本論文主旨在於應用拉凡格式法(Levenberg-Marquardt Method)配合套裝軟體CFD-ACE+，來探討三維反算問題於衝擊冷卻裝置下的散熱模組形狀最佳化設計之研究。本論文研究主題分為三個部分。
案例一，最佳化模組設計採用10×10陣列之方柱型鰭片，固定其體積、間距與高度，研究目標使熱阻為最小值，計算出最佳化不均勻寬度的散熱模組形狀。案例二，最佳化模組設計採用6×6陣列之方柱型鰭片，固定其體積與間距，研究目標使熱阻為最小值，計算出最佳化不均勻寬度與高度的散熱模組形狀。案例三，採用案例二的設計條件並將體積增大等同於案例一，設計出一不均勻寬度與一不均勻寬度與高度的散熱模組，比較其熱性能。
結果顯示，散熱模組的熱阻值經過最佳化設計後都能被減少。研究發現，最佳化後的散熱模組其出口風量有明顯增加。最後散熱模組進行實驗，再利用紅外線熱像儀進行測量，並且與CFD-ACE+ 模擬解得的鰭片厚度表面溫度進行驗證，也證明了模擬與實際上的結果非常相近。

A three-dimensional inverse design problem is examined in this thesis using a general purpose commercial code (CFD-ACE+) and the Levenberg-Marquardt Method (LMM) to estimate the optimal shapes of an impingement cooling heat sinks with different design variables. The study consists of three cases.
In case 1, the optimal heat sink was designed based on the original 10 by 10 squared fin array with a fixed fin volume, pitch and height. The objective of this study is to minimize the thermal resistance (Rth) of the fin array and to obtain the optimal dimensions of non-uniform fin widths. Experiments were performed to show the validity of the present design results. In case 2, the optimal heat sink was designed based on the original 6 by 6 squared fin array with a fixed fin volume and pitch. The objective of this study is to minimize the thermal resistance (Rth) of the fin array and to obtain the optimal dimensions of non-uniform fin widths and heights. In case 3, the fin volume in case 1 and design parameter in case 2 are utilized to design the optimal heat sink. In optimal heat sink #1, the non-uniform fin widths are taken as the design variables, while in optimal heat sink #2, the non-uniform fin widths and heights are chosen as the design variables. The objective of this study is to minimize the thermal resistance (Rth) of the fin array and to obtain the optimal dimensions of optimal heat sinks #1 and #2.
Results show that the thermal resistance of original heat sink can be reduced in the optimum heat sink modules due to the fact that the mass flow rate of air in optimal heat sink is increased. Finally, these heat sink modules are carried on the experimental verification. The result of temperature distribution is very similar between the experimental and numerical data.

[1] L.A. Brignoni, S.V. Garimella, Experimental optimization of confined air jet impingement on a pin fin heat sink, IEEE Trans. Compon. Packaging Technol. 22 (3) (1999) 399–404.

[2] J.G. Maveety, J.F. Hendricks, A heat sink performance study considering material, geometry, Reynolds number with air impingement, J. Electron. Packaging 121 (1999) 156–161.

[3] E. Sansoucy, P.H. Oosthuizen, G.R. Ahmed, An experimental study of the enhancement of air-cooling limits for telecom/datacom heat sink applications using an impinging air jet, J. Electron. Packaging 128 (2006) 166–171.

[4] H.Y. Li, S.M. Chao, G.L. Tsai, Thermal performance measurement of heat sinks with confined impinging jet by infrared thermography, Int. J. Heat Mass Transfer 48 (2005) 5386–5394.

[5] H.Y. Li, K.Y. Chen, Thermal performance of plate-fin heat sinks under confined impinging jet conditions, Int. J. Heat Mass Transfer 50 (2007) 1963–1970.

[6] Y. T. Yang and H. S. Peng, Numerical study of the heat sink with un-uniform fin width designs, International Journal of Heat and Mass Transfer, 52 (2009) 3473–3480.

[7] Y. T. Yang and H. S. Peng, Numerical study of pin-fin heat sink with un-uniform fin height designs, International Journal of Heat and Mass Transfer, 51 (2008) 4788–4796.

[8] C. J. Shih and G. C. Liu, Optimal design methodology of plate-fin heat sinks for electronic cooling using entropy generation strategy, IEEE Trans. Compon. Packag. Technol.,
27 (2004) 551–559.

[9] T. Furukawa and W. J. Yang, Reliability of heat sink optimization using entropy generation, in Proc. 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conf., AIAA-2002-3216 (2002) .

[10] O. A. Leon, G. D. Mey, E. Dick, and J. Vierendeels, Staggered heat sinks with aerodynamic cooling fins, Microelectron. Rel., 44 (2004) 1181–1187.

[11] E. Small, S. M. Sadeghipour and M. Asheghi, Heat sinks with enhanced heat transfer capability for electronic cooling applications, Journal of Electronic Packing, 128 (2006) 285–290.

[12] M. Iyengar and A. Bar-Cohen, Least-energy optimization of forced convection plate fin heat sinks, IEEE Trans. Components and Packaging Technologies , 26 (2003) 62–70.

[13] K. Park and S. Moon, Optimal design of heat exchangers using the progressive quadratic response surface model, International Journal of Heat and Mass Transfer, 42 (2005) 237–244.

[14] A. Shah, B. G. Sammakia, H. Srihari, and K. Ramakrishna, Optimization study for a parallel plate impingement heat sink, Journal of Electronic Packing, 128, (2006) 311–318.

[15] K. Park, D. H. Choi and K. S. Lee, Numerical shape optimization for high performance of a heat sink with pin-fins, Numerical Heat Transfer Part A, 46 (2004) 909–927.

[16] B. Sahin, K. Yakut, I. Kotcioglu and C. Celik, Optimum design parameters of a heat exchanger, Applied Energy, 82 (2005) 90–106.

[17] C. H. Huang, J. J. Lu and Herchang Ay, A three-dimensional heat sink module design algorithm with experimental verification”, International Journal of Heat and Mass Transfer, 54 (2011) 1482–1492.

[18] D. M. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, J. Soc. Indust. Appl. Math., 11 (1963) 431–441.

[19] CFD-RC user’s manual, ESI-CFD Inc., 2005.

[20] F. Lefevre and C. L. Niliot, Multiple transient point heat sources identification in heat diffusion: Application to experimental 2D problems, International Journal of Heat and Mass Transfer, 45 (2002) 1951–1964.

[21] C. H. Huang, Y. F. Chen and Herchang Ay, An inverse problem in determining the optimal position for piezoelectric fan with experimental verification, International Journal of Heat and Mass Transfer, 55 (2012) 5289–5301.

[22] S. J. Kline, The purposes of uncertainty analysis, ASME J. Fluid Engineering, 107 (1985) 153–160.

[23] M. C. Potter and D. C. Wiggert, Mechanics of Fluids, 3rd ed., BROOKS/COLE, (2002) 688–694.