes with approximately 0.2°C temperature
tolerance during the condition of opening the door. Also, the sample was able to
maintain the temperature 3 tability b etween 4 -9 minutes with a m aximurn temperature
tolerance of 1°C during the opening the door and lid of the box at the same time. As a
result of this research, it can be concluded that the temperature controller system is able
to regulate the sample temperature between a set temperature 0°C and -10°C. Moreover,
the twelve boxes are able to function according to requirements defined by Center of

Microbial Ecology.

109

w- \._IVI _“_‘F_J

 

Chapter 6

SUGGESTIONS FOR FUTURE RESEARCH

Even though this research has been completed, some suggestion can be made for
future research. These suggestions can help to improve the design of the box for
regulating the low temperature environment. One suggestion would be to improve the
mathematical modeling that was evaluated in Chapter 3. One way to improve this
mathematical modeling is to use three dimensions for modeling the flow of heat transfer
in the box. Using three dimensional analysis, the results could be used to optimize the
sample temperature performance during the conditions of automatic defrost, opening the
incubator door, and opening the door incubator and lid of the box at the same time.

Another suggestion to improve the design of the box is to test the box in an
incubator that does not have an automatic defrost condition. Using an incubator that does
not have an automatic defrost condition will keep the temperature inside the incubator
steady continuously except when opening the door incubator. But, this issue can be fixed
by using an incubator with an air conditioning system that can flow cold air on to the
sample when the incubator door is opened.

Besides improving the design of the box, it is suggested to conduct the research
for building an ideal box that can regulate an internal temperature in a liquid nitrogen
environment. Since liquid nitrogen can go down to -196°C, the possibility of building
this box to function in liquid nitrogen environment may be useful for biologists to
conduct research about the possibility of microorganism activity to survive in extreme

cold temperature environments. This could help scientist to prove that microorganism

110

activity can survive in extreme cold temperatures, meaning that there is possibility of a

life on Mars or other planets.

111

 

I? -H

APPENDICES

112

 

Instruction Manual for Operating the Temperature Controller

1.

2.

Place the box inside the incubator.

Connect the temperature sensor to the sensor terminals (S)

Connect the heater to the heater terminals (H).

Plug the temperature controller system into 115 VAC outlet and turn the unit on.
Calculate the desired reference voltage from the function:

Vref= O.2815*Tc + 8.9226

Using a multimeter set the reference voltage (RV) to the desired voltage by adjusting
the potentiometer (RA).

Monitor the temperature by checking the value of the temperature voltage (TV) to see
if the value of the temperature voltage matches with the value of the reference

voltage.

113

 

Procedure to Operate the Data Acquisition Software

1.

2.

9.

Go to MS Dos Prompt.

Type CD DASTC and press enter.

Type CD STD and press enter.

Type tcdloger and press enter.

Press enter twice until data acquisition screen shows up.

Go to logging, click enabled.

Type file name and press enter.

Go to log scan and put the desired number of scan (1-10,000).

Go to log interval and put the desired number of interval in second or minutes.

10. Go to acquisition and click start.

11. Go to log and click start.

114

“TEMPERATURE CONTROLLER DISABL- (ii-DIRECTION) a)

(sStyrofoam Properties»)
La = 0.026 (amt);
ka = 0.029 (tW/rn.k*);
Aa = 0.022(tm"2*):
rhoa = 50 (*kg/m‘3t);
Ca = 1000 (*J/kg.k*):
La

kaAa

Csty = rhoa Ca Aa La

Ra:

 

(«Styrofoam innert)

Lc = 0.064011");
kc = 0.029 (*W/mJu):
Ac = 0.0109(sm‘2t);

rhoc = 50 (*kg/m"3*):
Cc = 1000 (*J/kg.k*);
_ Lc
- kcAc
Cstyi = rhoc Cc Ac Lc

(*aluminum properties”)

Lb = 0.0035 (* mt);

kb 170 (*W/m.Kt);

Ab = 0.011(*m"2*);

rhob = 2790 (*kg/m“3*):

Cb = 883(* J/kg.K*);
Lb

Rb = m

Cal = rhob CbAbLb

(«Water propertie3*)

Lx 0.005 (flair);

kx 2.03 (*W/m.k*);

