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Comprehensive System-Level Optimization of Thermoelectric Devices for Electronic. Cooling Applications. Robert A. Taylor and Gary L. Solbrekken, Member, ...
IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 31, NO. 1, MARCH 2008

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Comprehensive System-Level Optimization of Thermoelectric Devices for Electronic Cooling Applications Robert A. Taylor and Gary L. Solbrekken, Member, IEEE

Abstract—Advanced cooling solutions are needed to address the growing challenges posed by future generations of microprocessors. This paper outlines an optimization methodology for electronic system based thermoelectric (TE) cooling. This study stresses that an optimum TE cooling system should keep the electronic device below a critical junction temperature while utilizing the smallest possible heat sink. The methodology considers the electric current and TE geometry that will minimize the junction temperature. A comparison is made between the junction temperature minimization scheme and the more conventional coefficient of performance (COP) maximization scheme. It is found that it is possible to design a TE solution that will both maximize the COP and minimize the junction temperature. Experimental measurements that validate the modeling are also presented. Index Terms—Electronic cooling, system optimization, thermoelectric (TE).

NOMENCLATURE Area [m ]. Electric current [A]. Thermal conductivity [W/mK]. Length [m]. Number of thermocouples. Heat flow [W].

min opt

Ambient. Average. TE cold side. Element. Electron heat pumping on cold side. Electron heat pumping on hot side. TE hot side. Junction. Joule heating. Minimum. Optimum.

TE

Heat sink. Thermoelectric.

ave

I. INTRODUCTION ECENTLY, there have been multiple studies exploring thermoelectric (TE) refrigeration applied to electronic systems. Simons, et al. [1] completed a server cooling application case study using a conventional off-the-shelf TE module. Their conclusion was that current TE materials cannot provide large enough coefficients of performance (COPs) to be competitive with conventional vapor compression refrigerators. A similar finding was reported by Phelan, et al. [2]. Bierschenk and Johnson showed that current materials can operate with COPs well above unity [3] provided the temperature difference across the TE module is kept below the maximum possible level. A study by Solbrekken, et al. [4] presented an operational envelope over which TE refrigeration provides a performance advantage over an air-cooled heat sink. That system based study was completed by determining the operating current such that the junction temperature is minimized in the presence of a finite thermal resistance heat sink. A later study showed that the operating current can be chosen to both maximize the COP and minimize the junction temperature [5]. In addition to TE system optimization studies outlined above, research is being conducted to develop better TE materials. Venkatasubramanian, et al. [6] have demonstrated a doubling in the TE figure-of-merit for superlattice materials. Other reports of new nano-engineered materials are reported in [7]–[10]. Ghamaty and Elsner are developing quantum-well materials while Skutterudites are being researched by Fleurial,

R

Electrical resistance . Temperature [K]. Input electric work [W]. TE material figure-of-merit,

Subscripts

K.

Symbols Seebeck coefficient [V/K]. Difference in value. TE element geometry area-to-length ratio [m]. Electric resistivity [ m]. Thermal resistance [K/W].

Manuscript received September 20, 2006; revised April 17, 2007. This work was recommended for publication by Associate Editor C. Lee upon evaluation of the reviewers comments. R. A. Taylor is with the Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287 USA. G. L. Solbrekken is with the Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCAPT.2007.906333

1521-3331/$25.00 © 2007 IEEE

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Fig. 2. Baseline system thermal resistance network. Fig. 1. Baseline system configuration.

et al. [11] and [12]. In each of the cases noted above, the material improvements are created by reducing the effective material thermal conductivity. This study takes an in-depth look into the optimization of an electronic system cooled by TE refrigeration. The COP maximizing and junction temperature minimizing approaches are reviewed and used to illustrate how TE operation can be optimized. A comparison between the two optimization approaches is conducted to demonstrate their relative merits and to identify a common point of operation that could be considered to be an overall optimum. That operating point maximizes the required heat sink thermal resistance for a problem with a specified maximum temperature, similar to what is encountered in electronic cooling (the junction temperature and ambient temperature are both typically specified). Experimental measurements are taken on commercial modules to validate the system modeling and to demonstrate the existence of a common optimum when both minimizing the junction temperature and maximizing the COP. II. MODELING Including a TE module in an electronic cooling system provides many opportunities for design optimization. System parameters such as the heat load, maximum junction temperature, and ambient temperature are typically defined by product requirements. Conversely, the geometry of the TE module, the applied current, and the heat sink thermal resistance are controlled by the design engineer. Therefore, it is in the best interest to select the TE module and operating current to maximize the thermal resistance of the heat sink to minimize consumed resources. It has been demonstrated in previous studies that to properly optimize the system performance, the entire electronic system needs to be modeled in addition to the TE module [4] and [5]. For purposes of this study the system is optimized when the junction temperature is minimized and/or the TE module COP is maximized. A. Baseline Configuration A baseline configuration is defined for this study that consists of an air-cooled heat sink attached directly to a heat source (CPU) with a thermal interface material (TIM) placed between the heat sink and heat source. Fig. 1 shows this configuration. A 1-D thermal resistance network for the baseline system is shown in Fig. 2.

