隨著電子構裝愈來愈高的散熱需求及在尺寸與重量同時要求縮小化與輕量化的趨勢下，應用於熱管理的各類型散熱座最佳化設計成為一個重要的研究領域。本論文研究首先對於各類型散熱座的流場及熱傳特性作了一系列的理論探討，所發展的理論模式與現有的實驗數據相比，所預測出的流場及熱傳特性皆相當吻合。文中討論的相關參數包括有熱源之尺寸和發熱量、散熱座之結構與材質、入口流速及流體之旁通效應。在實驗方面，本研究中建立了一套實驗系統及方法來探討在水平渠道內各類型散熱座在不同流體旁通效應下之熱流特性。在實驗中探討影響水平渠道內之強制對流之相關參數有：格拉雪夫數(Gr)、散熱座高度與渠道高度比、散熱座寬度與渠道寬度比以及雷諾數(Re)。由研究結果發現，紐賽數(Nu)會隨著流體的旁通效應以及雷諾數的改變而產生明顯的變化，對於不同類型鰭片的散熱座也可以得到相似的趨勢；根據經過實驗計劃法所得到的實驗數據，研究中對於各類型的散熱座在渠道內強制對流之熱流特性包括壓力降、等效熱傳係數、紐賽數及熱阻值等，皆以最小平方誤差法提出了新的經驗公式。所得之實驗結果也用來驗證了所發展出的理論模式的正確性。

本研究中更成功地發展出一套應用於各類型散熱座之系統性的最佳化方法，此方法可使設計者有效且快速地在多個限制條件下找出最佳化的散熱設計。首先利用實驗計劃法及變異數分析所作出的敏感度測試可快速地分出系統中相關參數之影響重要性；接著應用反應曲面法可得到熱阻與壓力降的迴歸曲面模型；最後再藉由數值最佳化方法來有效的求出在各種限制條件下的最佳化散熱設計。應用此最佳化方法及流程，研究中成功地對於各類型散熱座在包括壓力降、重量及空間等限制條件的組合下分別得到最佳化設計之結果。另外，以前述之理論模式及最佳化方法為基礎，研究中也開發出一套針對各類型散熱座之電腦輔助最佳化設計系統。此系統包括具友善操作介面的前置處理器、自動化分析器、最佳化運算器、應用多媒體互動技術的後置處理器、以及資料庫等次系統。應用上述研發出之電腦輔助最佳化設計系統，本研究亦針對各類型散熱座的最佳化設計做了詳盡的實例探討，結果皆驗證了本研究中開發之電腦輔助最佳化設計系統的優越性。

The increasing power requirement for electronics industry, combined with ever-shrinking size and weight allowances, is creating a greater need for optimal design of generalized heat sinks. In this study, the thermal and hydrodynamic models for confined heat sinks with various fin types have been successfully developed. Comparisons between the predicted heat transfer and fluid flow characteristics for both fully-confined and partially-confined generalized heat sinks with existing data are made with satisfactory agreements. In addition, a series of parametric studies, including effects of the size of heat source, power of heating load, the fin structures of heat sink, the conductivity of heat sink, inlet velocity, and the flow bypass conditions, for thermal design of heat sinks have been performed.
To conduct the experimental investigation on the fluid flow and heat transfer characteristics for confined generalized heat sinks, an experimental system has been successfully established with an adjustable test section. From the experimental data, the generalized correlations for both the thermal performance and the pressure drop of confined heat sinks are proposed as the functions of Reynolds number, top-bypass ratio, and the side-bypass ratio. Besides, for further validation of the present theoretical results, a comparison between the present predictions with the experimental data was made with a reasonable agreement. The maximum and average deviations are 25.8% and 11.7%, respectively, for the pressure drop; and 14.3% and 6.1%, respectively, for the thermal resistance.
