Effects of thermocouples physical size on the performance of the TEG TEH system

Transcription

1 *Corresponding author: Effects of thermocouples physical size on the performance of the TEG TEH system... Fankai Meng 1,,3, Lingen Chen 1,,3 * and Fengrui Sun 1,,3 1 Institute of Thermal Science and Power Engineering, Military Key Laboratory for Naval Ship Power Engineering, and 3 College of Power Engineering, Naval University of Engineering, Wuhan , China... Abstract The effects of thermocouples physical size on the performance of a thermoelectric heat pump (TEH) driven by a thermoelectric generator (TEG) device are investigated in this article. The physical size refers to the length and the cross-sectional area of the thermocouples. The performance analysis is multiobjective, including stable electrical current, heating load, coefficient of performance, maximum heating load and maximum heating temperature difference. A characteristic parameter, i.e. area length ratio, is defined to describe the thermocouples physical size. The influences of the parameter are analyzed by detailed numerical examples. A practical example is proposed to show how to select appropriate thermoelectric modules (TEMs) to construct a high-performance TEG TEH system satisfying different requirements. The results show that an improvement in its performance is possible by optimizing internal physical size of thermocouples. The conclusion obtained could be used for the selection of TEMs and the design of the TEG TEH system. Keywords: thermoelectric generator; thermoelectric heat pump; non-equilibrium thermodynamics; performance optimization Received 7 November 011; revised 4 October 013; accepted 6 October INTRODUCTION Semiconductor thermoelectric power generation, based on the Seebeck effect, and semiconductor thermoelectric cooling or heat pumping, based on the Peltier effect, are solid-state energy converters whose combination of thermal, electrical and semiconductor properties allows them to be used to convert waste heat into electricity or electrical power directly into cooling and heating [1]. That allows thermoelectric device has very interesting capabilities compared with conventional power generation, cooling and heating systems [ 5]. Over the past five decades, the thermoelectric devices have been used practically in widespread fields with the development of new thermoelectric materials with higher Peltier coefficients and increased coefficient of performance (COP) [6]. Many researchers have concerned about the physical properties of the thermoelectric material and the manufacturing techniques of thermoelectric modules (TEMs) [7 10]. In addition to the improvement in the thermoelectric material and module, the system analysis and optimization of the thermoelectric generator (TEG), thermoelectric cooler (TEC) and thermoelectric heat pump (TEH) are equally important in designing highperformance TEG, TEC and TEH. In general, conventional non-equilibrium thermodynamics [3, 11, 1] is used to analyze the performance of single-stage one- or multiple-element TEG [13 ], TEC [3 34] and TEH [35 39]. The TEG TEC and TEG TEH systems are available and have much potential application value and they could be highly compatible combinations if special consideration is given to determine the correct ratio between the numbers of couples of each [40 45]. They are different from the traditional thermoelectric systems which merely consist of the TEG, cooler or heat pump. Chen et al. [40] and Khattab and El Shenawy [41] built a model of single-stage TEC driven by single-stage TEG, i.e. a single-stage TEG TEC system, and analyzed the performance of the device. Meng et al. [4, 43] and Chen et al. [44, 45] built a model of single-stage TEH driven by single-stage TEG [37, 40], a model of two-stage TEC driven by two-stage TEG, i.e. a International Journal of Low-Carbon Technologies 016, 11, # The Author 013. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. doi: /ijlct/ctt080 Advance Access Publication 13 December

