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Investigation of Waste Heat Recovery in Data Centers by the
Thermoelectric Effect
by
Lawrence Lewis III
An Engineering Project Submitted
to the Graduate Faculty
of Rensselaer Polytechnic Institute
in Partial Fulfillment of the Requirements
of the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved
________________________________________
Professor Sudhangshu Bose, Ph.D., Project Advisor
Rensselaer Polytechnic Institute
Hartford, Connecticut
April, 2012
© Copyright 2012
by
Lawrence Lewis III
All Rights Reserved
ii
Contents
List of Tables ................................................................................................................................. iv
List of Figures ................................................................................................................................. v
Nomenclature ................................................................................................................................. vi
Acknowledgement ....................................................................................................................... viii
Abstract .......................................................................................................................................... ix
1.
2.
Introduction ........................................................................................................................... 10
1.1.
Background ................................................................................................................... 10
1.2.
Problem Description ..................................................................................................... 12
1.3.
Previous Work .............................................................................................................. 13
Methodology ......................................................................................................................... 14
2.1.
Fundamentals of Heat Transfer Applied to Thermoelectric Devices ........................... 15
2.2.
Thermoelectric Couple Basic Configuration ................................................................ 15
2.3.
Thermoelectric Generator Fundamental Principles ...................................................... 20
2.4.
Data Center Cooling Configuration .............................................................................. 23
2.4.1.
Convection Cooling .............................................................................................. 23
2.4.2.
Conduction Cooling .............................................................................................. 25
2.4.3.
Combination Air and Liquid Cooling ................................................................... 27
2.4.4.
Thermoelectric Device Implementation to Cooling Configuration ...................... 28
2.4.5.
Data Center Functional Parameters ...................................................................... 28
2.5.
Thermoelectric Material Selection ................................................................................ 34
2.6.
Thermoelectric Generator Implementation ................................................................... 38
3.
Results ................................................................................................................................... 39
4.
Conclusions ........................................................................................................................... 40
5.
References ............................................................................................................................. 41
6.
Appendix A- Sample Calculation of Power Generation ....................................................... 42
7.
Appendix B- Modeling of a Bismuth Telluride Pellet .......................................................... 44
iii
List of Tables
Table 1- Cooling Capability of Commercial Water Cooled Electronics Cabinets ....................... 29
Table 2- CFM Values for Given Temperature Differences with a 25 kW Heat Load.................. 30
Table 3- CFM Values for Commercial Water Cooled Electronics Cabinets Air-to-Liquid Heat
Exchangers .................................................................................................................................... 30
Table 4- Temperature Difference Calculated Using Equation (27) for Given Heat Loads and
CFM Values .................................................................................................................................. 31
Table 5 - Averaged Module Material Parameters [11] ................................................................. 42
Table 6 – Thermoelectric Generator Resistance Due to Series and Parallel Module
Configurations............................................................................................................................... 43
Table 7 - Resultant Temperature, Current, and Power for Varying Voltages .............................. 44
Table 8 - Resultant Temperature, Current, and Power for Varying Voltages .............................. 45
iv
List of Figures
Figure 1- ASHRAE Equipment Heat Load Trends [1] ................................................................. 11
Figure 2- Average Data Center Power Allocation for 12 Benchmarked Data Centers [3] ........... 12
Figure 3- Example of Thermoelectric Junction ............................................................................ 16
Figure 4- Thermoelectric Couple with P and N Type Semiconductors ........................................ 18
Figure 5- Multiple TE Devices Arranged in a Parallel Configuration.......................................... 19
Figure 6- Closed Loop Forced Convection Cooling of an Electronics Cabinet ........................... 24
Figure 7- Open Loop Forced Air Convection Cooling of Electronics Cabinets........................... 25
Figure 8- Conduction Cooled Electronics Cabinet Using a Cold Plate ........................................ 26
Figure 9- Convection Cooled Electronics Cabinet Rejecting Heat to an In-Cabinet Air-to-Water
Heat Exchanger ............................................................................................................................. 27
Figure 10- HP® Guidelines for Determining Approximate Heat Removal- Heat Capacity for One
Rack in a Single Rack Configuration for 25°C Server Intake Air ................................................ 34
Figure 11- ZT for P-type Thermoelectric Materials ..................................................................... 35
Figure 12- ZT for N-type Thermoelectric Materials..................................................................... 36
Figure 13- Material Properties of Bismuth Telluride Related to Temperature [10] ..................... 37
Figure 14- Standard Thermoelectric Module Configuration for Waste Heat Recovery ............... 38
Figure 15- Thermoelectric Module Configuration for Liquid Cooled Cabinets........................... 38
Figure 16- Change in Temperature Across TE Pellet Based on Electrical Potential.................... 45
Figure 17- Surface Temperature Across TE Pellet ....................................................................... 46
Figure 18- Electric Potential Across TE Pellet ............................................................................. 47
Figure 19- Current Density in TE Pellet ....................................................................................... 48
v
Nomenclature
Symbol
A
A
cP
I
K
L

m
NP
NS
NT
P
PO
Q
Qh
RC
RGENERATOR
RM
RL
T
Tavg
TC
TH
ΔT
V
V
VO
VOC
x
W
Z
Units
amperes
M2
J/(kg·K)
Amperes
W/K
m
kg/s
watts
watts
watts
watts
ohms
ohms
ohms
ohms
K
K
K
K
K
m3/s
V
V
V
m
watts
1/K
Description
Amperes, measure of current
Cross sectional area of pellet
Specific heat
Current
Thermal conductance
Length of pellet
Mass flow rate
Number of thermoelectric modules arranged in parallel
Number of thermoelectric modules arranged in series
Total number of thermoelectric modules
Power
Power output
Heat
Heat input to thermoelectric couple
Average internal resistance of thermoelectric couple
Total thermoelectric generator resistance
Average resistance of module
Load resistance
Temperature
Average Temperature
Temperature of cold junction
Temperature of hot junction
Temperature difference
Volumetric flow rate
Voltage
Voltage output
Open circuit voltage
distance
Measure of power
Figure of merit
Greek Symbols
Units
V/K
V/K
V/m
W/(m·K)
ohms
kg/m3
S/m
Description
Seebeck coefficient
Average Seebeck coefficient of module
Electric field
Thermal conductivity
Efficiency
Thermoelectric generator efficiency
Maximum efficiency
Resistance
Density
Electrical conductivity

M
ε

η
ηTEG
ηmax


σ
vi
Abbreviation
ASHRAE
CFM
CRAC
gpm
TE
TEG
Units
Description
American Society of Heating, Refrigeration, and AirConditioning Engineers, Inc.