Fig. 3. Sketch of a TE cooled electronic system.

Fig. 4. Thermal resistance network for TE cooled system.

sumed at both of the interfaces. The thermal resistance network is drawn in Fig. 4. and each represent the TIM and heat In Fig. 4, represents the thermal resisspreading resistances while tance of the final heat sink. It should be noted that each of these resistances could include a heat spreader, a heat pipe or some represents the conduction thermal form of liquid cooling. resistance of the TE module elements as defined in (1). As implied by Fig. 4, the operation of the TE module requires external input work. Similar to a vapor compression refrigerator, the work is needed to drive heat from cold to hot. The electric work is modeled as electron heat pumping at the hot and cold and ) and Joule heating junctions of the TE module ( . The total input work is eventually converted to heat which must be dissipated by the heat sink (as illustrated in Fig. 4 by the additional heat flow term through the heat sink resistance). This additional heat load raises the entire system temperature and limits the application of TE refrigeration relative to the baseline configuration. Rigorous system level modeling is the only way to estimate the temperature rise. It is of general interest to establish the amount of heat that can be cooled by the TE refrigerator. This is found through an energy balance around the cold junction of the TE module, and is given by [13]

(1)

B. TE Cooled Configuration A sketch of the TE configuration is shown in Fig. 3. The system is effectively the baseline configuration with a TE module placed between the heat sink and CPU. A TIM is as-

Electron Heat Pumping

Joule Heating

Conduction Heat Leak

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where (2) The temperature difference across the TE, T, is defined as . In (1), it is assumed that the absolute value of the Seebeck coefficient, the thermal conductivity and the electric resistivity for n-type and p-type materials are the same. Equation (2) refers to the area of one TE element divided by the length of that element. The input work, or electric power, used by the TE must overcome the Seebeck voltage as well as the Joule heating [13]

Fig. 5. COP as a function of current-

= 0.001 m and T = 50



C ( 323 K).

(3) Electron Heat Pumping

Joule Heating

Using these equations along with knowledge of the TIM and heat sink thermal resistance, the CPU junction temperature can be found (4) Here, the heat sink thermal resistance has been added to . the TIM and spreading thermal resistance to obtain . By counting the variables in That is, (1)–(4) we can see that there are 11 variable parameters . Two of these, current ( ) , can be optimized. The following discussion and geometry shows how they can be chosen for optimal performance.



= 1 A and T = 50

C

The corresponding optimum COP is

C. Coefficient of Performance Maximization Probably the most common optimization strategy for implementing TE modules is to utilize the devices in the most efficient way possible [1]–[3] by maximizing the COP. The method is based strictly on the performance of the device and does not explicitly account for the heat sink thermal resistance. The COP is defined as the ratio of the amount of heat pumped and the amount of work needed, or by combining (1) and (2) COP

Fig. 6. COP as a function of element geometry—I ( 323 K).

(5)

, and k, (5) For a given TE material with properties of suggests that there are four other unknown parameters to be , and I). determined in order to solve for the COP ( , and T are given It is common practice to assume that for a particular application, leaving the operating current to be optimized. Fig. 5 shows the COP as a function of the operating current 0.001 m and 50 C ( 323 K). The plot indicates with that there is a current which maximizes the COP. The process to find the optimum current is to take the derivative of (5) with respect to and set it equal to 0. The details can be found in many references, such as Angrist [13], with the resulting COP maximizing current given as (6)

COP

(7)

