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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 2T (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 KT 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 Qm (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 130.05343V K 31.22K 1.5 A6.45 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 A316.82 K 1 1.5 A2 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