3
ft /minute
Volumetric airflow in cubic feet per minute
Computer room air conditioning
gallons/minute Volumetric waterflow in gallons per minute
Thermoelectric
Thermoelectric generator
vii
Acknowledgement
I would like to acknowledge and thank my family for their constant support throughout
my education. To my sister Victoria, I am thankful for her willingness to listen to me, provide
me with different perspectives, and for her constant encouragement to pursue alternative energy
sources. I would also like to sincerely thank my advisor, Dr. Sudhangshu Bose, for his technical
guidance and support. And finally, I would like to thank Dr. Ernesto Gutierrez-Miravete for his
constant encouragement and guidance throughout my education at Rensselaer Polytechnic
Institute.
viii
Abstract
The thermoelectric effect has been proven as a source of cooling and small power
generation as defined by the Peltier-Seebeck effect. Thermoelectric modules, optimized by
semiconductors, have been used for temperature regulation by operating as a heat pump to
maintain computing devices and integrated circuits at optimum temperatures for improved
processing efficiency.
Thermoelectric modules have also been used to capture microwatt
electrical power from personal computing and other small scale devices by way of utilizing the
waste heat rejected through its heat sink. In modern data centers and server farms, water cooling
of electronics has been widely adapted as a more efficient cooling method than standard air
conditioning and ventilation systems due to its vastly larger thermal capacity. However, even
high density electronics cabinets and processing units are low level heat applications unfit for
waste heat recovery by standard thermodynamics cycles and heat pumps. When applying the
thermoelectric effect to the temperature difference between the heat source of the processing
electronics and the heat sink of a water cooling system, potential exists for practical and
economic energy recovery.
This study demonstrates the feasibility of waste energy recovery from high power density
electronics in data centers and server farms by way of the practical and economic application of
thermoelectricity.
An overview of thermoelectricity and the thermoelectric effect is given,
including a review of semiconductor materials and electronics cabinet cooling techniques. This
report describes an investigation into the efficiency of applying thermoelectricity to low
temperature waste heat situations. Conclusions are presented concerning the effectiveness of this
application towards waste heat utilization for power recovery.
ix
1. Introduction
1.1. Background
Traditional thermodynamic steam cycles require large amounts of heat to convert the
working fluid into a vapor form before it is passed through a turbine. That turbine drives a
generator to create electricity. However, in low heat applications, it is inefficient to use a
traditional cycle, such as the Rankine cycle, because there is insufficient heat to properly
convert the working fluid to a vapor. The initial cost of the equipment necessary for a
Rankine cycle, such as pumps and turbines, also makes traditional cycles unappealing due to
the low rate of return. Thermoelectricity, however, requires relatively little upfront cost. The
devices necessary are also small and the materials are less toxic. Unfortunately, they do not
generate power on the magnitude of the traditional steam cycles due to the low efficiency
levels of thermoelectric modules.
Applying the Peltier and Thomson effects,
thermoelectricity has been used frequently for thermal conditioning of electronics.
By
passing a current through a junction of two different conductors, a thermal gradient is
created. On the other hand, if a thermal gradient can be maintained between two junctions of
a thermoelectric (TE) module, then electrical power can be generated, also known as the
Seebeck effect.
As integrated circuits decrease in size yet increase in their power
consumption and essentially power density, traditional cooling systems may become obsolete
in their efforts to properly cool electronics for normal operation. While thermoelectricity has
been proven for cooling uses, opportunities are arising to benefit from power generation.
The power solicited may not be considerable, but waste energy is free, thereby increasing the
potential for economic and efficient reuse of energy.
The advantages of TE devices to be able to both cool electronics and generate power
can be leveraged to reduce data center operating costs. In Figure 1, the equipment heat loads
as provided by the American Society of Heating, Refrigeration, and Air-Conditioning
Engineers, Inc. (ASHRAE) can be seen [1].
10
Figure 1- ASHRAE Equipment Heat Load Trends [1]
The United States Environmental Protection Agency estimates that data centers and
server farms in the U.S. alone in 2006 represented approximately 1.5 percent of total
electricity consumption, or 61 billion kilowatt-hours (kWh) [2]. This figure is expected to
almost double over a 5-year period, amounting to over $7 billion in total electricity costs.
However, electronics are also increasing in efficiency, thus leading to less losses and better
use of the energy provided. For example, as seen in Figure 2, in 2010 HVAC cooling and
fans represented approximately 30 percent of data center power consumption.
11
Figure 2- Average Data Center Power Allocation for 12 Benchmarked Data Centers [3]
This percentage may decrease due to alternative cooling methods with increased efficiency.
The emphasis, however, is placed on the servers themselves and the efficiency of the
electronics. Over 40 percent of electrical power consumption in data centers is spent on
servers, and essentially all this power is rejected through waste heat. Since this waste heat is
rejected to ambient and no longer used, it represents energy that is essentially free and can be
potentially used as a green alternative energy source.
1.2. Problem Description
The objective of this project is to analyze the efficiency of applying TE devices to a
data center to assess the practicality and feasibility of waste heat recovery. Data centers
produce relatively low temperature waste heat when compared to other applications. The
efficiency of the electrical conductors used in thermoelectric waste heat recovery can be used
to assess the magnitude of power generation. Material selection is necessary to optimize the
efficiency of the thermoelectric modules while maintaining an economic solution as well as
selection of the optimum heat sink to make execution of TE devices in a data center realistic.
12
1.3. Previous Work
Several investigations and studies have been completed concerning the subject of
materials for TE devices and recovering waste heat as a green energy source. Thermoelectric
technology is used in countless applications to power small electronics, or harness enough
energy from large heat producing sources to power smaller applications, such as using the
waste heat from an automobile to power the internal computers. Most often, TE devices are
investigated for their use as a cooling device by benefiting from the Peltier effect.
An analysis of thermoelectric cooling of personal computer circuits and waste heat
power generation was conducted by C.A. Gould et al. [4]. This was conducted by mounting
TE modules onto personal computer microprocessors and operating the computers over
various levels of processing. For electrical power generation, a TE module was able to
generate a small amount of power in microwatts.
Automobile manufacturers have also investigated the use of TE devices for waste
heat recovery as explained by Meisner [5]. Following combustion, approximately 40 percent
of gasoline is exhausted through waste heat. The auto industry is working to capture some of
that waste heat through TE modules in the exhaust piping in order to power devices that
normally drain battery life. The goal is to redesign the auto electronics to run on battery
power as the primary power source rather than siphoning power generated by the combustion
of gasoline. The role of gasoline combustion would then be to charge the batteries vice
running the car. Thermoelectric modules can be used to supplement the gasoline combustion
for usable energy and therefore increasing fuel efficiency.
Overall, efficiency levels of TE devices are rated much less than conventional heat
engine cycles, thus granting minimal returns for generating electricity. Thus, data center
waste heat recovery has not been extensively documented due to the low temperature of the
heat rejected.