, is the average of and . We The average temperature, can see from (7) that COP is merely a function of the temperatures, , and the TE material. Fig. 5 shows that (6) and (7) do predict the maximum COP for the indicated temperature differences. The COP takes on values greater than 1 for T values less than 30 K, dismissing a widely held mis-perception that the COP for TE modules is necessarily low. The operating current is oftentimes the only parameter optimized. However (5) suggests that the geometry, , could also be optimized (the cold side temperature, , and the temperature difference, T, happen to be one sided functions without 50 C and 1 A in Fig. 6 optimums). Plotting (5) with graphically illustrates the parabolic relationship. Taking the partial derivative of the COP [(5)] with respect to and setting it equal to 0 provides the expression for the optimum. After some manipulation and recognizing that all material parameters and the electric current will be positive, the one physically meaningful solution is (8) Plotting (8) in Fig. 6 does show that the optimum has been found. What is interesting with (8) is that it can also be obtained

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Fig. 7. Junction temperature as a function of current— 25 C ( 298 K). 0.001 m, T

=



= 0.3 K/W, =

by solving (6) for . This implies that (6) and (8) are not independent of one another. Therefore either the current or can be arbitrarily chosen and the second parameter optimized. When the optimum COP operating current is used in a system configuration, the required heat sink thermal resistance needs to be determined, something not considered in [1] or [2]. For a given cooling load, , the required heat sink thermal resistance and T is [3] to obtain the assumed (9) There is a practical concern to using the optimum COP in a system configuration. As noted above the temperature difference, T, must be assumed. A common assumption is to use the maximum T from TE manufacturer data sheets. However that T is obtained by ignoring the impact of the heat sink and results in off-optimum system operation as noted by Solbrekken, et al. [4]. To truly optimize system performance using the COP maximization approach an iterative process must be used to establish a more appropriate T. D. Junction Temperature Minimization As just noted, the primary disadvantage of the COP optimization strategy is that it is necessary to assume a temperature difference across the TE module and the cold side temperature. This section will outline the process where those assumptions do not have to be made while ensuring the junction is minimized. In exchange, the COP will not necessarily be maximized. Current Optimization: Solbrekken et al. [4] recognized that for most applications, the TE temperature difference is a response to input conditions, such as the cooling load and heat sink thermal resistance, and is not known a priori. Further, the goal of electronic system performance is often to provide the lowest junction temperature possible. Therefore a new current optimization strategy was proposed whereby the junction temperature was minimized. To demonstrate that there is indeed an optimum current that will provide the minimum junction temperature, the junction temperature is plotted as a function of the electric current for a heat sink thermal resistance of 0.3 K/W, 0.001 m and a range of heat flows in Fig. 7. The plot shows

Fig. 8. Junction temperature versus geometry—I 25 C ( 298 K). T

=



= 4 A,

= 0.3 K/W,

that for each heat dissipation point there is one optimum current. An expression for the optimum current is found by taking the partial derivative of (4) and setting it equal to 0

(10) Equation (10) is unfortunately nonlinear in that it requires iteration about the cold side temperature, . Equation (10) is solved for each of the cases shown in Fig. 7 and can be seen to predict the minimum junction temperature for each case. As the heat load increases for a given TE module, the minimum ) increases, as does the optimum junction temperature (or current. Fig. 7 can also be looked at in a different way. For this configuration, 85 C can only be maintained up to approximately 75 W of heat dissipation. Therefore, the configuration must be changed to broaden the range of applicability for TE cooling. Aspect Ratio, , Optimization: There is no reason to believe that the TE module geometry cannot be optimized in addition to the electric current. The junction temperature is calculated for a heat sink resistance of 0.3 K/W and a constant input current of 4 A over a range of , the TE element area to length ratio. Fig. 8 shows that for large values of the junction temperature asymptotes to a constant value. This behavior can be explained by imagining that the overall TE footprint area is held constant. In this case a larger value of implies that the TE elements become vanishingly thin the overall system configuration reverts to the baseline case shown in Fig. 1 with a heat sink and TIM only. The asymptotic temperature from Fig. 8 is the same as would be achieved in that configuration. It is then obvious for higher heat loads that there is no advantage to using TE cooling over just a heat sink. For all but the 100 W heat load, there is a value of that does minimize the junction temperature. To find the optimum, the partial derivative of (4) is taken with respect to and set to 0. After some algebraic manipulation the expression is

(11)

TAYLOR AND SOLBREKKEN: COMPREHENSIVE SYSTEM-LEVEL OPTIMIZATION OF THERMOELECTRIC DEVICES

Fig. 9. T as a function of geometry—Q 25 C ( 298 K).