Ax: 0.00049(*m"2*):

rhox = 912 (*kg/m93t);

Cx: 1945 (*J/kg.K*);
Lx

kxAx

Cwater = rhox Cx Lx Lx

Rx:

(*unit area for slabs*)
A = 0.022(sm"2*);
h = 3 (*W/m‘Z Kt);

(«Convection and sytrofoam parts)

R1 = a}: + 0.5Ra (*K/Wt);

c1 = Csty (*J/Kt) ,-

(«styrofoam and aluminum part*)

115

 

R2 = O.5Ra+0.5Rb (*K/Wt);
C2 = Cal (tJ/Kt) :

(aluminum and sample holder parts)
R3 = 0.5Rb+ 0.5Rc(tK/W*);
C3 = Cstyi (*J/Kt)

(*sample holder and waters)
R4 = 0.5Rc+O.SRx (ax/Wt);
C4 = Cwater (*J/K*):

(water and sample holders)
R5 = 0.5Rx+ 0.5Rc (*K/wt);
C5 = Cstyi («J/Kt) ;

(*sample holder and aluminum*)
R6 = 0.5Rc+ 0.5Rb(*K/W*);
C6 = Ca1(*J/K*)

(«aluminum and styrofoam»)
R7 = 0.5Rb+0.5Ra (ark/Wt);
C7 = Csty (*J/Kt);

(*styrofoam and convection*)

R8 = F11: + 0.5Ra (*K/Wt);

maxT=9980;

incT=10;

Tout = (-11.82+ (13.63/ (1+Exp[-(t-S75.87+0.000000000001/2) /137.02])) a
(1-1/ (1+Exp[-(t-S7S.87+0.000000000001/2) /2579.22])))

 

 

 

 

 

 

 

 

 

 

 

 

solution =NDSolve[{C1 V1’[t] + Vl[t]R-2V2[t] == % (Tout -Vl[t] ) .

V1[t]R-2V2[t] == V2[t]R-3V3[t] “22”,”),
vzm -V3[t] 3 C3 v3’lt] + v3[t] -v4[c]

R3 R4 '
V3[t] —V4[t] __ , V4[t] -V5[t] V4[t] -V5[t] __

R4 " C4 W [t] i as ' as “

, vsm -V6[t] vsm —V6[t] __ , vein] -v7[c]
csvs [t] + as . R6 -- cs V6 [t] + R7 .
vslthjlwm == c7 v7'[e] + R—18 (v7(c] - (ToutH. v1[o -12.1,

mm = -12.02. v3(01-.= -12.3, vuol -12.2.
v5[01=—12.1,vs[01= -12.3, v7[01== -12.4}.
{V1, v2. v3, v4. vs, vs, W}. (t, o. max'l‘}]

91 = Plot[Bva1uate[Vl[t] /. solution] , (t, 0, max'r}]

92 = Plot[Eva1uate[V2 [t] /. solution], {t, 0, max'r}]
93 = Plot[Eva1uate[V3 [t] / . solution] . (t, 0, max'r}]

116

 

94 = Plotlealuate[v4[t] /. solution], (t,
95 = Plot[Eva1uate[V5[t] /. solution] , (t,
96 = Plot[Evaluate[V6[t] I . solution] . (t,
97 = Plot[Evaluate[V7 [t] /. solution] . (t,
98 = Plotl'rout, (t, 0. max?”

Show[91, 92, 93, 94, 95, 96, 97, 98]

117

0. warm]
0, MM
0, MM
0, MM

(*TEMPERATURE CONTROLLER DISABL- (Y-DIRECTION) a)

(*Styrofoam Properties.)

La = 0.026 (amt);
k8 = 0.029 (*W/mJu);
An = 0.0158(tm‘2fi):

rhoa = 50 (*kg/m‘3t):

Ca = 1000_(*J/k9.k*);
La

kaAa

Csty = rhoa Ca Aa La

Ra:

(*Styrofoam innerar)

Lc = 0.10 (“l“);
kc = 0.029 (*W/m.k*);
Ac = 0.0069(im‘29);

rhoc = 50 (*kg/m‘3t);
Cc = 1000 («J/legit);
LC
kc Ac
Cstyi = rhoc Cc Ac Lc

RC:

 

(*aluminum propertiesr)