2 F. Meng et al. two-stage TEG TEC system [38] and a model of two-stage TEH driven by two-stage TEG [39], and optimized their performances. However, there has been no investigation concerning the physical size of thermocouples for the combined thermoelectric device published in open literatures. Therefore, the present work aims to study the effect of physical size on the performance of the TEG TEH system using non-equilibrium thermodynamics. A CHARACTERISTIC PARAMETER: AREA LENGTH RATIO For some kind of the thermoelectric semiconductor material, the figure of merit is Z m ¼ a s=k, where a, s and k are the Seebeck coefficient, the electrical conductivity and the thermal conductivity of the P- or N-type semiconductor material, The above formula is for the same thermoelectric material. In the course of manufacture, for the given thermoelectric material, the figure of merit can be different because the thermocouple s physical size is various. For a TEH, the heating load supplied by one thermocouple is: Q h ¼ða P a N ÞIT h KðT h T c Þþ0:5I R When Q h ¼ 0 and the electrical current is equal to ða P a N ÞT h =R, the temperature difference between the hot and cold sides reaches the maximum: T d max ¼ 3ða P a N Þ T h RK ¼ 3Z ct h where the figure of merit of a thermocouple is defined as Z c ¼ a =ðrkþ, where a ¼ a P a N, R ¼ R P þ R N and K ¼ K P þ K N are the Seebeck coefficient, the electrical conductance and the thermal conductance of the thermocouple, A thermocouple is shown in Figure 1. For the P-type semiconductor leg, one has R P ¼ L P =ðs P A P Þ, K P ¼ k P A P =L P and the N-type semiconductor leg is in like manner, where L and A are the length and the cross-sectional area of the leg, One can see that the figure of merit is the function of the thermoelectric material and the thermocouple s physical size. ð1þ ðþ For a thermoelectric manufactory, the kinds of the thermoelectric material are limited. Therefore, it is more available to make various and high-performance TEMs using the given thermoelectric material to satisfy requirements of different users. A characteristic parameter, area length ratio, is defined to describe the physical size as v ¼ A L In general, for similar doped alloys, one has ja P jja N j, k P k N and s P s N approximately. Usually, the physical size of the P-type semiconductor leg and N-type semiconductor leg is the same for technology simplification. That is, A P ¼ A N and L P ¼ L N. One has a ¼ a P a N ¼ a P L P L N R ¼ R P þ R N ¼ þ s P A P s N A N ¼ 1 1 þ 1 v s P s N vs P K ¼ K P þ K N ¼ k PL P þ k NL N A P A N ¼ vðk P þ k N Þk P v Substituting Equations (4 6) into Equation (1), one has the heating load with the physical size parameter v as Q h ¼ at h kwðt h T c Þþ 1 sw I The TEMs (Figure ) are made up of thermocouples with different physical size. Therefore, a problem is how to select appropriate TEMs to construct a high-performance TEG TEH system satisfying different requirements. ð3þ ð4þ ð5þ ð6þ ð7þ Figure 1. Schematic diagram of a thermocouple. Figure. Two TEMs. 376 International Journal of Low-Carbon Technologies 016, 11,