13
2. Methodology
In order to determine the feasibility and economic practicality of using thermoelectricity
for large scale waste heat and energy recovery, the following approach will be adopted:
1. Establish a realistic data center based on published data and investigation. Then define
normal operating parameters for operation including, but not limited to, electronics
electrical power consumption, electronics heat rejection, electronics operating
temperature, cooling approach, cooling load requirements, and cooling system power
consumption.
2. Determine the potential thermal gradient between heat source and heat sink and relate to
an appropriate thermoelectric module material selection to optimize efficiency with
consideration to cost.
3. Based on cooling load requirements, determine the operating conditions for the cooling
system.
4. Design cooling system loop using traditional heat exchange equipment to reject full
electronics heat load and maintain constant cooling temperature.
Assumption: Cooling by way of the thermoelectric module will be neglected for this
investigation since a current is not being applied to the thermoelectric module.
5. Analyze, assess, and make recommendations towards whether heat sink is appropriate to
maximize temperature difference and energy recovery.
6. Investigate potential electricity generation based on chosen thermoelectric module and
efficiency calculations, properties of the materials, environmental conditions of the
electronics and cooling system, and figure of merit of the thermoelectric material.
7. Compare and analyze the model electricity generation for data center identified in Step 1
as well as the cost implications for using thermoelectric modules.
14
2.1. Fundamentals of Heat Transfer Applied to
Thermoelectric Devices
The use of TE couples for the practical use of recovering waste heat abides by the
laws of thermodynamics.
The First Law of Thermodynamics states that in a closed system, energy can neither
be created nor destroyed. However, the energy can be transferred to other forms of energy
such as heat as well as work. TE devices seek to capture the energy that is being transferred
to heat and return it back to a voltage, or essentially power, without the use of a conventional
heat engine, or thermodynamic cycle. These cycles, such as the Rankine cycle, convert heat
to work commonly by the use of equipment such as turbines, which then return the work to
energy by way of a generator.
The TE device applies the Seebeck effect, which transfers the heat to power like a
heat engine does, without the conventional equipment. While TE couples that apply the
Seebeck effect require semiconductors and are less efficient, they can recover waste heat
from low temperature applications that conventional heat engines cannot.
The Second Law of Thermodynamics, as defined by the “Clausius statement,” says
that, “No process is possible whose sole result is the transfer of heat from a body of lower
temperature to a body of higher temperature.”
Essentially, heat flows from a higher
temperature region or body to a lower temperature region or body and it is not possible to
convert heat completely into work since losses of heat will occur due to inefficiency. A TE
couple applies the Seebeck effect by using a temperature difference to create a voltage. This
is captured through the conduction of heat from what is termed the cold side (side facing the
heat source) of the TE couple to the hot side (side facing the heat sink).
2.2. Thermoelectric Couple Basic Configuration
The thermoelectric effect can be defined by two processes, the Peltier and Seebeck
effects.
The Peltier effect occurs when a voltage is applied to two connected electrical
conductors made of different materials. When the voltage is applied, a circuit can be created
that allows for continuous heat transport between the conductor’s junctions [6].
15
The opposite also applies such that a voltage can be generated by applying a
temperature difference to the two connected electrical conductors, which is known as the
Seebeck effect. This temperature difference results in a transfer of thermal energy across the
electrical conductors and causes charge carriers to also diffuse through the materials. These
charge carriers can be either electrons, or electron deficiencies called holes, and move within
the crystals of the materials by way of electron flow from the cold side to the hot side of the
TE couple.
The heat is transferred in the same direction as the charge carrier flow, from the cold
side of the TE couple to the hot side. By leaving positively charged nuclei to collect on the
cold side of the TE couple while the charge carriers move towards the hot side, a
thermoelectric voltage is generated. This results in the potential to generate an electrical
current if a complete circuit can be created, as seen in Figure 3.
Figure 3- Example of Thermoelectric Junction
Typically, semiconductors are used in TE couples because they can be doped with
additional electrons or electron holes creating species to increase the Seebeck coefficient.
Normal metal conductors have smaller coefficients due to equilibrium of positive and
16
negative charges in the material that would induce the thermoelectric voltage. A larger
amount of charge carriers on the hot side of the material results in a higher thermoelectric
voltage, and hence semiconductors are optimum for TE devices.
Meanwhile, a TE couple uses two dissimilar electrical semiconductors electrically in
parallel because if the two semiconductors used to complete the electrical circuit are the
same, then the charge carrier flow would negate itself. There will be equal and opposite
charge carrier flow between the two semiconductors (each individual leg is commonly
referred to as a pellet) rather than single direction charge carrier flow, which generates a
current flow. Commonly used semiconductors are N and P types. N type semiconductors
can be doped such that it has excess electrons, which move towards the positive side of the
TE couple. A P type semiconductor is so doped as to have a positively charged carrier and is
thus doped with holes, which move in a direction opposite to the flow of electrons. In both
semiconductors, the charge carriers direct the direction of heat flow, which proceeds in the
same direction as the charge carrier, but electrons and holes move in opposite directions.
This allows for a continuous electrical current to be generated.
Thermoelectric materials are gauged by their figure of merit, which represents their
quality of performance, or efficiency, and is defined by the following:
Z


(1)
Where  is the Seebeck coefficient,  is the electrical resistivity, and  is the
thermal conductivity. The Seebeck coefficient is a material parameter used to determine the

efficiency of a given thermoelectric material because it is a measure of the thermoelectric
power of a material. This thermoelectric power, or thermopower, of a material measures the
magnitude of voltage stimulated in response to a temperature difference across that material.
The larger a thermoelectric voltage that can be induced combined with a higher Seebeck
coefficient results in a higher efficiency.
Low electrical resistivity and thermal conductivity are necessary for a high figure of
merit. The figure of merit is commonly multiplied by temperature because both the electrical
resistivity and thermal conductivity are temperature dependent, therefore making the figure
of merit temperature dependent. This also provides the dimensionless figure of merit. The
figure of merit can also be defined based on the electrical conductivity  as seen here:
17
ZT 
 2T

(2)
The maximum efficiency η of a TE device can be defined using the figure of merit,
as well as the temperatures of the hot and cold junctions, TH and TC, respectively.
max 
TH  TC 1  ZT  1
T
TH
1  ZT  C
TH
(3)
P and N type materials have different figures of merit and are averaged to determine
a material’s overall quality. To maximize the efficiency of a TE device, P and N type
semiconductors are placed in series electrically, but are thermally in parallel, which creates a
couple as seen below in Figure 4.
Figure 4- Thermoelectric Couple with P and N Type Semiconductors
As stated previously, the cold side of this couple is facing the heat source, where the
heat is absorbed, and the hot side is where the heat is rejected to the heat sink.