Lb =0.0035 (iv an);
kb = 170 (*W/mdtt);
Ab = 0.00725(*m"2*):

rhob = 2790 (*kg/m93t):
Cb = 883(* J/kg.xa):
Lb
kbAb
Cal = rhob CbAbLb

Rb:

 

(*Water properties*)

Lx = 0.01(*m*);

kx = 2.03 (*W/m.k*);

Ax: 0.00049(*m"2*);

rhox = 912 (*kg/m‘3t);

Cx: 1945 (tJ/ngU):
Lx

m

Cwater = rhox CxLxAx

Rx:

(*unit area for slabsr)
A: 0.022 (*m‘Zt);
h = 10(tW/m‘2 Kt);

(«Convection and sytrofoam partsr)

R1 = T‘rlA— + 0.5Ra (*K/Wt);

C1 = Csty (*J/Kir);

(*styrofoam and aluminum part1»)

118

R2 = 0.5Ra+0.5Rb (tK/Wt) ;
C2 = Cal (*J/Kt);

(taluminum and sample holder part4»)
R3 = 0.5Rb+ 0.5 Rc(*K/W*);
C3 = Cstyth/Kt)

(*sample holder and water*)
R4 = 0.5Rc + 0.5Rx («IX/Wt):
C4 = Cwater (*J/Kt):

(*water and sample holder*)
R5 = 0.5Rx+ 0.5Rc (*K/Wt);
C5 = Cstyi (*J/Kt);

(*sample holder and aluminum.)
R6 = 0.5Rc+ 0.5Rb(*K/W*);
C6 =Ca1(*J/Kt)

(*aluminum and styrofoam»)
R7 = 0.5Rb+0.5Ra (ix/Wt);
C7 = Csty (*J/Kt);

(*styrofoam and convection*)

R8 = h—1A_ + 0.5Ra (ax/War);
maxT=19990;

incT=10;

Tout = (-14.27 + (15.45/ (1 +Exp[-(t-903.09+0.000000000001/2) /119

(1 - 1/(1+Exp[—(t-903.09 - 0.000000000001/2) /29oo.73])))

v1[t] -v2[tl if (Tout-Vlicl),

 

solution = NDSolve[{C1 Vl’ [t] +

 

 

 

 

 

 

 

 

.69])) *

 

 

R2 R

V1[t]R-2V2[t] == V2[t]R-3V3[t] +C2V2’[t],
V2[t] -V3[t] a C3 v3’lt] + vam -V4[t]

R3 R4 ’
V3[t] —V4[t] __ , V4[t] -V5[t] V4[t] -V5[t] __

R4 "C4 V4 “:1 + RS ’ RS "

, vsm -V6[t] vsm -V6[t] __ , vsm —v7[c]
C5 VS [t] + R6 , R6 —— C6V6 [t] + R7 ,
V6{tl -V7[t] __ , _1_ - -- -

R7 --c7 V? [t] + R8 (v7[e] (Tout)), v1[o -- 14.31,
v2[0] —14.87, v3[0] = —14.82, v4[01 -14.96,
v5[ol = —14.96, mm = -14.96, v7[01== —1s.1},

{V1, v2, v3, v4, vs, vs, v7}, (1:, o, max'r}]
91 = Plot[Evaluate[V1[t] /. solution]. (t, 0, maxT}]

92 = Plot[Evaluate[V2[t] /. solution]. (t. 0, maxT}]
93 = Plot[Evaluate[V3[t] /. solution] , {t, 0, maxT}]

119

94 = Plot[Evaluate[v4[t] /. solution] , (t, 0, max'l'}]
95 = Plot[Evaluate[V5[t] /. solution], (t. 0, MN
96 = PlotlEvaluate[V6[t] /. solution], (t, 0, max'r}]
97 = Plot[Evaluate[V7[t] /. solution], (t, 0, M”
98 = Plotl'rout, (t, 0, maxT}]

Showlgl, 92, 93, 94, 95, 96, 97, 98]

 

120

(*TMERATURE CONTROLLER DISABL- (Z-DIRECTION) *)

(«Styrofoam Propertiesrr)
La = 0.026 (amt);
ka = 0.029 (tW/m.k*);
Aa = 0.055(tm‘2t);
rhoa = 50 (*kg/m93t);
Ca = 1000 (*J/k9.k*);
- _E‘_.
kaAa '
Csty = rhoa Ca La Aa;

