熱電技術由於具有環境友善性且可提供乾淨的能源轉換，近年來已成為受矚目的綠能科技之一。然而熱電元件的最大缺陷是相對較低的能量轉換效率。為了解決此問題，不少研究者選擇經濟又有效的熱源；另一方面，為了進一步推廣綠色能源的概念，因此，有學者研究使用廢熱或太陽能來作為熱電系統的熱源。本研究即是以有限元素法針對四種不同的熱電系統來發展數值模型並探討其性能表現。隨溫度變化的材料性質以及接觸阻抗、熱損失對性能的影響都將考慮在本研究中。系統性能則根據散熱設計與幾何設計來做最佳化。第一個熱電系統中所探討的是結合氣冷散熱系統之熱電發電器，其中性能表現採用兩階段的最佳化方式。研究結果推薦藉由增加散熱鰭片的正面面積以減少散熱鰭片的長度來做為氣冷散熱系統之設計方向。在第二個熱電系統中，則是採用可用能分析來評估各種不可逆性對熱電發電器之性能影響。研究結果顯示對於小電流之應用，減少熱儲溫度或是增加冷儲溫度可以提昇熱電發電器之可用能效率。第三個熱電系統乃是探討熱電發電與致冷整合之系統，也就是說於本系統中，熱電致冷晶片是直接由熱電發電器所驅動。其結果顯示當熱電發電器的晶粒長度改變時，整體系統表現將高度相關於其邊界條件。另一方面，不管熱電發電器的熱面邊界條件為何，當熱電致冷晶片的晶粒長度改變時，總是可以找到最佳的冷卻功率及性能係數。最後的熱電系統則是討論平板集熱之太陽能熱電發電器。在此系統中採用本研究所建立的等效模型來簡化並加速數值模擬的計算。其結果顯示太陽能熱電發電器的性能隨平板基材的面積增加而提昇；然而，冷面在給定的強制對流條件下，性能無法藉由改變熱對流係數來提昇。三種晶粒幾何尺寸中，最小的晶粒搭配90×90 mm2的平板基材面積可獲得最大的系統效率4.15%。而最大晶粒的性能只有在三種晶粒的熱聚比一致時才能顯現其優勢。本研究除可得知熱電系統之運作特性外，並可做為未來熱電系統設計之參考及依據。

Recently, the thermoelectric technology becomes one of the attractive green energy technologies due to its environmental friendliness and clean energy conversion. However, its primary drawback is the low energy conversion efficiency. In order to overcome this obstacle, a proper choice of economic and efficient heat source is crucial. In this aspect, using waste heat or solar energy as the heat source of thermoelectric system is a feasible countermeasure. In this study, numerical models for four kinds of thermoelectric systems are developed by using the finite element scheme to investigate their performances. Temperature-dependent material properties in association with the effects of contact resistance and heat loss on system performance are considered. The system performance is optimized through the thermal design and geometric design. In the first system, the performance of the thermoelectric generator (TEG) in association with an air-cooling system designed using two-stage optimization is investigated. The results show that decreasing the length of the heat sink by increasing its frontal area is the recommended design approach. In the second system, the effects of multi-irreversibilities on TEG performance are evaluated using exergy analysis. The results suggest that when the application of the small electrical current is considered, decreasing the hot-reservoir temperature or increasing the cold-reservoir temperature can improve the exergy efficiency. In the third system, an integrated thermoelectric generation-cooling system is performed where a thermoelectric cooler (TEC) is powered directly by a TEG. The results show that when the TEG length is changed, the entire behavior of system performance depends highly on the boundary condition. On the other hand, the maximum distributions of cooling power and coefficient of performance (COP) are exhibited when the TEC length is altered, whether the hot surface of TEG is given by a fixed temperature or heat transfer rate. In the eventual system, the performance of a thermal-concentrated solar TEG is investigated using an equivalent model which is developed to simplify and accelerate the numerical computation. The results show that the performance of the solar TEG can be improved by increasing the substrate area, but that a varying convection heat transfer coefficient under the forced convection condition has a tiny effect on the performance. In the three geometric types, the smallest element with the substrate area of 90×90 mm2 provides the maximum system efficiency of 4.15%, whereas the largest element gives the better performance only when the thermal concentration ratios of the three types are identical. The study not only enables us to figure out the system characteristics of performance, the obtained results are also able to provide useful references for the design of thermoelectric systems.