In addition, a systematical design optimization method, which allow the thermal engineer to meet several design objectives and constraints simultaneously and effectively, has been successfully presented and applied to the optimal designs for generalized heat sinks in this study. First of all, a statistical method for the sensitivity analysis is performed to determine the key factors that are critical to the design; and a response surface methodology (RSM) is applied to establish explicit regression models for the thermal resistance and the pressure drop in terms of the design factors with an well-organized design of experiments (DOE). By employing the gradient-based numerical optimization technique, a series of constrained optimal designs can be efficiently performed. Comparisons between these predicted optimal designs and those evaluated by the theoretical calculations are also made with satisfactory agreements. With the developed design optimization method, optimal designs for generalized heat sinks, includes the parallel-plate fin (ppf), pin-fin array (pfa), and strip-fin array (sfa), were successfully explored with multiple design constraints of pressure drop, mass, and space limitations.
Furthermore, an effective and user-friendly optimal computer-aided design (CAD) system for automatically predicting the optimal thermal performance for confined generalized heat sinks has been successfully developed. In the pre-processor, a user-friendly interface for problem definition has been constructed in order to efficiently collect the required data for the thermal analyzer and optimizer. And a thermal analyzer for confined heat sink has been successfully developed according to the present theoretical calculations. The performances studied include the pressure drop, local and average heat transfer coefficients, local temperature distribution, and the overall thermal resistance. Besides, corresponding to the presented design optimization method, the design optimizer has been established with the functions of the design of experiments, the construction of response surface models, and the programming of numerical optimization. After obtaining the optimal design, the real-time 3-D model, predicted color isotherms, and all the predicted performances can be displayed in the developed post-processor. Moreover, an interactive function has been applied for providing a direct communication between the user and the computer for the detailed information about the optimal design. Finally, to demonstrate the superiorities of the present developed optimal CAD system, two sample applications of thermal optimal designs for generalized heat sinks under multiple constraints have been effectively performed.

[1] Viswanath, R., Wakharkar, V., Watwe, A., and Lebonheur, V., 2000, " Thermal Performance Challenges from Silicon to Systems," Intel Technology Journal, Q3.
[2] Ellison, G. N., 1989, Thermal Computations for Electronic Equipment, 2nd Ed., Van Nostrand Reinhold Corporation, New York.
[3] Sparrow, E. M., and Grannis, V. B., 1990, “Pressure Drop Characteristics of Heat Exchangers Consisting of Arrays of Diamond-Shaped Pin Fins,” Int. J. Heat Transfer. Vol. 34, No. 3, pp. 589-600.
[4] Linton, R. L., and Agonafer, D., 1995, “Coarse and Detailed CFD Modeling of a Finned Heat Sink,”IEEE Trans., Comp., Packag., Manufact., Technol. A, Vol. 18, pp. 517-520.
[5] Mills, A. F., 1999, Basic Heat and Mass Transfer, Prentice-Hall, New Jersey.
[6] Ishizuka, M., Yokono, Y., and Hisano, K., 1999, "Experimental Study on the Performance of Compact Heat Sink for LSI Packages," Advances in Electronic Packaging, EEP-Vol. 26, pp. 713-718.
[7] Narasimhan, S., Bar-Cohen, A. and Nair, R., 2003, “Flow and Pressure Field Characteristics in the Porous Block Compact Modeling of Parallel Plate Heat Sinks,” IEEE Transactions on Components and Packaging Technologies, Vol. 26, No. 1, March.
[8] Jeng, T. M., Wang, M. P., and Hung, Y. H., 2003, “ Performance Prediction for Partially-Confined Heat Sinks,” 2003 Proceedings of INTERPACK, IPACK2003-35021, Maui, Hawaii, July 6-11.
[9] Wang, M. P., Wu, T. Y., Horng, J. T., and Hung, Y. H., 2005, “Fluid Flow Characteristics for Partially-Confined Compact Plain-Plate-Fin Heat Sinks,” 2005 ASME Proceedings of Heat Transfer, HT2005-72225, San Francisco, CA, July 17-22.