Ra

(*aluminum propertiesr)

Lb = 0.0035 (* mil):
kb = 170 («W/th);
Ab = 0.0319(tm‘2t);

rhob = 2790 (tkg/m"3t);

Cb = 883(* J/k9.K*);
Lb

Rb - kbAb '

Cal = rhobeLbAb;

 

(*unit area for slab3*)
A=0.055 (*m22t);
h=3 (*W/m‘2 Kt),-

(«water propar)

Lx = 0.035 (*m*);

kx = 2.03 (*W/m.k*):

Ax = 0.0000785(*m"2*):

rhox = 912 (*kg/m‘3t):

Cx = 1945 (*J/k9.K*);
Lx

m‘

Cwater = rhox Cx LxAx;

Rx:

(*Convection and sytrofoam parts)

R1 = % + 0.5Ra (*K/Wt)

C1 = Csty (*J/Kt)

(*styrofoam and aluminum partt)
R2 = 0.5Ra+0.5Rb («K/Wt)
C2 = Cal (aJ/Ka)

(*aluminum 8: water part1»)
R3 = 0.5Rb+ 0.5Rx(*K/Wt)
C3 = Cwater

(sweater and aluminum parts)

R4 = O.5Rx+0.SRb (*X/Wt);
C4 =Cal (*J/Kfi) .'

121

(6 aluminum and styrofoam parts)
R5 = 0.5Rb+ 0.5Ra («R/w.) ;
C5 =C8ty (MI/Kt);

(*Convection and sytrofoam part*)
1
hA

 

R6: 0.5Ra+ (*K/Wt);

max'r = 20000;
inc'r = 30,-
Tout = (-12.69 + 0.011 t — 0.0000043 (t) "2 + 0.00000000059 (t) "3 -
0.00000000000068 (t) f4 - 0.0000000000000053 (t) ‘5) /
(1 - 0.00058 t + 0.00000025 (t) "2 - 0.000000000033 (t) "3 +
0.00000000000073 (t) "4 + 0.000000000000000295 (t) “5)

solution:NDSolve[{C1V1’[t] + Wm "Wm == R—ll- (Tout-Vlltl).

R2

R2 R3 R3
C3V3’[t] + V3”) ’th] , V3tt] ’V4[t] =c4v4’lt] + “Rig-3“” .

R4 R4
V4[t] -V5[t] =C5V5’[t] + V5[t] -Tout
R5

 

 

 

 

 

 

, v1[01= -14.39,

 

 

R6
v2{0] = -14.45, V3[0] -14.4522, V4[0] = —14.32, V5[0] == -14.92},

{V1, v2, V3, V4, v5}, {t, o, maxT}]

91 = Plot[Eva1uate[V1[t] / . solution] .
{t, 0, max'r}, PlotRange-a (Automatic, {5, -20}}] ,-

92 = Plot[Evaluate[V2[t] /. solution], {t, 0, maxT},
PlotRange -) {Automatic, {5, -20} H;

93 = Plot[ENaluate[V3[t] /. solution], {t, 0, maxT],
PlotRange -> {Automatic, {6, —20} H;

94 = Plot[Evaluate[V4[t] /. solution], {t, 0, mad},
PlotRange 6 {Automatic, {5, ~20} }] ;

95 = Plot[Evaluate[V5[t] /. solution], {t, 0, maxT],
PlotRange -+ {Automatic, {5, -20} l];

96 = Plot[{Tout], {t, 0, max'r]];

Show[91, 92, 93, 94, 95.

