本論文主旨在於應用拉凡格式法(Levenberg-Marquardt Method)搭配套裝軟體 CFD-ACE+，探討三維反算問題於自然對流情況下的軸對稱LED散熱鰭片外型最佳化設計之研究。
一般的工程問題利用正算求解物理量，將已知條件輸入系統模式求解，稱為正算問題(Direct Problem)。而藉由其他可測量或計算的資料，反算得到物理量，這一類的問題我們稱之為反算問題(Inverse Problem)。反算設計問題也可用於最佳化設計問題，因反算設計問題可利用目前已知的參數或物理量，對複雜的工程問題作最佳化處理。
本研究探討不同的鰭片高度配置與重複陣列數對於鰭片熱阻的影響，在不增加鰭片質量的條件下達到散熱能力的最佳化，並利用紅外線熱像儀實際實驗量測散熱鰭片表面溫度分佈，以比較數值模擬與實際實驗的差異。
散熱鰭片形狀經過最佳化後熱阻確實能夠降低，並且發現即便減少部分鰭片材料亦不會造成熱阻顯著增加。經實驗驗證後，也證實數值模擬結果與實際實驗情況十分吻合。

SUMMARY

A fin shape design problem is considered in this thesis utilizing the Levenberg-Marquardt Method (LMM) and a commercial package CFD-ACE+. The objective is to design the optimal fin shape of the radial heat sink for light-emitting diode (LED) lighting devices and to enhance the cooling performance of the heat sink. The working condition of the heat sink is assumed natural convection condition and the effect of radiation heat transfer between heat sink and air is included. Numerical experiments indicated that by utilizing the fin heights as the design variables, the best heat sink performance can be obtained since the system thermal resistance can be further reduced by 16.8 % and 11.0 % than the original and Type 2 design heat sinks, respectively. Finally, three types of heat sinks with fins are carried on the experimental verification. The results from experiments show that with the designed optimal fin shapes the cooling performance of the heat sink is indeed better than those with the initial and existing fin designs, besides, the numerical and experimental temperature distributions on the measured surfaces are very much similar.

Keywords : Levenberg-Marquardt Method ; heat sink for LED ;
Optimal fin design

1. Huang, C. H., Lu, J. J., and Ay, H., “A three-dimensional heat sink module design algorithm with experimental verification”, International Journal of Heat and Mass Transfer, Vol.54, pp. 1482–1492, 2011
2. Marquardt, D. M., “An algorithm for least-squares estimation of nonlinear parameters”, J. Soc. Indust. Appl. Math., Vol. 11, pp. 431–441, 1963
3. CFD-RC user’s manual, ESI-CFD Inc., 2013.
4. Bougriou, C., Bessaih, R., Gall, R. L., Solecki, J. C., “Measurement of the temperature distribution on a circular plane fin by infrared thermography technique” Applied Thermal Engineering, Vol. 24, pp. 813-825, 2004.
5. Meinders, E. R., Meer, Th. H. van der, Hanjalic, K., Lasance, C. J. M., “Application of infrared thermography to the evaluation of local convective heat transfer on arrays of cubical protrusions” International Journal of Heat and Fluid Flow, Vol. 18, pp. 152-159, 1997.
6. Elshafei, E. A. M. , “Natural convection heat transfer from a heat sink with hollow/perforated circular pin fins” Energy, Vol. 35, pp. 2870–7, 2010.
7. Sertkaya, A. A. , Bilir, Şefik, Kargıcı, S. ,“Experimental investigation of the effects of orientation angle on heat transfer performance of pin-finned surfaces in natural convection” Energy, Vol 36, pp. 1513–1517, 2011.
8. Harahap, F. , Setio, D. “Correlations for heat dissipation and natural convection heat-transfer from horizontally-based, vertically-finned arrays” Applied Energy, Vol. 69, pp. 29–38, 2001.
9. Yu, S. H. , Lee, K. S. , Yook, S. J. “Natural convection around a radial heat sink” Int J Heat Mass Transfer, Vol. 53, pp. 2935–2938, 2010.
10. Yu, S. H. , Lee, K. S. , Yook, S. J. “Optimum design of a radial heat sink under natural convection” Int J Heat Mass Transfer, Vol. 54, pp. 2499–2505, 2011.
11. Yu, S. H. , Jang, D. , Lee, K. S. “Effect of radiation in a radial heat sink under natural convection” Int J Heat Mass Transfer, Vol. 55, pp. 505–509,2012.
12. Jang, D. , Yu, S. H. , Lee, K. S. “Multidisciplinary optimization of a pin-fin radial heat sink for LED lighting applications” Int J Heat Mass Transfer, Vol. 55, pp. 515–521, 2012
13. Jang, D. , Yook, S. J. , Lee, K. S. “Optimum design of a radial heat sink with a fin-height profile for high-power LED lighting applications”, Applied Energy, Vol. 116, pp. 260-268, 2014
14. Kanyakam, S. , Bureerat, S. “Multiobjective evolutionary optimization of splayed pin-fin heat sink”, Engineering Applications of Computational Fluid Mechanics, Vol. 5, pp. 553-565, 2011
15. Shah, A., Sammakia, B.G., Srihari, H., Ramakrishna, K. “A numerical study of the thermal performance of an impingement heat sink-fin shape optimization”, IEEE Trans Compon Packag Technol, Vol. 27, pp. 710-717, 2004
16. Yang, Y. , Peng, H. , “Numerical study of pin-fin heat sink with un-uniform fin height design”, Int J Heat Mass Transfer, Vol. 51, pp. 4788-4796, 2008
17. Saravanan, S. , Sivaraj, C. , “Coupled thermal radiation and natural convection heat transfer in a cavity with a heated plate inside”, International Journal of Heat and Fluid Flow, Vol. 40, pp. 54-64, 2013