[10] Matsushima, H., Yanagida, T., and Kondo, Y., 1992, “Algorithm for Predicting the Thermal Resistance of Finned LSI Packages Mounted on a Circuit Board,” Heat Transfer Japanese Research, Vol. 21, No. 5, pp. 504-517.
[11] You, H. I., and Chang, C. H., 1997, “Numerical Prediction of Heat Transfer Coefficent for a Pin –Fin Channel Flow,” ASME J. Heat Transfer, Vol. 119, pp840-843.
[12] Sparrow, E. M., Baliga, B. R., Patankar, S. V., 1978, "Forced Convection Heat Transfer from a Shrouded Fin Array with and without Tip Clearance," ASME J. Heat Transfer, Vol. 100, pp. 572-579.
[13] Sparrow, E. M., and Kadle, D. S., 1986, “Effect of Tip-to-shroud Clearance on Turbulent Heat Transfer from a Shrouded, Longitudinal Fin Array,” ASME J. Heat Transfer. Vol. 108., pp.519-524.
[14] Wirtz, R. A., Chen, W. M., and Zhou, R. H., 1994, “Effect of Flow Bypass on the Performance of Longitudinal Fin Heat Sinks,” ASME J. Electronic Packaging, Vol. 116, pp. 206-211.
[15] Jonsson, H., and Moshfegh, B., 2001, “Modeling of the Thermal and Hydraulic Performance of Plate Fin, Strip Fin, and Pin Fin Heat Sinks—Influence of Flow Bypass, ” IEEE Transactions on Components and Packaging Technologies, Vol. 24, No. 2, June.
[16] Wu, T. Y., Wang, M. P., Horng, J. T., Chang, S. F., and Hung, Y. H., 2005, “Forced Convective Heat Transfer for Partially-Confined Compact PPF Heat Sinks with Top-Bypass Effect,” 2005 Proceedings of INTERPACK, IPACK2005-73121, San Francisco, CA, July 17-22.
[17] Vanderplaats, G. N., 1993, Numerical Optimization Techniques for Engineering Design, McGraw-Hill, Singapore.
[18] Wu, C. F., and Hamada, M., 2000, Experiments – Planning, Analysis, and Parameter Design Optimization, John Wiley & Sons, New York.
[19] Belegundu, A. D., and Chandrupatla, T. R., 1999, Optimization Concepts and Applications in Engineering, Prentice Hall, New Jersey.
[20] Lee, S., 1995, “Optimum Design and Selection of Heat Sinks,” 11th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, San Jose, California, Feb. 7-9, pp. 48-54.
[21] Constans, E. W., Belegundu, A. D., and Kulkarni, A. K., 1994, “Optimization of a Pin-Fin Sink: A Design Tool,” 1994 International Mechanical Engineering Congress and Exposition, Chicago, Illinois, Nov. 6-11, EEP-Vol.9, pp. 25-32.
[22] Azer, K., and Mandrone, C. D., 1994, “Effect of Pin Fin Density of the Thermal Performance of Unshrouded Pin Fin Heat Sinks,” ASME J. Electronic Packaging, Vol. 116, No. 4, pp. 306-309.
[23] Shaukatullah, H., Storr, W. R., Hansen, B. J., and Gaynes, M. A., 1996, “Design and Optimization of Pin Fin Heat Sinks for Low Velocity Applications,” 12th IEEE SEMI-THERM Symposium, pp. 151-163.
[24] Box, G. E. P., and Wilson, K. B., 1951, “On the Experimental Attainment of Optimum Conditions,” J. Royal Statistics Society, Series B, No. 13, pp. 1-45.
[25] Box, G. E. P., and Behnken, D. W., 1960, “Some New Three Level Designs for the Study of Quantitative Variables,” Technometrics, Vol. 2, pp.455-475.
[26] Box, G. E. P., and Draper, N. R., 1987, Empirical Model-Building and Response Surfaces, John Wiley & Sons, New York.
[27] Monthomery, D. C., 2001, Design and Analysis of Experiments, 5th Ed., John Wiley & Sons, New York.