Seen in the example couple above, a ceramic substrate exists as an electrical
insulator between the heat source and the conductor as well as between the conductor and
heat sink. This is used to prevent an electrical short circuit between the conductors and the
heat source and sink. Ceramics are commonly used as the electrical insulator because they
generally have a high thermal conductivity to minimize the thermal gradient between the
18
conductors and the heat source and sink.
Copper is commonly used as the electrical
conductor to complete the circuit with the semiconductors.
When multiple TE devices are used thermally in parallel and electrically in series, it
resembles the thermoelectric generator (TEG) configuration seen in Figure 5.
Figure 5- Multiple TE Devices Arranged in a Parallel Configuration
By linking multiple TE couples in series electrically, the TEG can operate at a larger
voltage. Industry standards indicate that TEG modules can have on the magnitude of 71 or
127 couples operating at upwards of 6A.
19
2.3. Thermoelectric Generator Fundamental Principles
The open circuit voltage, VOC, generated for a single TE couple can be derived from
the following equation:
VOC    B T    A T dT
T2
T1
(4)
The voltage is commonly reported as micro-volts per temperature difference in
Kelvin. The Seebeck coefficients A and B represent the thermopowers of the two semiconductor metals A and B as a function of the temperatures T1 and T2, which represent the
temperatures of the hot and cold thermal junctions.
If the temperature difference dT between the two junctions of a material is
negligible, then the Seebeck coefficient of a material can be approximated as follows:
 
dV
dT
(5)
The thermoelectric voltage dV is seen between the two junctions of the two electrical
conductors.
The Seebeck coefficient can be related to the electric field  and the temperature
gradient
dT
by the following equation:
dx

x
(6)
dT / dx 
Equation (4) is non-linear and depends on the conductor’s absolute temperature,
material, and molecular structure. However, if the coefficients are essentially constant over
the measured thermal gradient, then the voltage generated can be approximated with the
following formula:
VOC   B   A   T2  T1 
(7)
VOC  T
(8)
or simply:
Equation (4) applies when no load (RL=0) is connected to the TE couple. However,
when a load is connected, the output voltage drops due to internal resistance, and the current,
in amperes, can be defined by:
20
I
VOC
RC  RL 
(9)
With the average internal resistance of a TE couple represented by RC and the load
resistance by RL. Substituting equation (8) into (9), the current can be written as:
I
T
(10)
RC  R L
The output voltage is then calculated as seen here:
VO  T  IRC
(11)
The total heat input to the TE couple is represented by:
Q H  IT H 
1 2
I RC  KT
2
(12)
Both the internal resistance, RC and the thermal conductance K are derived from the
material properties of the TE couple by way of the density,  , and thermal conductivity,  ,
of the TE couple.
RC 
K
L
(13)
A
A
(14)
L
However, once the heat input is known, the efficiency of the generator can be
determined.
 TEG 
VI
QH
(15)
The resultant power output of the TE module is given by:
PO  VO I
(16)
PO  I 2 R L
(17)
or,
When substituting equation (10) into equation (9), the efficiency of a couple, or
TEG, can be rewritten as:
 TEG 
PO
QH
(18)
21
The average module Seebeck coefficient,  M , average module resistance, RM, and
average thermal conductance, KM, are temperature dependent values that can be approximated
at an average module temperature.
Tavg 
TH  TC
2
(19)
Now, the previous formulas apply when dealing with a single TE module. However,
when multiple modules are used in order to meet load demands, the modules may be
connected in series, parallel, or a combination.
The total number of modules, NT, relates to the number in series and parallel, NS and
NP, respectively as shown here:
NT  N S N P
(20)
This impacts the current passing through the load resistance as shown here:
I
N S  M T
NS
RM  R L
NP
(21)
The maximum efficiency of power generation occurs when the module resistance is
equal to the load resistance, as represented.
Substituting this into equation (21), and
multiplying by VO, the output power from the TEG is determined by the following formula:
PO  VO I 
N T  M T 
4 RM
2
(22)
And the maximum power is determined by:
Pmax 
 M T 2
(23)
4RM
From this relationship, it can be seen that the power generated is directly
proportional to the square of the temperature difference between the hot and cold junctions.
Thus, to maximize the potential for power generation, the goal is to maximize temperature
difference.
When using a TEG with multiple modules connected in a series-parallel
configuration, the maximum efficiency, and power generation, occur when the total internal
resistance of the TEG is equal to the load resistance. The TEG resistance can be determined
using the average module resistance, as seen here:
22
RGENERATOR 
NS
RM
NP
(24)
Now, the output voltage of a TEG must be rewritten to address multiple modules
versus a single thermoelectric couple.
The output voltage, using the average module
resistance, RM , is given by:
VO  N S  M T  IRGENERATOR
(25)
2.4. Data Center Cooling Configuration
Data centers come in wide arrays of functionality.
As the power densities of
electronics continue to increase, so does the heat load within data centers. This has lead to
numerous cooling solutions for electronics cooling that are efficient, reliable, and cost
effective. The approaches used for electronics cooling are convection to air, conduction to
liquid, or a combination of the two. The data center facility and impacts of the cooling
system are taken in consideration implementing that cooling system into the facility
infrastructure as well as to electronics enclosure integration.
2.4.1.
Convection Cooling
Convection cooling is employed by passing conditioned air over electronics
equipment or components within the electronics enclosure to remove waste heat by
convection. The conditioning of this air can occur both internally and externally to the
cabinet.
When performing the air conditioning external to the cabinet, two basic
approaches may be utilized.
The first approach is a closed loop forced convection cooling system that
relies on large ventilation components, or computer room air conditioning (CRAC) units,
and a network of supply and return distribution ductwork to circulate the air between the
ventilation components and each electronics enclosure.
The air is forced through the
electronic components within the cabinets, thus producing heat transfer via convection as
seen in Figure 6.
23
Figure 6- Closed Loop Forced Convection Cooling of an Electronics Cabinet
This air is then vented to the ambient environment or directly ducted away
from the electronics where it is conditioned again by way of a chiller, and eventually the
heat is rejected to the ambient environment outside of the data center facility. As heat
loads increase, this approach requires substantial arrangement volume for large
ventilation components that would be necessary to penetrate the various electronics
enclosures and distribution ductwork.
The second approach, Figure 7, is an open loop forced convection cooling
system that relies on fans within the cabinets to draw ambient air over the electronic
components to remove heat through convection. The heated air is discharged back to the
ambient environment. This heated air is then conditioned via the facilities ventilation
system’s chillers. This approach usually dictates an isolated electronics area with a lower
ambient temperature that is below the acceptable ambient air temperature range for
manned areas.
24
Figure 7- Open Loop Forced Air Convection Cooling of Electronics Cabinets
Separation of personnel from the electronics equipment provides an
opportunity to maintain ambient temperatures within the electronics area at these reduced
temperatures by way of thermally isolating the equipment areas. However, this also
requires maintaining the facility space within temperature tolerances and may encounter
issues with temperature stability. Data centers have seen “hot spots” of air temperatures
exceeding the cooling air inlet temperature requirements, which may impact reliability
and performance of the electronics.