PlotRange-r {Automatic, {5, -30]], AspectRatio—r 1.0]

122

“TEMPERATURE CONTROLLER DISABL-
(OPENING THE INCUBATOR DOOR CONDITIONMr)

(tStyrofoam Propertiesw)
La = 0.026 (*m*):
ka 0.029 (*W/m.k*);
Aa 0.055(tm‘21r):
rhoa = 50 (*kglm‘36);
Ca = 1000 (*J/k9.k*);
La

ka Aa
Csty = rhoa Ca La Aa

Ra:

 

(taluminum propertiesrr)
Lb = 0.0035 (* mt):

kb 170 (*W/th):

Ab 0.0319(tm92t);
rhob = 2790 (*kg/m‘3t);
Cb = 883(* J/kg-K*);

Lb
Rb - fie;
Cal = rhobeLbAb

(«unit area for slab5*)
A=0.055 (*m"2*);
h=3 (*W/m‘z Kt);

(*water propi)

Lx = 0.035 (smut):

kx = 2.03 (*W/m.k*);

Ax: 0.0000785(*m"2*):

rhox = 912 (*kg/m‘3t);

Cx = 1945 (*J/k9.K*)i
Lx

kx Ax
Cwater : rhox Cx Lx Ax

 

(*Convection and sytrofoam part.)

R1 = 31: + 0.5Ra (*K/Wt);

C1 = Csty (*J/Kt):

(*styrofoam and aluminum partt)
R2 = 0.5Ra+ 0.5Rb (tit/Wt);
C2 = Cal (*J/Kir);

(*aluminum 6. water parts-r)
R3 = 0.5Rb+ 0.5Rx(*K/Wt);
C3 = Cwater

(*water and aluminum part1»)
R4 = 0.5Rx+ 0.5Rb (*K/Wt);

123

 

C4 = Cal (*J/Kt) ;

(« aluminum and styrofoam part«)
R5 : 0.5Rb+ 0.5Ra («K/9h) ,-
C5 = Csty («J/10);

(«Convection and sytrofoam part«)

R6: 0.5Ra +

 

1

11A («K/Wt);

maxT=5000;

incT=10;

Tout: (-15.65+15.73 (t) “0.5—0.022«t) /
(1+0.84 (t)“0.5-0.0035t+0.0000143(t)"1.5)

v1[t] -V2[t]

 

solution = NDSolve[{C1 V1’ [t] + :: % (Tout - V1 [t] ) .

 

 

 

 

 

 

 

R2
v1[t]R—2V2[t] == V2[t]R-3V3[t] +C2v2,[t]' V2[t:]R-3v3[tl ==
, V3[t] -V4[t] V3[t] -V4[t] .. , V4[t] -V5[t]
C3 V3 [t] 4» R4 . R4 “C4V4 [t] + RS .
V4[th-Svsltl =C5V5'[t] + V5[thgTout ' V1[0l 44.89,

V2[0] := -14.79, v3{ol -.= -14.72, v4{ol : -14.79, v5{ol -1s.74},
{V1, v2, V3, v4, V5}, {t, o, maxT}]

91 : Plot[Evaluate[V1 [t] / . solution] ,
{t, 0, maxT}, PlotRange-r {Automatic, {10, -20}}];

92 : Plot[Evaluate[V2[t] /. solution], {t, 0, maxT},
PlotRange—r {Automatic, {5, -20}}];

93 : Plot[Eva1uate[V3[t] /. solution], {t, 0, maxT},
PlotRange-> {Automatic, {6, -20}}];

94 = Plot[Eva1uate[v4[t] /. solution], {t, 0, maxT] ,
PlotRange -> {Automatic, {5, -20}}] ,-

95 = Plot[Evaluate[V5[t] / . solution], {t, 0, maxT} ,
PlotRange-r {Automatic, {10, -20}}];

96 : Plot[{Tout], {t, 0, malel;

Show[91, 92, 93, 94, 95, 96,

PlotRange-r {Automatic, {5, -30}], AspectRatio-r 1.0]

124

 

(*TMERATURE CONTRLLER DISABL-
(OPENING THE INCUBATOR DOOR AND TOP OF THE BOX AT THE SAME TIME”

(«Styrofoam Properties«)

La = 0.026 («1m»):
ka : 0.029 («W/m.k«):
Aa : 0.055(«m“2«);

rhoa : 50 («k9/m‘3«);
Ca : 1000 («J/k9.k«);
La
kaAa
Csty : rhoa Ca La Aa

Ra:

 

(taluminum properties«)
Lb : 0.0035 (« m«):

kb 170 («W/m.K*):

Ab 0.0319(«m‘2«);
rhob : 2790 («k9/m“3«);
Cb : 883(« J/k9.K«);

Lb
Rb - kbAb
Cal = rhob Cb LbAb

(«unit area for slabs«)
A1 = 0.055 («m"2«);