= 100 W,

= 0.3 K/W, T =

The junction temperature at the optimum value of is plotted in Fig. 8 and is seen to predict the minimum temperature for heat flow cases up to the 75 W case. For the 100 W case the calculated optimum for is negative, which is physically unrealistic. Looking further into the calculation reveals that for the 100 W case the first term in the denominator of (11) becomes negative. The first grouping of terms in the denominator is the difference between the Peltier cooling for a single element and the heat load-per-element. If the amount of heat that needs to be dissipated exceeds the Peltier cooling capacity it is obvious that adding the TE module will not provide an advantage over a heat sink alone. Combined Geometry and Current Optimization: The previous two sections outlined the process for independently optimizing the TE element aspect ratio and the electric. For system implementation there is no reason to not optimize both parameters simultaneously. Furthermore the number of thermocouples, , has not been discussed. The present discussion will focus on simultaneously optimizing those parameters. An example of simultaneous optimization of the electric current and TE element aspect ratio is shown in Fig. 9 for a range of . The heat load is 100 W and the heat sink thermal resistance is set at 0.3 K/W. For each of the data points the optimum current is found using (10). It can be seen that the gamma value that minimizes shifts to smaller values (thicker elements for a given footprint area) as the number of thermocouples increases. What is interesting, however, is that regardless of , the value of the minimum junction temperature appears to be the same. Manipulating the optimization equations suggests that the product should be a correlating parameter and is hence plotted in of Fig. 10 for each of the data points from Fig. 9. Clearly successfully correlates the junction temperature for the combined optimization and provides an additional degree of freedom that can be chosen ( or can be arbitrarily chosen as long as the other is selectively chosen according to the optimum). The same behavior is seen for different heat dissipation values. The value that provides the minimum junction temperature for a of range of heat dissipation values is shown in Fig. 11. Fig. 11 also shows the comparison of an optimized TE cooled system and the baseline configuration of a heat sink alone. At heat loads

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Fig. 10. T versus module footprint ratio—Q T 25 C ( 298 K).

=



Fig. 11. Optimum geometry as a function of 25 C ( 298 K).



Q

= 100 W,

0

= 0.3 K/W,

= 0.3 K/W, T =

less than 100 W there is a substantial benefit in using TE refrigeration, while at 150 W there is virtually no difference between the configurations. Heat Sink Influence: For the previous minimum junction temperature analysis the heat sink thermal resistance has been assumed to be constant, answering the question of what the optimum system performance would be for a given heat sink. An alternate approach is to set the junction temperature at say 85 C ( 358 K) and determine the necessary heat sink to achieve that temperature while still optimizing the current and TE geometry. From Fig. 11 it can be seen that an 85 C junction temperature will result when using a 0.3 K/W heat sink and the optimum geometry at a heat load of about 110 W. In this section we seek to find the smallest heat sink (largest thermal resistance) that will keep the junction temperature at 85 C for different heat loads. The optimization, (10) and (11) are solved by holding constant. The solution process is iterative and was completed using a C program. Fig. 12 presents the heat sink thermal resistance required to achieve an 85 C junction temperature over a range values, as well as the maximum heat sink resistance of for a given heat load. The maximum resistance (smallest heat is about 1 m. Further, as the sink) interestingly occurs when value of increases, the heat sink resistance tails off slowly

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T

Fig. 14. Comparison of COP and optimization approaches ( 100 W for and 35 K for COP ).

T

Fig. 12. Maximum thermal resistance versus module footprint ratio to achieve 85 C ( 358 K).