[1] R.E. Simons, M.J. Ellsworth, R.C. Chu, “An assessment of module cooling enhancement with thermoelectric coolers,” J. Heat Transfer-Trans. ASME, vol. 127, pp. 76-84, 2005.
[2] K.H. Wu, C.I. Hung, “Thickness scaling characterization of thermoelectric module for small-scale electronic cooling,” J. Chin. Soc. Mech. Eng., vol. 30, pp. 475-481, 2009.
[3] T.C. Cheng, C.H. Cheng, Z.Z. Huang, G.C. Liao, “Development of an energy-saving module via combination of solar cells and thermoelectric coolers for green building applications,” Energy, vol. 36, pp. 133-140, 2011.
[4] W.H. Chen, C.Y. Liao, C.I. Hung, “A numerical study on the performance of miniature thermoelectric cooler affected by Thomson effect,” Appl. Energy, vol. 89, pp. 464-473, 2012.
[5] D. Champier, J.P. Bedecarrats, M. Rivaletto, F. Strub, “Thermoelectric power generation from biomass cook stoves,” Energy, vol. 35, pp. 935-942, 2010.
[6] D. Champier, J.P. Bedecarrats, T. Kousksou, M. Rivaletto, F. Strub, P. Pignolet, “Study of a TE (thermoelectric) generator incorporated in a multifunction wood stove,” Energy, vol. 36, pp. 1518-1526, 2011.
[7] A. Martínez, D. Astrain, A. Rodríguez, “Experimental and analytical study on thermoelectric self cooling of devices,” Energy, vol. 36, pp. 5250-5260, 2011.
[8] S. Kim, “Analysis and modeling of effective temperature differences and electrical parameters of thermoelectric generators,” Appl. Energy, vol. 102, pp. 1458-1463, 2013.
[9] S. Maneewan, S. Chindaruksa, “Thermoelectric power generation system using waste heat from biomass drying,” J. Electron. Mater., vol. 38, pp. 974-980, 2009.
[10] A.Z. Sahin, B.S. Yilbas, S.Z. Shuja, O. Momin, “Investigation into topping cycle: thermal efficiency with and without presence of thermoelectric generator,” Energy, vol. 36, pp. 4048-4054, 2011.
[11] Y. Pan, B. Lin, J. Chen, “Performance analysis and parametric optimal design of an irreversible multi-couple thermoelectric refrigerator under various operating conditions,” Appl. Energy, vol. 84, pp. 882-892, 2007.
[12] F.J. Disalvo, “Thermoelectric cooling and power generation,” Science, vol. 285, pp. 703-706, 1999.
[13] C.H. Cheng, S.Y. Huang, T.C. Cheng, “A three-dimensional theoretical model for predicting transient thermal behavior of thermoelectric coolers,” Int. J. Heat Mass Transfer, vol. 53, pp. 2001-2011, 2010.
[14] A. Shakouri, “Recent developments in semiconductor thermoelectric physics and materials,” Annu. Rev. Mater. Res., vol. 41, pp. 399-431, 2011.
[15] G. Chen, Nanoscale energy transport and conversion, Oxford University Press, Oxford, 2005.
[16] L.E. Bell, “Cooling, heating, generating power, and recovering waste heat with thermoelectric systems,” Science, vol. 321, pp. 1457-1461, 2008.
[17] B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, et al., “High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys,” Science, vol. 320, pp. 634-638, 2008.
[18] J.S. Rhyee, K.H. Lee, S.M. Lee, E. Cho, S. Kim, E. Lee, et al., “Peierls distortion as a route to high thermoelectric performance in In4Se3-δ crystals,” Nature, vol. 459, pp. 965-968, 2009.