A2 : 0.0000785(*m"2*);

h = 20(«W/m‘2 Kat);

(«water prop«)

Lx = 0.035 («m«):

kx : 2.03 («W/m.k«):

Ax = 0.0000785(«m"2«):

rhox : 912 («kg/m"3«);

Cx : 1945 («J/k9.K«):
Lx

m

Cwater : rhox Cx LxAx

Rx:

(«Convection and sytrofoam part«)
1

hAl

C1 = Csty («J/Kit);

R1:

 

+ 0.5Ra («K/Wit);

(«styrofoam and aluminum part«)
R2 = 0.5Ra+ 0.5Rb («K/Vi“);
C2 = Cal («J/Kt);

(«aluminum 8: water part«)
R3 : 0.5Rb+ 0.5Rx(«K/W«);
C3 : Cwater

(«water and convection part«)

125

 

 

 

 

R4 = 0.5m: + 11:2 (ax/m).-
maxT: 5165:
incT:5;
Tout: 16.08-0.006 (t) +0.000043 (t) "1.5+0.32 (t) A0.5
solution:NDSolve[{C1V1'[t] + V1[t]R-2V2[t] == Ril (Tout-v1[t]),
V1[t] -V2[t] __ V2[t] —v3{e] ,
R2 -- R3 +C2V2 [t],
V2[t] -V3[t] V3[t] -Tout

 

== C3 V3’[t] +

 

R3 R4 .v1{01 ==-0.58.

V2[0] =-.. -12.05, v3{0] a -12.84}, {V1, v2, V3}, {t, o, maxT},
MaxSteps -) 6000, PrecisionGoal -) 0 . 5, WorkingPrecision -» l]

91 : Plot[Eva1uate[V1 [t] / . solution] ,
{t, 0, maxT], PlotRange—r {Automatic, {-20, 20}}];
92 = Plot[Evaluate[V2[t] /. solution] , {t, 0, maxT},
PlotRange-r {Automatic, {~20, 20}}];
93 = Plot[Evaluate[V3[t] /. solution], {t, 0, maxT},
PlotRange-r {Automatic, {-20, 20}}],-
94 : Plot[{Tout}, {t, 0, maxT]];
Showlgl, 92, 93, 94, PlotRange-r {Automatic, {-20, 20]], AspectRatio-r 1.0]

126

 

(«TEMPERATURE CONTROLLER ENABLED (AUTOMATIC DEFROST CONDITION.)

(«Styrofoam Properties«)

La = 0.026 («m«);
ka : 0.029 («W/m.k«):
Aa : 0.055(«m‘2«);

rhoa : 50 («kg/m“3«):
Ca = 1000 («J/k9.k«);
La
kaAa
Csty = rhoa Ca LaAa

Ra:

 

(«aluminum properties«)

Lb = 0.0035 (« nu);
kb = 170 («W/m.K«);
Ab = 0.0319(«m‘2«);

rhob : 2790 («k9/m"3«);
Cb : 883(« J/k9.K«):

Lb
Rb - 116—A‘s
Cal = rhob Cb Lb Ab

(«unit area for slabs«)
A: 0.055 («m‘2«);
h = 25(«W/m‘2 K«);

(«water prop«)

Lx = 0.035 («m«);

kx 2.03 («W/m.k«);

Ax : 0.0000785(«m"2«);

rhox : 912 («k9/m"3«);

Cx : 1945 («J/k9.K«);
Lx

kx Ax
Cwater : rhox Cx Lx Ax

 

Rx:

(«Convection and sytrofoam part«)

31 = lil—A + 0.5Ra («K/W«);

c1 = Csty («J/xi»),-

(«styrofoam and aluminum part«)
R2 = 0.5Ra+ 0.5Rb («K/Wit);
C2 : Cal («J/10);

(«aluminum 6: water part«)
R3 : 0.5Rb+0.5Rx(«K/w«);
C3 : Cwater

(«water and part«)

R4 = 0.5Rx+0.5Rb («K/ith):
C4 =Ca1 («J/K«);

127

(« aluminum and styrofoam part«)
R5 : 0.5Rb+ 0.5Ra («K/War),-
C5 = Csty («J/Th);

(«Convection and sytrofoam part«)