3 Effects of thermocouples physical size 3 THERMODYNAMIC MODEL AND PERFORMANCE OF A TEG TEH SYSTEM A schematic diagram of a TEG TEH system is shown in Figure 3. The device consists of a TEG and a TEH in series. The direct-current power source of the TEH is the output current of the TEG. The TEG consists of m 1 thermocouples. Each thermocouple is composed of a P-type and an N-type semiconductor legs. The thermoelectric generating element is assumed to be insulated, both electrically and thermally, from its surroundings. The Joulean loss generates an internal heat I R 1, where R 1 is the total internal electrical resistance of the thermocouple and I the working electrical current generating from the thermocouple. The conduction heat loss is K 1 ðt h1 T c1 Þ, where K 1 is the thermal conductance of a thermocouple, T h1 the hot side temperature and T c1 the cold side temperature. The rates of heat flow through the hot side and the cold sides are Q h1 and Q c1, The structure of the TEH is similar to the TEG. It consists of m thermocouples. The rates of heat flow through the hot side and the cold sides are Q h and Q c, According to the theory of non-equilibrium thermodynamics, for the TEG, one has Q h1 ¼ m 1 ½a 1 IT h1 þ K 1 ðt h1 T c1 Þ 0:5I R 1 Š Q c1 ¼ m 1 ½a 1 IT c1 þ K 1 ðt h1 T c1 Þþ0:5I R 1 Š where a 1 ¼ a P1 a N1, a P1 and a N1 are the Seebeck coefficients of the P- and N-type semiconductor legs for each TEG thermocouple, For the TEH, one has Q h ¼ m ½a IT h K ðt h T c Þþ0:5I R Š Q c ¼ m ½a IT c K ðt h T c Þ 0:5I R Š ð8þ ð9þ ð10þ ð11þ where a ¼ a P a N, a P and a N are the Seebeck coefficients of the P- and N-type semiconductor legs for each TEH thermocouple, The overall system is a closed-loop circuit, and the heat flow of the system is in balance, one has Q h1 þ Q c ¼ Q c1 þ Q h ð1þ The same thermoelectric material of the TEG and TEH thermocouples is chosen, i.e. a 1 ¼ a, k 1 ¼ k and s 1 ¼ s. The total number (M) of thermocouples of the combined thermoelectric device is finite and M ¼ m 1 þ m holds. In order to describe the allocation of the thermocouples, a ratio of the number of thermocouples is defined, i.e. number of thermocouples of TEG to that of the whole TEG TEH system: x ¼ m 1 =M. Then, one has m 1 ¼ Mx and m ¼ Mð1 xþ. Substituting Equations (4 6) into Equations (8 11) and then into Equation (1), respectively, one can obtain the system stable current I as follows I ¼ 1 asv 1 v T x C x ð13þ where T x ¼ xðt h1 T c1 þ T h T c ÞþT c T h and C x ¼ xv 1 xv v 1. Substituting Equation (13) into Equation (11) yields the heating load Q h ¼ Mð1 xþ 0:5a 3 sv 1 v T x C x T h 6 kv ðt h T c Þþ 0:5v 7 4 a sv 1 T 5 x Cx ð14þ The COP can be obtained by COP ¼ Q h =Q h1. When T h! T c, the heating load approaches the maximum. Substituting T h ¼ T c into Equation (14) yields the maximum heating load: " # Q h max ¼ Mð1 xþ 0:5a sv 1 v xðt h1 T c1 Þ þ 0:5v a sv 1 ðxt h1 xt c1 Þ C x T c Cx ð15þ Figure 3. Schematic diagram of a combined TEH. International Journal of Low-Carbon Technologies 016, 11,

4 F. Meng et al. When T h approaches the maximum, the heating load Q h approaches zero. Making Equation (14) equal to zero, one can solve the extreme heating temperature T h max and then obtain the maximum heating temperature difference by T d max ¼ T h max T c. 4 EFFECT OF PHYSICAL SIZE OF THERMOCOUPLES As physical size is taken into account, there are two particular cases: one is the thermocouples physical size of TEG and TEH are the same, i.e. v 1 ¼ v, and another is the physical size of TEG and TEH is different, i.e. v 1 = v. Two particular cases are analyzed, Table 1 lists the parameters of the thermoelectric material and working conditions chosen in the calculations. 4.1 TEG and TEH with the same physical size Figures 4 6 show the characteristic of the electrical current, heating load and maximum heating load vs. the area length ratio v with the given working conditions. One can see that the electrical current, the heating load and the maximum heating load are in direct proportion to the area length ratio. They are all increasing functions of the area length ratio. However, the area length ratio has no effect on the COP and heating temperature difference. They all remain constants. That is, if the area length ratio of TEG and TEH changes synchronously, the COP and heating load remain constants. 4. Effects of TEG physical size Figures 7 11 show the characteristic of electrical current, heating load, COP, maximum heating load and maximum heating temperature difference vs. the TEG area length ratio v 1 with given working conditions. In the calculations, v ¼ 4mm is set. One can see that the electrical current, heating load, maximum heating load and maximum heating temperature difference are all increasing functions of the TEG area length ratio. As v 1 ¼ A 1 =L 1, increasing the cross-sectional area or decreasing the length of TEG thermocouples can increase the heating load, maximum heating load and maximum heating temperature difference. The COP is not a monotonic function of the TEG area length ratio. There is an optimum v 1 corresponding to the maximum COP. The optimum v 1 also changes with the thermocouples ratio x. When the thermocouples ratio x increases, the Table 1. Thermoelectric material parameters, size and working conditions. a ðv/k) k ðw/k m) s ðm/ V) A ðmm Þ L ðmm) v ðmm) M x T h1,k T c1,k T h,k T c,k Figure 4. Electrical current vs. area length ratio. Figure 5. Heating load vs. area length ratio. Figure 6. Maximum heating load vs. area length ratio. COP decreases and the optimum v 1 decreases. The heating load, maximum heating load and maximum heating temperature difference smoothly transit from near zero at the low range of v 1 to approaching their limiting large value as v 1 exceeds some value. This means too large area length ratio of the TEG is not necessary as the performance is improved little in large range of v International Journal of Low-Carbon Technologies 016, 11,