Convection cooling by air is the most common approach to forced cooling due
to a lower relative cost and easier implementation than liquid cooling. However, air also
has a low thermal capacity, thereby making it less efficient than liquids for heat removal
as heat loads increase.
2.4.2.
Conduction Cooling
Liquid cooling is generally employed for high heat load applications since
liquids such as water have a thermal capacity of approximately 3,500 times larger than
air. This translates into the heat source rejecting more heat into the liquid cooled heat
sink, and the temperature increase of the liquid will be less than that of water.
Per the ASHRAE liquid cooling guidelines [7], liquid cooling has been
implemented by liquid circulated to and from the electronics enclosure for operation.
25
This is commonly done through two closed liquid cooling loops. One cooling loop
provides the liquid directly within the electronics enclosures for waste heat removal and
rejects the waste heat to the second loop, which is cooling liquid supplied to data center
by the facility. The facility provided liquid cooling loop is known as a primary loop,
whereas the loop interfacing with the electronics is a passive secondary loop that just
circulates liquids through heat exchangers. This secondary loop circulates a conditioned
liquid to meet the electronics requirements. Besides being conditioned to temperature
requirements, this may also include quality such as contaminant levels, filtration levels,
and conductivity levels. Fluid choice can range from water (potentially deionized) to
refrigerants and dielectric fluids. Depending on environmental conditions, particularly
data center operating dew point, cooling water commonly interfaces with base of the
electronics enclosures due to condensation or liquid leakage concerns.
When employing only liquid conduction cooling, cooling liquid is pumped
through devices such as cold plates within the enclosures to which heat producing
components are mounted and through which heat is conducted into the liquid, as seen in
Figure 8. This heat is subsequently transferred to the facility primary cooling loop via
liquid to liquid heat exchangers external to the electronics cabinets, and ultimately
rejected to ambient outside of the facility.
Figure 8- Conduction Cooled Electronics Cabinet Using a Cold Plate
26
2.4.3.
Combination Air and Liquid Cooling
The most common approach to liquid cooling of electronics enclosures is to
implement an air to liquid heat exchanger within the cabinet whereby all waste heat is
rejected from the enclosures through the cooling liquid, Figure 9.
This utilizes a
combination of both air and water for waste heat removal. The electronics are cooled as
identified above by passing conditioned air over the components.
The air is then
conditioned internal to the cabinet by way of the air to liquid heat exchanger, which is
made up of a compact cooling coil and fan assembly. This assembly can be located in
multiple configurations within the enclosure, but consideration should be taken to avoid
dripping onto the electronics components in the event of condensation or leakage as
stated above. This assembly is most often used in an arrangement within the enclosure
that directs the cooling air in a loop and thus does not mix the hot and cold air streams.
This maximizes heat removal and decreases temperature stability issues common with the
open loop forced convection approach identified above.
Figure 9- Convection Cooled Electronics Cabinet Rejecting Heat to an In-Cabinet Air-to-Water Heat
Exchanger
While numerous other configurations exist utilizing both air and liquid as
mediums for waste heat removal, this study is limited to the conventional methods of
waste heat removal.
27
2.4.4.
Thermoelectric Device Implementation to Cooling
Configuration
In order to maximize TE module implementation, a closed cabinet liquid
cooling system is considered optimum.
A localized cooling system internal to the
electronics enclosures provides thermal junctions that the TE devices can be attached to
while minimizing contact resistance. Also, by using a closed system where all waste heat
is rejected through a single source that has a consolidated footprint, the temperature
difference can be maximized while minimizing losses of waste heat to ambient.
Accordingly, all energy entering the cabinet is assumed to be discarded through waste
heat.
Liquid cooling systems are also more efficient at waste heat removal for large
heat density applications. As the power density of electronics continues to increase,
liquid cooling allows for future growth in data center functionality as well as decreasing
operating costs.
2.4.5.
Data Center Functional Parameters
2.4.5.1.
Data Center Air Temperature
Per ASHRAE [8], data centers are typically considered to be under Class
A1 due to commonly having tightly controlled environmental parameters. These
parameters include the operating temperature, relative humidity and consequently
dew point. They are also considered to be involved with mission critical operations.
While some data centers may not fall into this category, Class A1 is used in this study
to represent the typical data center environmental requirements. However, ASHRAE
guidelines are intended as recommendations rather than limitations.
Regardless,
Class A1 parameters are used.
As such, this study is interested in the normal operating temperature band
of the typical data center.
As seen in the ASHRAE Class A1 guidelines, the
operational temperature is specified as 18°-27°C (64.4°-80.6°F) or 15°-32°C (59°89.6°F) allowable. To maximize the temperature difference between the junctions of
a TEG, the upper limit of the electronics cooling air temperature is set at 27°C
(80.6°F).
28
2.4.5.2.
Data Center Cabinet Heat Load
An investigation of known data center operators and electronics cabinet
manufacturers was completed to determine a nominal heat load value for a single
typical water cooling cabinet. After inspection of water cooled units by APC®,
Black Box Networking Solutions®, HP®, Intel®, and Rittal®, the cooling capacity
of the single cabinets is seen to range from 20 kilowatts (kW) to 37 kW for standard
level high density electronics cabinets with negligible heat losses to ambient for each
unit.
Table 1- Cooling Capability of Commercial Water Cooled Electronics Cabinets
Manufacturer
APC® InRow Direct Expansion Cabinets
Black Box Networking Solutions® EliteTM
Cabinets with Coolant Management System
Hewlett Packard® Modular Cooling System
kW
37
Intel®1
24
Rittal® Liquid Cooling Package Standard
Modules
20
33
35
Electronics cabinet manufacturers are constantly upgrading their
technology to meet the cooling demands of modern electronics. Numerous other
manufacturers also provide solutions to supplement current cabinet technology to
improve the cooling capacity. For this project, the standard heat load of a single
electronics cabinet is defined conservatively at 25 kW based on the above values.
2.4.5.3.
Data Center Air Flow Rate
When employing air-to-liquid heat exchangers internal to the electronics
cabinets, the ability of the heat exchanger to effectively cool the electronics is
dependent on the volume of air throughput expressed in cubic feet per minute (CFM).
By increasing the airflow across the electronics per a given time, the heat removal
capacity increases. This is primarily controlled by the use of fans that supplement
Based on Intel® Information Technology Brief “Expanding Data Center Capacity with Water-Cooled Cabinets”
from June 2007
1
29
cooling coils in a heat exchanger. The size of the fans used directly correlates to
CFM; the larger the fan, the more the airflow. However, as fan size, revolutions per
minute (RPM), and the number of fan blades increase, so does the cost associated
with the unit and vibration and acoustic noise levels. Also, fans have limits, because
even as they increase in CFM, they cannot cool to lower than the surrounding
temperature [9].