R6= 0.5Ra +

 

hi, («K/we);
Q/z Q[y_/; y<-—6.7] :10.87;
Q/: Q[y_/,fy>=-6.7] =0,-

maxT=27480;
incT=30;
Tout = (-16.48+0.86 (t) “0.5-0.013 (t)) / (1-0.046 (t) “0.54-0.00079 (t))

 

 

 

 

 

 

 

 

 

solution=NDSolve[{C1V1’[t] + V1[t]R-2V2[t] == T11- (Tout-V1[t]),
Q[V2[t]] + V1[t]R-2V2[t] == V2[t]R-3V3[t] +C2 V2’[t],
V2[t] -v3[t] a C3 V3’[t] + v3[t] -V4[t]
R3 R4 '
v3[t] -V4[t] .. , V4[t] -v5[t]
R4 -C4V4 [t] + RS ,
V4[t] -V5[t] _ , V5[t] -Tout _ _
R5 .-C5V5 [t] + R6 , V1[0] .. 11.95.

V2[0] z: -7.26, V3[0] a -8.22, V4[0] a -10.42, V5[0] == -12.69}.
{V1, V2, V3, V4, V5}, {t, 0, maxT}, MaxSteps-r 5000,
PrecisionGoal -> 1, Workingprecision-r 1]

91 : Plot[Evaluate[Vl [t] / . solution],
{t, 0, maxT}, PlotRange—1{Automatic, {5, -20}}];

92 : Plot[Evaluate[V2[t] /. solution], {t, 0, maxT},
PlotRange-r {Automatic, {5, -20]]];

93 : Plot[Evaluate[V3[t] /. solution], {t, 0, maxT},
PlotRange -r {Automatic, {6, -20}}],-

94 = Plot[Evaluate[V4[t] /. solution], {t, 0, maxT},
PlotRange —) {Automatic, {5, -20]}];

95 : Plot[Evaluate[V5[t] /. solution] , {t, 0, maxT} ,
PlotRange-r {Automatic, {5, -20}}];

96 : Plot[Q[V2{t]] /. solution, {t, 0, mad},
PlotRange-I {Automatic, {0, 11}]];

97 : Plot[{Tout}, {t, 0, maxT}];

Showlgl, 92, 93, 94, 95, 96, 97,

PlotRange—r {Automatic, (5, -30}), AspectRatio-sl.0]

128

 

( «DESIGN OPTIMIZATIONII)

(«Styrofoam Properties«)

La = 0.026(«m«);
ka : 0.029 («W/m.k«);
Aa = 0.055(«m‘2«);

rhoa : 50 («k9/m"3«);
Ca = 1000 («J/k9.k«);
La
kaAa
Csty : rhoa Ca La Aa

 

R6=

(«aluminum properties«)
Lb : 0.0035 (« nu);

kb 170 («W/m.K«);

Ab : 0.0319(«m‘2«);
rhob : 2790 («k9/m"3«):
Cb : 883(« J/k9.I(«);

Lb
Rb - kbAb
Cal = rhob Cb LbAb

(«unit area for slabs«)
A=0.055(«m"2«); ’
h=25(«W/m"2 Ki);

(«water prop«)

Lx : 0.017 («m«);

kx 2.03 («W/m.k«);

Ax: 0.000637(«m"2«);

rhox : 912 («k9/m"3«);

Cx : 1945 («J/k9.K«) ;
Lx

kx Ax
Cwater : rhox Cx Lx Ax

Rx:

 

(«Styrofoam Properties«)
Ls 0.025 («m«):
ks 0.029 («W/m.k«);
As : 0.0319(«m‘2«);
rhos : 50 («k9/m"3«):
Cs : 1000 («J/k9.k«):
L3
= ksAs
Cst : rhos Cs Ls As

R8

(«Convection and sytrofoam part«)
R1 = a + 0.5Ra («K/1h):

C1 : Csty («J/IO);

(«styrofoam and aluminum part«)

129

 

R2 : 0.5Ra+0.SRb («X/W1»);
C2 = Cal («J/1h):

(«aluminum 8: water part«)
R3 : 0.5Rb+0.5Rx(«K/W«);
C3 : Cwater

(«water and styrofoam cover part.)
R4 = 0.5Rx+ 0.5Ra («K/Wit);
C4 : Cst («J/10);