[19] K. Biswas, J. He, I.D. Blum, C.I. Wu, T.P. Hogan, D.N. Seidman, et al., “High-performance bulk thermoelectrics with all-scale hierarchical architectures,” Nature, vol. 489, pp. 414-418, 2012.
[20] X. Gou, H. Xiao, S. Yang, “Modeling, experimental study and optimization on low-temperature waste heat thermoelectric generator system,” Appl. Energy, vol. 87, pp. 3131-3136, 2010.
[21] S.H. Noie-Baghban, G.R. Majideian, “Waste heat recovery using heat pipe heat exchanger (HPHE) for surgery rooms in hospitals,” Appl. Therm. Eng., vol. 20, pp. 1271-1282, 2000.
[22] W.H. Chen, J.C. Chen, “Combustion characteristics and energy recovery of a small mass burn incinerator,” Int. Comm. Heat Mass Transfer, vol. 28, pp. 299-310, 2001.
[23] W.H. Chen, Y.C. Chung, J.L. Liu, “Analysis on energy consumption and performance of reheating furnaces in a hot strip mill,” Int. Comm. Heat Mass Transfer, vol. 32, pp. 695-706, 2005.
[24] H.Y. Shih, Y.C. Huang, “Thermal design and model analysis of the Swiss-roll recuperator for an innovative micro gas turbine,” Appl. Therm. Eng., vol. 29, pp. 1493-1499, 2009.
[25] W.H. Chen, T.W. Chiu, C.I. Hung, “Enhancement effect of heat recovery on hydrogen production from catalytic partial oxidation of methane,” Int. J. Hydrogen Energy, vol. 35, pp. 7427-7440, 2010.
[26] D.M. Rowe, “Thermoelectric waste heat recovery as a renewable energy source,” Int. J. Innov. Energy Syst. Power, vol. 1, pp. 13-23, 2006.
[27] Y.Y. Hsiao, W.C. Chang, S.L. Chen, “A mathematic model of thermoelectric module with applications on waste heat recovery from automobile engine,” Energy, vol. 35, pp. 1447-1454, 2010.
[28] C.T. Hsu, G.Y. Huang, H.S. Chu, B. Yu, D.J. Yao, “Experiments and simulations on low-temperature waste heat harvesting system by thermoelectric power generators,” Appl. Energy, vol. 88, pp. 1291-1297, 2011.
[29] W.H. Chen, C.Y. Liao, C.I. Hung, W.L. Haung, “Experimental study on thermoelectric modules for power generation at various operating conditions,” Energy, vol. 45, pp. 874-881, 2012.
[30] S. Mekhilef, R. Saidur, A. Safari, “A review on solar energy use in industries,” Renew. Sustain. Energy Rev., vol. 15, pp. 1777-1790, 2011.
[31] P. Li, L. Cai, P. Zhai, X. Tang, Q. Zhang, M. Niino, “Design of a concentration solar thermoelectric generator,” J. Electron. Mater., vol. 39, pp. 1522-1530, 2010.
[32] H. Fan, R. Singh, A. Akbarzadeh, “Electric power generation from thermoelectric cells using a solar dish concentrator,” J. Electron. Mater., vol. 40, pp. 1311-1320, 2011.
[33] T. Yang, J. Xiao, P. Li, P. Zhai, Q. Zhang, “Simulation and optimization for system integration of a solar thermoelectric device,” J. Electron. Mater., vol. 40, pp. 967-973, 2011.
[34] J. Xiao, T. Yang, P. Li, P. Zhai, Q. Zhang, “Thermal design and management for performance optimization of solar thermoelectric generator,” Appl. Energy, vol. 93, pp. 33-38, 2012.
[35] D. Kraemer, B. Poudel, H.P. Feng, J.C. Caylor, B. Yu, X. Yan, et al., “High-performance flat-panel solar thermoelectric generators with high thermal concentration,” Nature Mater., vol. 10, pp. 532-538, 2011.
[36] G. Chen, “Theoretical efficiency of solar thermoelectric energy generators,” J. Appl. Phys., vol. 109, pp. 104908, 2011.