One way to determine the optimum amount of CFM necessary for the
cooling load is to use the following formula that correlates the heat load, airflow, and
temperature difference between intake and exhaust air temperatures in °F.
Watts  .316  CFM  T
(26)
This can be rearranged to solve for CFM:
CFM 
Watts
.316  T
(27)
Typical data centers use a T value of 20°-30°F. Applying the electronics
heat load defined above of 25 kW to equation (27), the corresponding CFM values for
each of these temperature differences is as follows:
Table 2- CFM Values for Given Temperature Differences with a 25 kW Heat Load
T
20°F
30°F
CFM
3956
2637
For comparison, the CFM values used by air-to-liquid heat exchangers for
the water cooled cabinet manufacturers identified in Table 1 are listed in Table 3.
Table 3- CFM Values for Commercial Water Cooled Electronics Cabinets Air-to-Liquid Heat Exchangers
Manufacturer
APC® InRow Direct Expansion Cabinets
Black Box Networking Solutions® EliteTM
Cabinets with Coolant Management System
Hewlett Packard® Modular Cooling System
Intel®2
CFM
2290
2500
2500
800-1200
Rittal® Liquid Cooling Package Standard
Modules
Up to 1412
Based on Intel® White Paper “The State of Data Center Cooling” by Michael K. Patterson and Dave Fenwick,
March 2008
2
30
The CFM values in Table 3, when related to their respective heat loads in
Table 1, would require T values far in excess of 40°F as calculated and displayed in
Table 4.
Table 4- Temperature Difference Calculated Using Equation (27) for Given Heat Loads and CFM Values
Manufacturer
APC® InRow Direct Expansion Cabinets
Black Box Networking Solutions® EliteTM
Cabinets with Coolant Management System
Hewlett Packard® Modular Cooling System
T (°F)
51.1
41.8
44.3
Intel®
63.3
Rittal® Liquid Cooling Package Standard
Modules
44.8
These CFM values suggest that the electronics cooling systems for the
listed cabinet manufacturers have cooling capabilities above and beyond what is
suggested through equation (27).
Thus, based on the CFM calculated for a 30°F temperature difference
using equation (27), and the values in Table 3, the in cabinet airflow for this project is
set at 2500 CFM.
2.4.5.4.
Data Center Cooling Liquid Selection
Fluid selection for liquid cooling application can have a large impact, but
the liquid used for the cabinet cooling loop is not of utmost importance for this
project due to the focus on operating temperature rather than liquid performance. The
objective is to optimize the T across the TE module in order to maximize power
generation.
However, the liquid does dictate both economic and environmental
impacts.
Common coolant selections for liquid cooling applications are water,
deionized water, ethylene glycol, and other dielectric fluids. The coolant selection for
this application is a product of thermal needs, such as thermal conductivity and heat
capacity. Consequently, Section 2.4.5.1 and Section 2.4.5.3 have established both the
cabinet operating air temperature and the appropriate temperature difference between
the intake and exhaust air flowing through the cabinet. This provides an operational
temperature window for the coolant.
31
Glycol solutions have beneficial thermal properties such as a low freezing
point, which can increase the temperature difference across the TE module. It also
has a high thermal conductivity and specific heat, which makes it ideal for this
application. However, glycol solutions do not offer as high a thermal conductivity as
water, and introduce toxicity or environmental concerns of dealing with such fluids.
The benefit of glycol is to offer freeze protection, but typical data centers do not
control their dew point to such low levels that excessive condensation may become a
concern. Thus, glycol solutions are not considered for this project.
Dielectric fluids are popular for electronics industry cooling systems
because of their non-conductive properties that could be a concern to sensitive
electronics. Like glycol solutions, their benefit is that they can operate over a wide
temperature range. However, the thermal conductivity of dielectric fluids is at least
four times less than that of water, and therefore is considered for this project.
Water offers high thermal conductivity and heat capacity levels for this
cooling application. The conductive and corrosive properties of the water can change
depending on whether the end user desires deionized water. Deionized water is
commonly preferred for electronics cooling applications because it is non-conductive
and acts an insulator to electronics. This may increase the cost of the system by
introducing filtration standards and necessitating higher quality piping materials to
resist corrosion. However, the change in thermal properties is negligible. Whether
deionized or not, water offers a low cost cooling solution as long as corrosion is
monitored. Due to the low environmental impact, large thermal conductivity, and
high heat capacity, water is appropriately selected as the coolant for the liquid cooling
system.
2.4.5.5.
Data Center Chilled Water Temperature
The operational temperature for the data center secondary cooling loop is
an important balance between cooling system efficiency and TE module performance.
One of the objectives of this project is to reduce energy use, therefore emphasis is
placed on the efficiency of the chilled water system secondary to primary loop heat
exchanger. Per U.S. Department of Energy Best Practices [10], high efficiency
32
chilled water systems operate with a medium temperature chilled water.
This
translates to a cooling water temperature of 55°F or higher. The benefit of using a
higher cooling water temperature, in addition to chiller efficiency, is a reduced risk of
condensation. Operating above the data center ambient air dew point avoids the
necessity for dehumidification and conditioning of ambient air.
Otherwise,
condensation mitigation practices must be implemented, such as condensation
draining and ruggedizing of components including the cabinet heat exchangers, TE
modules, and potentially the electronics being cooled.
This medium level
temperature also assists cooling system design when implementing economizers,
which can be employed by the data center but are outside the scope of this project.
Thus, for this project, 55°F will be adopted for the chilled water operating
temperature. This is used as a guideline and may be deviated from to meet specific
user demands.
2.4.5.6.
Data Center Chilled Water Flow Rate
Chilled water flow rates are dependent upon many factors. Arrangement
impacts are of particular concern to electronics cabinets manufacturers as much as
temperature. Higher flow-to-load ratios minimize cabinet heat exchanger size but
adversely impact the facility water distribution equipment, such as increasing the size
of pumps and distribution piping. In this study, initial water temperature is the only
concern, thus the flow rate will be selected based on existing water cooling systems.
Guidelines from HP® for their single water cooled server rack configuration are seen
below.
33
Figure 10- HP® Guidelines for Determining Approximate Heat Removal- Heat Capacity for One Rack in a
Single Rack Configuration for 25°C Server Intake Air 3
Based on Figure 10, and the cabinet heat load selection in Section 2.4.5.2,
the chilled water flow rate selected for the cooling of a single electronics cabinet is
approximately 10 gpm when using 12.5°C (54.5°F) chilled water.