(«Styrofoam cover and aluminum«)
R5 : 0.5Rs+ 0.5Rb («K/11h);
C5 : Cal («J/10);

(«aluminum and styrofoam part«)
R6 = 0.5Rb+ 0.5Ra («K/9h);
C6 = Csty («J/K«);

(«Convection and sytrofoam part«)

R7: 0.5Ra +

 

hlA (*K/W*):
o/: Q[y_/; y<-—6.7] :10.87;
Ql: Q[y_/.'y>:—6.7] =0,-

maxT:27480;
incT: 30;
Tout: (-16.48+0.86 (t) ”0.5-0.013 (t)) / (1-0.046 (t) "0.5+0.00079 (t))

solution=NDSolve[{C1V1’[t] + V1[t]—V2[t] =

 

1
H (Tout -V1[t] ) ,

 

 

 

 

 

 

 

 

 

R2
inzltll + V1[t]R-2V2[t] z: V2[t]R-3V3[t] +C2 v21“,
V2[t] -V3[t] __ , v3[t] -v4[t] v3[t] -v4{c]
R3 -- c3 v3 [e] + M , R4
C4V4'[t] + V4[t1R-Svslt] , V4[th-Svs[tl ==c5 V5,“) + VSIthii Tout .
V5[t]};6vmtl C6 V6'ltl + “”16““, mm] .-= 41.95, v2{01 a -7.26,

V3[0] = —8.22, V4[0] :: —9.22, V5[0] z: -10.42, V6[0] = -12.69},
{V1, V2, V3, V4, V5, V6}, {t, 0, maxT}, MaxSteps-I 5000,
PrecisionGoal -« 1, WorkingPrecision —) l]

91 : Plot[Evaluate[Vl [t] / . solution],
{t, 0, maxT}, PlotRange-I {Automatic, {5, —20}}] :

g2 : Plot[Evaluate[V2 [t] / . solution], {t, 0, maxT},
PlotRange -« {Automatic, {5, -20}]] ;

93 : Plot[Evaluate[V3[t] /. solution], {t, 0, maxT},
PlotRange -» {Automatic, {6, -20} }] ;

94 : Plot[Evaluate[V4[t] /. solution] , {t, 0, maxT},
PlotRange -9 {Automatic, {5, -20]}],-

95 : Plot[Evaluate[V5[t] /. solution] , {t, 0, maxT},

130

 

PlotRange-I {Automatic, {5, -20}}];

96 = Plot[Evaluate[V6[t] /. solution], (t, 0, maxT] ,
PlotRange-r {Automatic, {5, -20}}],-

97 : Plot[QlVthH /. solution, {t, 0, maxT},
PlotRange-r {Automatic, {0, 11}}];

98 : Plot[{Tout}, {t, 0, maxT]],-

Show[91, 92, 93, 94, 95, 96, 97, 98,

P10tRan9e-«(Automatic, {5, -30}}, AspectRatio-11.0]

131

 

--.NK— '1‘

BIBLIOGRAPHY

1. Gilichinsky, D. (1993). Viable Microorganisms in Permafrost: The Spectrum of
Possible Applications to New Investigations in Science for Cold Regions.

2. Williams, D. (1989). Advances in Microbial Ecology. NY: Plenum Press.

3. McKay, P., Friedman, E., and Meyer, M. From Siberia to Ma_r§,

4. Gilichinsky, D., McGrath, J., Rivkina, E., Tiedje, J., and Wagener, S. (1998).
Biogeochemical Activity of Anaerobic Microorganisms from Buried Permafrost
Sediments.

5. Kalinina, L., Aerobic Bacteria of Permafrost Siberia Coil.

6. Kalinina, L., McGrath, J., and Wagener, S. Cold Adaptation of Permafrost
Microorganisms.

7. DeWitt, D. and Incropera, F. (1996). Introduction to Heat Transfer. NY: Wiley
and Sons, Inc.

8. Holman, J. (1976). Heat Transfer. NY: McGraw-Hill, Inc.

9. Rizzoni, G. (1996). Principles and Applications of Electrical Engineering.
Boston: Times Mirror Higher Education Group, Inc.

10. Nilsson, J. (1993). Electrical Circuits. NY: Addison-Wesley, Inc.

132

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