[37] C. Lertsatitthanakorn, L. Wiset, S. Atthajariyakul, “Evaluation of the thermal comfort of a thermoelectric ceiling cooling panel (TE-CCP) system,” J. Electron. Mater., vol. 38, pp. 1472-1477, 2009.
[38] X. Chen, B. Lin, J. Chen, “The parametric optimum design of a new combined system of semiconductor thermoelectric devices,” Appl. Energy, vol. 83, pp. 681-686, 2006.
[39] N.M. Khattab, E.T.E. Shenawy, “Optimal operation of thermoelectric cooler driven by solar thermoelectric generator,” Energy Convers. Manage.,vol. 47, pp. 407-426, 2006.
[40] F. Meng, L. Chen, F. Sun, C. Wu, “Thermodynamic analysis and optimization of a new-type thermoelectric heat pump driven by a thermoelectric generator,” Int. J. Ambient Energy, vol. 30, pp. 95-101, 2009.
[41] F. Meng, L. Chen, F. Sun, “Multiobjective analysis of physical dimension on the performance,” Int. J. Low-Carbon Tech., vol. 5, pp. 193-200, 2010.
[42] M. Hodes, “Optimal pellet geometries for thermoelectric power generation,” IEEE Trans. Compon. Packag. Technol., vol. 33, pp. 307-318, 2010.
[43] J. Esarte, G. Min, D.M. Rowe, “Modelling heat exchangers for thermoelectric generators,” J. Power Sources, vol. 93, pp. 72-76, 2001.
[44] L. Chen, J. Gong, F. Sun, C. Wu, “Effect of heat transfer on the performance of thermoelectric generators,” Int. J. Therm. Sci., vol. 41, pp. 95-99, 2002.
[45] D. Astrain, J.G. Vián, A. Martínez, A. Rodríguez, “Study of the influence of heat exchangers’ thermal resistances on a thermoelectric generation system,” Energy, vol. 35, pp. 602-610, 2010.
[46] A. Martínez, J.G. Vián, D. Astrain, A. Rodríguez, I. Berrio, “Optimization of the heat exchangers of a thermoelectric generation system,” J. Electron. Mater., vol. 39, pp. 1463-1468, 2010.
[47] A. Rezania, L.A. Rosendahl, “Evaluating thermoelectric power generation device performance using a rectangular microchannel heat sink,” J. Electron. Mater., vol. 40, pp. 481-488, 2011.
[48] X.C. Xuan, “Optimum design of a thermoelectric device,” Semicond. Sci. Technol., vol. 17, pp. 114-119, 2002.
[49] M. Kubo, M. Shinoda, T. Furuhata, K. Kitagawa, “Optimization of the incision size and cold-end temperature of a thermoelectric device,” Energy, vol. 30, pp. 2156-2170, 2005.
[50] K.H. Lee, O.J. Kim, “Analysis on the cooling performance of the thermoelectric micro-cooler,” Int. J. Heat Mass Transfer, vol. 50, pp. 1982-1992, 2007.
[51] B.S. Yilbas, A.Z. Sahin, “Thermoelectric device and optimum external load parameter and slenderness ratio,” Energy, vol. 35, pp. 5380-5384, 2010.
[52] B. Jang, S. Han, J.Y. Kim, “Optimal design for micro-thermoelectric generators using finite element analysis,” Microelectron. Eng., vol. 88, pp. 775-778, 2011.
[53] C. Wu, “Analysis of waste-heat thermoelectric power generators,” Appl. Therm. Eng., vol. 16, pp. 63-69, 1996.
[54] J. Chen, “The maximum power output and maximum efficiency of an irreversible Carnot heat engine,” J. Phys. D: Appl. Phys., vol. 27, pp. 1144-1149, 1994.
[55] J. Chen, C. Wu, “Analysis on the performance of a thermoelectric generator,” J. Energy Resour. Technol.-Trans. ASME, vol. 122, pp. 61-63, 2000.