T =



T

Fig. 13. Comparison of COP and 100 W for and 5 K for COP

T

1T =

Q =

optimization approaches ( ).

and appears to asymptote to a constant value. The explanation for this trend is the same as was used to describe the asymptotic behavior of Fig. 9. Based on this interpretation, the difference between the maximum thermal resistance and the asymptotic value is the advantage of using TE refrigeration over a directly attached heat sink (Fig. 1). III. OPTIMIZATION COMPARISON TE optimization in the context of an electronic cooling system has been explored from the standpoint of maximizing the operating COP and minimizing the junction temperature. It is instructive to compare the two approaches. A. Operating Current Comparison Recall from above that was calculated by assuming a temperature difference across the TE module for the COP maximization scheme. This creates three performance regimes that can be examined for that geometry—one where the resulting for the approach is larger, equal to, and smaller than that assumed for the COP approach. A plot of COP and for the first regime where T is larger for is shown in Fig. 13. 100 W and The conditions used to generate Fig. 13 are 0.3815 K/W for the analysis. The heat sink resis-

1T =

Q =

tance was chosen such that the resulting junction temperature is is set to be 5 K and the TE 85 C. For the COP analysis, , cold side temperature, , is set to 60 C. The geometry, is set at 1.4 m for both analysis schemes and the ambient temperature is assumed to be 25 C ( 298 K). The upper parabolic curve (solid diamonds) and the positively sloped line (solid triangles) correspond to the junction temperaand COP approaches. The corresponding ture for the shape open symbol curves represent the COP for the two apapproach proaches. It is interesting to observe that for the the COP does not have an extrema while the junction temperature for the COP approach does not have an extrema. approach has In Fig. 13, the current calculated from the a COP that is less than COP . Surprisingly, the junction temperature at the COP current is lower then that obtained using approach. To explain how this is possible considering the the effort expended to develop the minimum junction temperature model, one needs to consider the amount of heat dissipated with 5 K and 60 C ( when using COP 85 C or 358 K). Using (1) the heat dissipation is found to be about 27 W as compared with the 100 W dissipated with the approach (recall that is not set when using the COP method typically used). It is therefore not surprising that the COP method would predict a lower junction temperature. A similar comparison can be made, this time assuming T analysis is 35 K and all other parameters kept for the COP the same as in Fig. 13. This time, in Fig. 14, it is seen that for approach is indeed lower then that for COP . Furthe is higher than the COP for COP . The ther, the COP for explanation for this behavior is similar to the previous explanation, this time with the heat dissipation for the COP method being about 140 W when assuming T to be 35 K. The previous two comparisons with responses that are counter-intuitive based on how T is chosen leads to the question of if it is possible to minimize the junction temperature AND maximize the COP at the same time for a given heat load and a specified junction temperature. Through an iterative process it is concluded that it is indeed possible. Fig. 15 shows that for a junction temperature of 85 C ( 358 K) and a heat and COP operating point will load of 100 W, the is set at 1.4 m and the heat sink be exactly the same if thermal resistance is 0.3815 K/W. This can be interpreted as the

TAYLOR AND SOLBREKKEN: COMPREHENSIVE SYSTEM-LEVEL OPTIMIZATION OF THERMOELECTRIC DEVICES

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Fig. 15. COP and junction temperature as a function on geometry for both 100 W and 21.35 K). methods (

Q =

1T =

cheapest heat sink that would keep the electronic component from operating above 85 C. It should be noted that and the heat sink thermal resistance were found from Fig. 12. Recognizing that the heat sink resistance is a measure of resource consumption, it makes intuitive sense that using a heat sink with the largest thermal resistance will result in the largest possible COP, a result that is supported by the independent COP analysis using the COP model. The T and inputs to the COP model were obanalysis, illustrating how the two optitained from the mization strategies can be used in concert to obtain what can be considered to be a true optimum operating condition. Based on these results the author’s recommend conducting a rigorous system based optimization where both the COP and junction temperature are optimized to ensure the most effective use of cooling resources. Note that for a given geometry, there will be and COP co-exist [5]. one operating point where

Fig. 16. Flow bench test facility.

Fig. 17. Experimental test section.

IV. EXPERIMENTAL TESTING The optimization modeling, including the claim that it is possible to obtain an operating configuration that minimizes the junction temperature and maximizes the COP has been subjected to experimental verification. One reason for verifying the conclusions is because it is widely held that the optimum COP current will not yield the coldest junction. Also, the aforementioned models assume 1-D heat flow (air gaps between TE elements conduct no heat) and that the TE material properties are independent of temperature. Experimental measurements are taken on off-the-shelf modules to test the modeling assumptions and to observe the simultaneous-optimal point of operation (see Fig. 15). The test bed was built at the University of Missouri as part of an undergraduate research project [14]. The test bed consists of a flow bench and duct system, as shown in Fig. 16. The test assembly based on the model in Fig. 3 was placed in the duct, as shown in Fig. 17. The heat sink was characterized in a previous study to provide a relationship between the heat sink thermal resistance and air velocity [14]. The first set of experiments is intended to validate the optimum current for a given thermoelectric module. To do this, the thermoelectric cold side, , is measured with a thermo, and the air velocity—and thus the couple. The input heat,