2.5. Thermoelectric Material Selection
Based on the data center functional parameters defined above in Section 2.4.5, the
materials for the TE device can be determined. The heat transfer equation seen below can be
used to calculate the temperature of the electronics exhaust air.
 cP T
Qm
(28)
 is the air flow rate, cP is the specific
Where Q represents the cabinet heat load, m
heat, and T represents the temperature difference between the exhaust temperature entering
the air-to-water heat exchanger and the electronics intake air temperature. Rearranging
equation (28) and substituting for T , the exhaust air temperature, or essentially the hot
junction temperature, is calculated here.
3
HP Modular Cooling System Generation 2 Site Preparation Guide- February 2008
34
TH 
Q
 TC
m c P
(29)
 for air can be defined as:
Where m
m  V
(30)
For this temperature level, the most commonly used semiconductor material choice
is Bismuth Telluride (Bi2Te3). This material has a high figure of merit for the relatively low
operating temperature range applicable to electronics cooling. Figure 11 shows a chart of the
dimensionless figure of merit for various P-type semiconductors over a wide temperature
range.
Figure 11- ZT for P-type Thermoelectric Materials4
As can be seen, Bi2Te3 has the highest figure of merit compared to other materials in
the lower temperature range. Likewise, when charting N-type semiconductors in Figure 12,
Bi2Te3 still has the highest figure of merit for the applicable temperature range.
4
Snyder, J. http://www.its.caltech.edu/~jsnyder/thermoelectrics/science_page.htm
35
Figure 12- ZT for N-type Thermoelectric Materials5
The material properties of Bi2Te3 related to temperature can be seen below in
Figure 13. They include the figure of merit, Seebeck coefficient, electrical resistivity, and
thermal conductivity.
As stated earlier in Section 2.3, these values are temperature
dependent and are commonly used at the average temperature for this application, which is
approximately 301.24K (28°C).
5
Snyder, J. http://www.its.caltech.edu/~jsnyder/thermoelectrics/science_page.htm
36
Figure 13- Material Properties of Bismuth Telluride Related to Temperature [10]
For the desired average temperature of approximately 30°C, the figure of merit is
again at a maximum although the Seebeck coefficient is steadily increasing. The resistivity
is also at a low value, which benefits the TE couple performance. Also stated in Section 2.2,
copper is commonly used to connect the semiconductor pellets when creating a circuit due its
similar temperature dependency that results in its low electrical resistivity and high thermal
conductivity to match the semiconductor material.
Overall, Bismuth Telluride offers the most common and practical material selection
for this application and temperature range.
37
2.6. Thermoelectric Generator Implementation
Standard practice for connecting TEGs for the purpose of waste heat recovery is to
use to directly connect the TEG to the heat producing object for the heat source, in this case
the electronics packages. This can be completing using either solder or connecting screws.
The TEG is then connected to a fin array that is used as a heat sink as seen in Figure 14. A
fan is regularly implemented to blow air across the fin array for convective cooling.
Figure 14- Standard Thermoelectric Module Configuration for Waste Heat Recovery
However, in this application the cooling air would only be operating at
approximately 300K, thereby limiting the temperature difference across the TEG. Thus, for a
liquid cooled cabinet, a way to implement the TEG would be to attach the modules to the
heat sink, in this case cooling coils. The fin array would be placed on the upstream side of
the cooling coil, thereby letting the hot air at approximately 316K operate as the heat source.
The cooling coil, operating at 285K would then be the heat sink for heat rejection, seen in
Figure 15.
Figure 15- Thermoelectric Module Configuration for Liquid Cooled Cabinets
38
3. Results
The data center parameters defined in Section 2.4 were applied to a typical TEG using the
material properties defined in Section 2.5. First, a pellet of a TE couple was modeled using
COMSOL Multiphysics as seen in Appendix B. This modeling showed that a single pellet of a
TE couple, regardless of whether it was p- or n-type, can generate an approximate voltage of
0.015V when a thermal gradient of approximately 31K is applied. When extrapolated to a single
254-pellet thermoelectric module, low single digit voltages can be generated.
After validating the ability to generate a voltage, a practical energy generation scenario
was calculated as seen in Appendix B. Applying the equations described in Section 2.3 to the
operating temperatures of the data center defined in Section 2.4, the number of TE modules and
optimum configuration were determined. In this application, in order to generate a power output
of approximately 18W, operating with a 12V output and 1.5A current, approximately 65 TE
modules were required for the TEG. The module chosen was a typical 127-couple, 6A module.
In order to maximize efficiency of the TEG, the modules were connected in a series-parallel
configuration to attempt to equal the resistance load. This resulted in a configuration of 4
parallel strings of 13 modules placed in series.
The heat input to a single TE module is approximately 38W, and approximately 2500W for
the TEG. The resulting efficiency of the TEG was approximately 0.7%.
39
4. Conclusions
A standard data center was defined using real world practical components and functional
operating conditions. A TEG was created based on the operating conditions of that data center,
primarily focusing on the operating temperature of the servers, cooling air temperature, and
cooling system heat sink. While an infinite amount of configurations exist that may better define
an operational scenario, this investigation provided an evaluation of a typical data center and a
simple application of thermoelectrics. Unfortunately, as seen in Appendix A, and discussed in
Section 3, the approximate efficiency in using TEGs for waste heat recovery for low temperature
data centers is below 1%. As stated earlier in Section 2.3, the power output is directly related to
the square of the temperature difference.
In this application, a temperature difference of
approximately 30K was achieved while trying to optimize that temperature difference.
With increasing heat densities in liquid cooled electronics cabinets, the effort of producing
approximately 18W from a 25000W cabinet is not practical. Given the costs of standard model
thermoelectric modules, this can result in thousands of dollars in order to implement a 65 module
TEG. While the power generation is feasible, the costs of implementing such a system make it
ineffective.
A return on the initial investment would not be achieved before the servers
themselves became outdated.
While thermoelectrics are appropriate for applications with low power devices, where
moving devices are not desired, and physical size is a concern, they do not have the efficiency
desired to make an impact on a data center level. The temperature difference created between
standard operating electronics and standard cooling systems is not large enough. Typically, a
temperature difference of greater than 100°C is desired for measurable returns.
Thus, thermoelectric devices can be used for waste heat recovery, but they have minimal
efficiency and prove to be not cost effective for data centers.
40
5. References
The following published works will be used as guidance and references in performing this study:
[1] American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc. Datacom
Equipment Power Trends and Cooling Applications, ©2005.
[2] U.S. Environmental Protection Agency ENERGY STAR Program. Report to Congress on
Server and Data Center Energy Efficiency Public Law 109-43, 2 August 2007.
[3] Koomey, Jonathan G., Ph.D. Estimating Total Power Consumption by Servers in the U.S.
and the World. Lawrence Berkeley National Laboratory, 15 February 2007.
[4] Gould, C.A.; Shammas, N.Y.A.; Gainger, S.; Taylor, I.; Thermoelectric cooling of
microelectronic circuits and waste heat electrical power generation in a desktop personal
computer. Staffordshire University, Beaconside, Stafford, UK. Elsevier B.V. 2010.