[56] X. Niu, J. Yu, S. Wang, “Experimental study on low-temperature waste heat thermoelectric generator,” J. Power Sources, vol. 188, pp. 621-626, 2009.
[57] M. Chen, L.A. Rosendahl, T. Condra, “A three-dimensional numerical model of thermoelectric generators in fluid power systems,” Int. J. Heat Mass Transfer, vol. 54, pp. 345-355, 2011.
[58] J. Sharp, J. Bierschenk, H.B. Jr Lyon, “Overview of solid-state thermoelectric refrigerators and possible applications to on-chip thermal management,” Proc. IEEE, vol. 94, pp. 1602-1612, 2006.
[59] G. Min, D.M. Rowe, “Improved model for calculating the coefficient of performance of a Peltier module,” Energy Convers. Manage., vol. 41, pp. 163-171, 2000.
[60] Y.T. Yang, H.S. Peng, “Numerical study of pin-fin heat sink with un-uniform fin height design,” Int. J. Heat Mass Transfer, vol. 51, pp. 4788-4796, 2008.
[61] I. Dincer, M.A. Rosen, Exergy, energy, environment and sustainable development, 1st ed., Elsevier, Oxford, UK, 2007.
[62] M.F. Orhan, I. Dincer, M.A. Rosen, “An exergy-cost-energy-mass analysis of a hybrid copper-chlorine thermochemical cycle for hydrogen production,” Int. J. Hydrogen Energy, vol. 35, pp. 4831-4838, 2010.
[63] C.D. Rakopoulos, E.G. Giakoumis, “Second-law analyses applied to internal combustion engines operation,” Prog. Energy Combust. Sci., vol. 32, pp. 2-47, 2006.
[64] S.K. Tyagi, S. Wang, M.K. Singhal, S.C. Kaushik, S.R. Park, “Exergy analysis and parametric study of concentrating type solar collectors,” Int. J. Therm. Sci., vol. 46, pp. 1304-1310, 2007.
[65] J. Wang, Y. Dai, L. Gao, “Exergy analyses and parametric optimizations for different cogeneration power plants in cement industry,” Appl. Energy, vol. 86, pp. 941-948, 2009.
[66] L. Ozgener, O. Ozgener, “Monitoring of energy exergy efficiencies and exergoeconmic parameters of geothermal district heating systems (GDHSs),” Appl. Energy, vol. 86, pp. 1704-1711, 2009.
[67] L. Barelli, G. Bidini, F. Gallorini, A. Ottaviano, “An energetic-exergetic analysis of a residential CHP system based on PEM fuel cell,” Appl. Energy, vol. 88, pp. 4334-4342, 2011.
[68] M. Zebarjadi, K. Esfarjani, M.S. Dresselhaus, Z.F. Ren, G. Chen, “Perspectives on thermoelectrics; from fundamentals to device applications,” Energy Environ. Sci., vol. 5, pp. 5147-5162, 2012.
[69] S. Chatterjee, K.G. Pandey, “Thermoelectric cold-chain chests for storing / transporting vaccines in remote regions,” Appl. Energy, vol. 76, pp. 415-433, 2003.
[70] Industrial Technology Research Institute, https://www.itri.org.tw/chi/index.asp.
[71] Z. Duan, Y.S. Muzychka, “Experimental investigation of heat transfer in impingement air cooled plate fin heat sinks,” J. Electron. Packag., vol. 128, pp. 412-418, 2006.
[72] E.E. Antonova, C.C. Looman, “Finite elements for thermoelectric device analysis in ANSYS,” 24th International Conference on Thermoelectrics, pp. 215-218, 2005.
[73] Q.C. Zhang, “High efficiency Al-N cermet solar coatings with double cermet layer film structures,” J. Phys. D: Appl. Phys., vol. 32, pp. 1938-1944, 1999.
[74] P.P. Silvester, R.L. Ferrari, Finite elements for electrical engineers, 3rd ed., Cambridge University Press, New York, 1996.
[75] S. Moaveni, Finite element analysis: theory and applications with ANSYS, 2nd ed., Prentice Hall, New Jersey, 2003.