heat sink thermal resistance—are held constant. The input current to the thermoelectric module is varied around the predicted optimum to demonstrate the ability of the analytic model to predict junction temperature and COP. In the second set of experiments, the junction temperature is held constant by varying the heat sink thermal resistance as suggested by (8), while the TE current is varied. The estimated heat loss through the apparatus insulation is between 1.0 and 1.5 W and the temperature measurement uncertainty at a 95% confidence level is estimated to be 1.2 K. When the initial raw data was compared with the analytic models there was a significant discrepancy. However, when temperature dependent properties as quoted in [15] were applied to the model, the predictions were much closer to the measurements. Figs. 18 and 19 compare the analytic predictions (“ M” in the legends) with the experimental (“ EX” in the legends) junction temperature and COP measurements. For both and COP models, it can be seen that the experthe imental data closely follows the predicted trends. Further, the measurements are within experimental uncertainty of the model predictions, validating the efficacy of the derived models. model, current, heat load, and heat sink For the COP thermal resistance must be changed to achieve the target

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V. CONCLUSION

Fig. 18. Comparison between experimental and predicted junction temperature.

Fig. 19. Experimental versus predicted COP.

temperature, 286 K for the case shown in Fig. 18. The heat sink thermal resistance and heat load are relatively difficult to control, and hence there is a larger deviation between the of the COP measurements and predictions as seen in the model. Also, in the COP experiments, higher currents cannot be tested as the required heat sink thermal resistance is smaller then was feasible with the current heat sink. The lower current bound was chosen to be sufficiently far enough away from the optimum point in Fig. 13. Recall from Fig. 15 that there is one optimum point in which both methods align for a given module and a given heat sink. 0.337 m), the heat load and For the TE module tested ( heat sink thermal resistance predicted at the optimum point is 15.5 W and 0.6 K/W. Indeed it can be seen from Fig. 18 the current that minimizes the junction temperature is about 3.5 A (triangles). At the same time, from Fig. 19 it can be seen that the current that provides the maximum COP (diamond symbols) is also about 3.5 A. This finding does demonstrate that for a given TE geometry and heat flow there is an optimum current that will simultaneously maximize the COP and minimize the junction temperature. One notable result of the measurements is that the COP can achieve values of 1.0 and larger for input currents of 2.0 A and smaller. This reinforces the previous claims that TE COP values is small enough. well above unity are possible if the

This study has provided an in-depth look into the system based optimization of TE cooling applied to electronics. The study showed that two approaches may be used for optimization; the conventional COP maximization approach and the junction temperature minimization approach. The COP maximization strategy is based on device level performance while the junction temperature minimization approach was developed with system level parameters in mind. The system was constrained to have an ambient temperature of 25 C (298 K) and a junction temperature of 85 C (358 K). The development of the junction temperature minimization process is outlined, demonstrating that the electric current applied to a TE module and the TE element geometry can be chosen to minimize the junction temperature for a given heat load and heat sink thermal resistance. The given heat load and heat sink thermal resistance are chosen to be the independent parameters as they are typically specified conditions in a system design. An alternate approach was explored where the maximum junction temperature is specified as opposed to the heat apsink thermal resistance. By contrast, the typical COP proach requires one to assume a temperature difference across the TE module and the cold side temperature. apA comparison of optimization done using the COP proach and the approach demonstrated that unexpected behavior can occur, such as the approach yielding a higher COP then the COP model. It was demonstrated that the reason stems from the need to assume for the COP approach when in a system configuration is rarely known a priori. This is one of the arguments for using caution when trying to utilizing one of the optimization approaches. A significant result from the optimization comparison study is the fact that for a given heat load and specified junction tem, opperature, it is possible to optimize the TE geometry erating current, and heat sink thermal resistance such that BOTH the COP and junction temperature are optimized. Experimental measurements taken on an off-the-shelf TE module validates the existence of this operating point. It is postulated that this is truly the optimum operating configuration for a system. A second law analysis is warranted to establish that this is indeed true. REFERENCES [1] R. E. Simons and R. C. Chu, “Applications of thermoelectric cooling to electronic equipment: A review and analysis,” in Proc. 16th IEEE Semi-Therm, Mar. 21–23, 2000, pp. 1–9. [2] P. E. Phelan, V. A. Chiriac, and T.-Y. T. Lee, “Current and future miniature refrigeration cooling technologies for high power microelectronics,” IEEE Trans. Compon. Packag. Technol., vol. 25, no. 3, pp. 356–365, Sep. 2002. [3] J. L. Bierschenk and D. A. Johnson, “Extending the limits of air cooling using thermoelectric enhanced heat sinks,” in Proc. Itherm’04, 2004, pp. 679–684. [4] G. L. Solbrekken, K. Yazawa, and A. Bar-Cohen, “Chip level refrigeration of portable electronic equipment using thermoelectric devices,” in Proc. InterPack’03, Maui, HI, Jul. 6–11, 2003, [CD ROM]. [5] R. Taylor and G. L. Solbrekken, “An improved optimization approach for thermoelectric refrigeration applied to portable electronic equipment,” in Proc. InterPACK’05, San Francisco, CA, Jul. 17–22, 2005, [CD ROM]. [6] R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O’Quinn, “Thin-film thermoelectric devices with high room-temperature figures of merit,” Nature, vol. 413, no. 11, pp. 597–602, 2001.