5 Effects of thermocouples physical size Figure 7. Electrical current vs. TEG area length ratio. Figure 8. Heating load vs. TEG area length ratio. Figure 9. COP vs. TEG area length ratio. Comparing four curves in one figure, one can see that a larger thermocouples ratio leads to a larger electrical current, a smaller COP, a smaller maximum heating load and a larger maximum heating temperature difference. Figure 10. Maximum heating load vs. TEG area length ratio. Figure 11. Maximum temperature difference vs. TEG area length ratio. 4.3 Effects of TEH physical size Figures 1 16 show the characteristic of electrical current, heating load, COP, maximum heating load and maximum heating temperature difference vs. the TEH area length ratio v with given working conditions. In the calculations, v 1 ¼ 4mm is set. From Figures 1 and 15, one can see that the electrical current and maximum heating load are increasing functions of the TEH area length ratio. When the TEH area length ratio v exceeds 10 mm, the maximum heating load increases slowly and approaches its limit. That is, increasing the TEH area length ratio could improve the maximum heating load, but there is a limit which cannot be overrun. From Figures 13 and 14, one can see that both the heating load and COP have extreme values. There are two optimum TEH area length ratio v Q and v COP corresponding to the maximum heating load and maximum COP, In general, the two optimum TEH area length ratios are different from each other. From Figure 16, one can see that the maximum heating temperature difference is a decreasing function of the TEH area International Journal of Low-Carbon Technologies 016, 11,

6 F. Meng et al. Figure 1. Electrical current vs. TEH area length ratio. Figure 13. Heating load vs. TEH area length ratio. Figure 14. COP vs. TEH area length ratio. length ratio. When v is in small value, the maximum heating temperature difference decreases rapidly with the increase in v. When v is in larger value, the maximum heating temperature difference decreases slowly. Moreover, the larger thermocouple ratio x, the larger effect of TEH area length ratio v on the maximum heating temperature difference. Figure 15. Maximum heating load vs. TEH area length ratio. Figure 16. Maximum temperature difference vs. TEH area length ratio. 5 A PRACTICAL REPRESENTATIVE EXAMPLE Parameters of two typical TEMs made by a manufactory are shown in Table. The TEMs are made of the same thermoelectric material and different physical size. Every type TEM has 35, 71 or 17 thermocouples. Possible configurations and the corresponding performance are shown in Table 3. The stable working electrical current and COP are calculated at T d1 ¼ T h1 T c1 ¼ 150K and T d ¼ T h T c ¼ 0K. Because the rational thermocouples ratio x is approximately [40 45], the configuration of m 1 m is set to From the above discussion, one can conclude that a larger v 1 leads to a larger maximum heating load, while a larger v 1 and smaller v lead to a larger maximum heating temperature difference. From the table, one can clearly see that for a larger COP, configuration I II is the best choice; for a larger maximum heating load, configuration I I is the best choice; and for a larger 380 International Journal of Low-Carbon Technologies 016, 11,