[76] P. Teertstra, M.M. Yovanovioch, J.R. Culham, “Analytical forced convection modeling of plate fin heat sinks,” 15th IEEE SEMI-THERM Symposium, pp. 34-41, 1999.
[77] S. Mereu, E. Sciubba, A. Bejan, “The optimal cooling of a stack of heat generating boards with fixed pressure drop, flowrate or pumping power,” Int. J. Heat Mass Transfer, vol. 36, pp. 3677-3686, 1993.
[78] T. Bello-Ochende, L. Liebenberg, J.P. Meyer, “Constructal cooling channels for micro-channel heat sinks,” Int. J. Heat Mass Transfer, vol. 50, pp. 4141-4150, 2007.
[79] F. Meng, L. Chen, F. Sun, “A numerical model and comparative investigation of a thermoelectric generator with multi-irreversibilities,” Energy, vol. 36, pp. 3513-3522, 2011.
[80] C.K. Loh, D. Nelson, D.J. Chou, “Thermal characterization of fan-heat sink systems in miniature axial fan and micro blower airflow,” 17th IEEE SEMI-THERM Symposium, pp. 111-116, 2001.
[81] D. Copeland, “Optimization of parallel plate heatsinks for forced convection,” 16th IEEE SEMI-THERM Symposium, pp. 266-272, 2000.
[82] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of heat and mass transfer, 6th ed., John Wiley & Sons, Hoboken, 2007.
[83] D.W. Copeland, “Fundamental performance limits of heatsinks,” J. Electron. Packag., vol. 125, pp. 221-225, 2003.
[84] M.A. Moron, C. Romero, F.R. Ruiz Del Portal, “Generating well-behaved utility functions for compromise programming,” J. Optim. Theory Appl., vol. 91, pp. 643-649, 1996.
[85] M. Eswararmoorthy, S. Shanmugam, “Thermodynamic analysis of solar parabolic dish thermoelectric generator,” Int. J. Renewable Energy Technol., vol. 1, pp. 348-360, 2010.
[86] R. Ahiska, K. Ahiska, “New method for investigation of parameters of real thermoelectric modules,” Energy Convers. Manage., vol. 51, pp. 338-345, 2010.
[87] J.L. Pérez-Aparicio, R. Palma, R.L. Taylor, “Finite element analysis and material sensitivity of Peltier thermoelectric cells coolers,” Int. J. Heat Mass Transfer, vol. 55, pp. 1363-1374, 2012.
[88] H. Xiao, X. Gou, S. Yang, “Detailed modeling and irreversible transfer process analysis of a multi-element thermoelectric generator system,” J. Electron. Mater., vol. 40, pp. 1195-1201, 2011.
[89] G. Liang, J. Zhou, X. Huang, “Analytical model of parallel thermoelectric generator,” Appl. Energy, vol. 88, pp. 5193-5199, 2011.
[90] Tande Energy and Temperature Associates PTY. CO., http://www.tande.com.tw/.
[91] S. Lee, S. Song, V. Au, K.P. Moran, “Constriction / spreading resistance model for electronic packing,” ASME/JSME Therm. Eng. Conf., vol. 4, pp. 199-206, 1995.
[92] Y.S. Chen, K.H. Chien, C.C. Wang, T.C. Hung, Y.M. Ferng, B.S. Pei, “Investigations of the thermal spreading effects of rectangular conduction plates and vapor chamber,” J. Electron. Packag., vol. 129, pp. 348-355, 2007.
[93] R.M. Soliman, M.A. El-Hadek, S.I. Abdu, “Stress analysis of multi-layer electronic and mechanical systems (MEMS) under fatigue and impact loading conditions,” Int. J. Mech. Mater. Des., vol. 6, pp. 359-365, 2010.
[94] A. Bejan, Convection heat transfer, 2nd ed., John Wiley & Sons, New York 1995.
[95] C.C. Wang, C.I. Hung, W.H. Chen, “Design of heat sink for improving the performance of thermoelectric generator using two-stage optimization,” Energy, vol. 39, pp. 236-245, 2012.