[5] Meisner, Gregory P. Advanced Thermoelectric Materials and Generator Technology for
AutomotiveWaste Heat at GM. General Motors Global Research and Development, Warren,
MI. January 2011.
[6] Saied, Widah. Essentials of Thermoelectric (TE) Cooling, With an Emphasis in Thermal
Control of Electronics. San Jose State University. www.engr.sjsu.edu.
[7] American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Liquid
Cooling Guidelines for Datacom Equipment Centers. Atlanta. ©2006.
[8] American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. 2011
Thermal Guidelines for Data Processing Environments – Expanded Data Center Classes and
Usage Guidance. ©2011.
[9] Pentair Technical Products. Overview & Design of Data Center Cabinets, Anoka,
Minnesota. 2010.
[10] Bar-Cohen, A., Solbrekken G. L., and Yazawa, K. (2005). Thermoelectric Powered
Convective Cooling of Microprocessors, IEEE Transactions of Advanced Packaging, 28(2).
[11] Ferrotec (USA) Corporation. Thermal Reference Guide. 2012,
http://www.ferrotec.com/technology/thermal/thermoelectric-reference-guide/.
41
6. Appendix A- Sample Calculation of Power
Generation
Given:
TH = 110.7°F = 316.82K
TC = 55°F = 285.65K
VO = 12 volts
I = 1.5 amperes
Solve:
TH  TC 316.82K  285.65K 
= 301.24K

2
2
V
12V
RL  O 
 8
I 1.5 A
PO  VO I  12V 1.5 A  18W
T  TH  TC  316.82K  285.65K  31.22K
Tavg 
From Reference [7], the module parameters of a 127-couple Ferrotec Corporation module at an
average temperature of 31.22K:
Table 5 - Averaged Module Material Parameters [11]
4A
°C
30
K
303.2
6A
M
RM
KM
RM
KM
V/K
0.05343
ohms
3.7193
W/K
0.3469
ohms
2.4796
W/K
0.5204
 M is the module averaged Seebeck coefficient
RM is the module averaged resistance
K M is the module averaged thermal conductance
The output power for a single 6-amp module is:
 T 2 0.05343V K  31.22K
Pmax  M

 0.28W
4 RM
4  2.4796
The number of modules necessary to achieve the desired power output is:
P
18W
NT  O 
 64.37
Pmax 0.28W
This translates to 65 modules.


42
Equation (24) is used to determine the optimum series-parallel configuration for maximum
efficiency by trying to get the TEG internal to equal the load resistance ( 8 ).
N
RGENERATOR  S RM
NP
Table 6 – Thermoelectric Generator Resistance Due to Series and Parallel Module Configurations
NS
NP
RGENERATOR
( )
65
33
22
17
13
1
2
3
4
5
161.17
40.91
18.18
10.54
6.45
Connecting four parallel strings of thirteen modules provides a TEG resistance of 6.45  , which
closely matches the desired load resistance of 8 .
The output voltage is determined using equation (25):
VO  N S  M T  IRGENERATOR  130.05343V K 31.22K   1.5 A6.45  12.01V
No fine tuning of the voltage is required because it is almost exact to the desired voltage value of
12V.
PO
VO 2 12.01


 18.03W
RL
8.0
The heat input per module is found using equation (12):
Q H   M IT H 
1 2
I RM  K M T 
2
 0.05343V K 1.5 A316.82 K  
1
1.5 A2 2.4796   0.5204 W K 31.22 K   38.85W
2
For 65 modules in the TEG, the total heat input is 2525.2W
Thereby the efficiency of the TEG is:
TEG 
PO
18.03W

 0.0071 or 0.7%
QH 2525.2W
43
7. Appendix B- Modeling of a Bismuth Telluride Pellet
Modeling of a Bismuth Terruride TE pellet using COMSOL Multiphysics software.
Pellet size, 1mm x 1mm x 6mm, with 0.1mm copper electrodes on either side.
Property
Symbol and Unit
Bismuth Telluride
Copper
Thermal conductivity
k- W/(m·K)
1.6
350
Electric conductivity
σ- S/m
1.1e5
5.9e8
Seebeck coefficient
S- V/K
P: 200e-6
6.5e-6
N:-200e-6
The bottom of the pellet was maintained at 0V and the top of the pellet maintained at 316.82K.
The voltage for the top of the pellet was varied until the operating temperature difference was
achieved.
Table 7 - Resultant Temperature, Current, and Power for Varying Voltages
Across a Single Bismuth Telluride 1mm x 1mm x 6mm Pellet
Voltage
(V)
0.05
0.04
0.03
0.02
0.018
0.016
0.015
0.0148
0.014
0.012
0.01
Temperature
(K)
242.27
249.83
261.29
276.45
279.91
283.5
285.35
285.72
287.23
291.09
295.08
Current
Density
(A/m2)
6.65E+05
5.04E+05
3.58E+05
2.26E+05
2.01E+05
1.77E+05
1.65E+05
1.63E+05
1.53E+05
1.30E+05
1.07E+05
44
Current
(A)
0.6654
0.50432
0.35813
0.226
0.20119
0.17688
0.16492
0.16255
0.15309
0.12979
0.10699
Power
(W)
0.03327
0.020173
0.010744
0.00452
0.003621
0.00283
0.002474
0.002406
0.002143
0.001557
0.00107
Table 8 - Resultant Temperature, Current, and Power for Varying Voltages
Across a Single Bismuth Telluride 2mm x 2mm x 6mm Pellet
Voltage
(V)
0.05
0.04
0.03
0.02
0.018
0.016
0.015
0.0148
0.014
0.012
0.01
Temperature
(K)
242.27
249.83
261.29
276.45
279.91
283.5
285.35
285.72
287.23
291.09
295.08
Current
Density
(A/m2)
6.65E+05
5.04E+05
3.58E+05
2.26E+05
2.01E+05
1.77E+05
1.65E+05
1.63E+05
1.53E+05
1.30E+05
1.07E+05
Current
(A)
2.6616
2.01728
1.43252
0.904
0.80476
0.70752
0.65968
0.6502
0.61236
0.51916
0.42796
Power
(W)
0.13308
0.080691
0.042976
0.01808
0.014486
0.01132
0.009895
0.009623
0.008573
0.00623
0.00428
dT vs. Electric Potential
80
Temperature Change (K)
70
60
50
40
30
20
10
0
0
0.01
0.02
0.03
0.04
0.05
Electric Potential (V)
Figure 16- Change in Temperature Across TE Pellet Based on Electrical Potential
45
0.06
Figure 17- Surface Temperature Across TE Pellet
46
Figure 18- Electric Potential Across TE Pellet
47
Figure 19- Current Density in TE Pellet
48