7 Effects of thermocouples physical size Table. Parameters of two typical TEMs. Type m a ðv/k) k ðw/k m) s ðm/ V) A ðmm Þ L ðmm) v ðmm) TEM-I 35/71/ TEM-II 35/71/ Table 3. Possible configurations and the corresponding performance. Configuration m 1 m v 1 v (mm) I (A) COP Q h max ðwþ T d max ðkþ I I I II II I II II maximum heating temperature difference, configuration I II is the best choice. The best choices are underlined in the table. 6 CONCLUSION The effect of the physical size of thermocouples on the performance of the TEG TEH system is investigated in this article. The results show that an improvement in its performance is possible by optimizing the internal physical size of the thermocouples. A larger v 1 leads to a larger maximum heating load and there is an optimum v corresponding to the maximum heating load. Larger v 1 and smaller v lead to a larger maximum heating temperature difference. If the area length ratio of TEG and TEH changes synchronously, the COP and heating load remain constants. The principles obtained could be helpful to select appropriate TEMs to construct a high-performance TEG TEH system satisfying different requirements. The results obtained herein may provide some guidelines for the design and application of practical combined thermoelectric devices. ACKNOWLEDGEMENTS This article is supported by National Basic Research Program of China (No. 01CB70405), National Natural Science Foundation of China (No ) and Natural Science Foundation of Naval University of Engineering (No. HGDYDJJ100). The authors wish to thank the reviewers for their careful, unbiased and constructive suggestions, which led to this revised manuscript. REFERENCES [1] Bell LE. Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science 008;31: [] Angrist SW. Direct Energy Conversion, 4th edn. Allyn and Bacon Inc., 199. [3] Rowe DM (ed). CRC Handbook of Thermoelectrics. CRC Press, [4] Di Salvo FJ. Thermoelectric cooling and power generation. Science 1999;85: [5] Ma X, Riffat SB. Thermoelectric: a review of present and potential applications. Appl Thermal Eng 003;3: [6] Poudel B, Hao Q, Ma Y. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science 008;30: [7] Zhong H, Liang YC, Samudra GS, et al. Practical superjunction MOSFET device performance under given process thermal cycles. Semicond Sci Tech 004;19: [8] Ovsyannikov S, Shchennikov VV, Ponosov YS, et al. Application of highpressure thermoelectric technique for characterization of semiconductor microsamples: PbX-based compounds. J Phys D Appl Phys 004;37: [9] Min G, Rowe DM, Kontostavlakis K. Thermoelectric figure-of-merit under large temperature differences. J Phys D Appl Phys 004;37: [10] Chen M, Lu SS, Liao B. On the figure of merit of thermoelectric generators. Trans ASME J Energy Res Tech 005;17: [11] Wiśniewski S, Staniszewski B, Szymanik R. Thermodynamics of Non-equilibrium Processes. D. Reidel Pub. CoCalifornia, [1] Bejan A. Advanced Engineering Thermodynamics, nd edn. Wiley, [13] Sisman A, Yavuz H. The effect of Joule losses on the total efficiency of a thermoelectric power cycle. Energy Int J 1995;0: [14] Chen J, Yan Z. The influence of Thomson effect on the maximum power output and maximum efficiency of a thermoelectric generator. J Appl Phys 1996;79: [15] Chen J, Yan Z, Wu L. Non-equilibrium thermodynamic analysis of thermoelectric device. Energy Int J 1997;: [16] Rowe DM, Min G. Evaluation of thermoelectric modules for power generation. J Power Sources 1998;73: [17] Omer SA, Infield DG. Design optimization of thermoelectric a devices for solar power generation. Sol Energy Mater Sol Cell 1998;53:67 8. [18] Mayergoyz ID, Andrel D. Statistical analysis of semiconductor devices. J Appl Phys 001;90: [19] Naji M, Alata M, Al-Nimr MA. Transient behavior of a thermoelectric device. Proc IMechE Part A J Power Energy 003;17(6A): [0] Nuwayhid RY, Shihadeh A, Ghaddar N. Development and testing of a domestic woodstove thermoelectric generator with natural convection cooling. Energy Convers Manage 005;46: [1] Chen M, Rosendahl L, Bach I, et al. Irreversible transfer processes of thermoelectric generators. Am J Phys 007;75: [] Yu JL, Zhao H. A numerical model for thermoelectric generator with the parallel-plate heat exchanger. J Power Sources 007;17: [3] Huang BJ, Chin CJ, Duang CL. A design method of thermoelectric cooler. Int J Refrig 000;3: International Journal of Low-Carbon Technologies 016, 11,

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