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[7] G. Chen, T. Zeng, T. Borca-Tasciuc, and D. Song, “Phonon engineering in nanostructures for solid-state energy conversion,” Mater. Sci. Eng. A, vol. 292, pp. 155–161, 2000. [8] M. S. Dresselhaus, T. Koga, X. Sun, S. B. Cronin, K. L. Wang, and W. Chen, “Low dimensional thermoelectrics,” in Proc. 16th Int. Conf. Thermoelect., 1997, pp. 12–20. [9] X. Fan, C. Croke, J. E. Bowers, and A. Shakouri, “SiGeC/Si superlattice micro cooler,” Appl. Phys. Lett., vol. 78, no. 11, pp. 1580–1582, 2001. [10] G. L. Solbrekken, Y. Zhang, A. Bar-Cohen, and A. Shakouri, “Use of superlattice thermionic emission for “Hot Spot” reduction in a convectively-cooled chip,” in Proc. Itherm’04, Las Vegas, NV, Jun. 1–4, 2004, pp. 610–616. [11] S. Ghamaty and N. Elsner, “Development of quantum well thermoelectric device,” in Proc. 18th Int. Conf. Thermoelect., Baltimore, MD, Aug. 30–Sept. 2 1999, pp. 485–488. [12] J. P. Fleurial, A. Borshchevsky, T. Caillat, and R. Ewell, “New materials and devices for thermoelectric applications,” in Proc. 32nd Intersoc. Energy Conv. Eng. Conf., Honolulu, HI, Jul. 27–Aug. 1 1997, vol. 2, pp. 1080–1086. [13] S. W. Angrist, Direct Energy Conversion, 4th ed. Boston, MA: Allyn and Bacon, 1982. [14] K. Scheel, “Heat Sink Characterization,” B.S. thesis, Univ. Missouri, Columbia, Sep. 2005. [15] D. M. Rowe, “The thermoelectric properties of heavily doped hotpressed germanium-silicon alloys,” J. Phys. D: App. Phys., vol. 2, pp. 1497–1502.

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Robert A. Taylor received the B.S. and M.S. degrees in mechanical engineering from the University of Missouri, Columbia, in 2004 and 2005, respectively, and is now pursuing the Ph.D. degree in mechanical engineering at Arizona State University, Tempe. His research interests lie in heat transfer and fluid systems with a focus on power generation and energy efficiency.

Gary L. Solbrekken (M’06) received the B.S. degree in mechanical engineering from Rose-Hulman Institute of Technology, Terre Haute, IN, in 1993 and the M.S. and Ph.D. degrees in mechanical engineering from the University of Minnesota, Minneapolis, in 1995 and 2003, respectively. Between 1996 and 2000, he was a Lab Manager at Intel Corporation responsible for the thermal characterization of microprocessors. In 2003, he became an Assistant Professor of mechanical engineering at the University of Missouri, Columbia. His research interests are in the area of thermal management, energy conversion, thermal metrology development, and biological heat transfer.