本文以反算法及商業套裝軟體搭配實驗數據探討自然對流下板鰭式熱沉於封閉外殼內之散熱情形。本文反算法使用有限差分法配合最小平方法及實驗溫度數據估算鰭片上之熱傳係數。鰭片上熱傳係數可能為不均勻分佈，因此進行反算法前先將鰭片分割為數個小區域，並假設小區域上之熱傳係數為一未知常數，進而求得鰭片上溫度分布及平均熱傳係數，並與相關經驗公式比較。為了驗證本文結果之正確性及可靠性，本文再以商業套裝軟體配合適當流動模式、網格點數及實驗溫度數據求得鰭片上量測位置之溫度。所得結果將與本文反算結果相比較，並進一步分析封閉外殼內之空氣溫度與速度分佈情形。結果顯示，鰭片上之平均熱傳係數隨著鰭片間距及雷利數增加而增加，且隨鰭片高度增加而減少。流動模式及網格點數對所得結果之影響可能不容忽視。

The present study applies the inverse method and computational fluid dynamics commercial software with the experimental data to investigate the heat transfer characteristics of the heat sink in a closed enclosure. The inverse method with finite difference method in conjunction with the least squares scheme is used to determine the average heat transfer coefficient on the fin. Due to the non-uniform distribution of the heat transfer coefficient, the plate-fin is divided into several sub-fin regions before performing the inverse scheme. The average heat transfer coefficient on each sub-fin region is assumed to be unknown. The inverse method is then applied to obtain the temperature distribution and average heat transfer coefficient. The results will compare with the empirical correlation. The present study also applies commercial software with appropriate flow model and grid points and the experimental temperature data to obtain fin temperatures at measurement locations. The temperature and velocity distribution in the closed enclosure are obtained. The average heat transfer coefficient on the fins increases with increasing fin spacing or Rayleigh number, and decreases with increasing fin height. The effects of the flow model and grid points on the results can not be ignored.

[1] K. E. Starner, H. N. McManus, “An experimental investigation of free-convection heat transfer from rectangular fin arrays,” ASME J. Heat Transfer, vol. 85, pp. 273-278, 1963.
[2] F. Harahap, H. N. McManus JR., “Natural convection heat transfer from horizontal rectangular fin arrays,” ASME J. Heat Transfer, vol. 89, pp. 32-38, 1967.
[3] F. Harahap, D. Setio, “Correlations for heat dissipation and natural convection heat-transfer from horizontally-based, vertically-finned arrays,” Appl. Energy, vol. 69, pp. 29-38, 2001.
[4] F. Harahap, E. Rudianto, I. G. D. M. E. Pradnyana, “Measurements of steady-state heat dissipation from miniaturized horizontally-based straight rectangular fin arrays,” Heat Mass Transfer, vol. 41, pp. 280-288, 2005.
[5] F. Harahap, H. Lesmana, I. K. T. Arya Sume Dirgayasa, “Measurements of heat dissipation from miniaturized vertical rectangular fin arrays under dominant natural convection conditions,” Heat Mass Transfer, vol. 42, pp. 1025-1036, 2006.
[6] Ilker Tari, Mehdi Mehrtash, “Natural convection heat transfer from inclined plate-fin heat sinks,” Int. J. Heat Mass Transfer, vol. 56, pp. 574-593, 2013.
[7] N. C. Markatos, K. A. Pericleous, “Laminar and turbulent natural convection in an enclosed cavity,” Int. J. Heat Mass Transfer, vol. 27, pp. 755-772, 1984.
[8] Y. Le Peutrec, G. Lauriat, “Effects of the heat transfer at the side walls on natural convection in cavities,” ASME J. Heat Transfer, vol. 112, pp. 370-378, 1990.
[9] T. Fusegi, J. M. Hyun, K. Kuwahara, B. Farouk, “A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure,” Int. J. Heat Mass Transfer, vol. 34, pp. 1543-1557, 1991.
[10] S. A. Nada, “Natural convection heat transfer in horizontal and vertical closed narrow enclosures with heated narrow enclosures with heated rectangular finned base plate,” Int. J. Heat Mass Transfer, vol. 50, pp. 667-679, 2007.
[11] C. W. Leung, S. D. Probert, M. J. Shilston, “Heat exchanger design: optimum uniform separation between rectangular fins protruding from a vertical rectangular base,” Applied Energy, vol. 19, pp. 287-299, 1985.
[12] S. M. Elsherbiny, E. H. Ragab, “Laminar natural convection in inclined rectangular cavities with a localized heat source,” Alexandria Engineering Journal, vol. 52, pp. 249-257, 2013.
[13] E. Yu, Y. Joshi, “Heat transfer enhancement from enclosed discrete components using pin-fin heat sinks,” Int. J. Heat Mass Transfer, vol. 45, pp. 4957-4966, 2002.
[14] E. Arquis, M. Rady, “Study of natural convection heat transfer in a finned horizontal fluid layer,” Int. J. Thermal Science, vol. 44, pp. 43-52, 2005.
[15] M. Hasnaoui, P. Vasseur, E. Bilgen, “Natural convection in rectangular enclosures with adiabatic fins attached on the heated wall,” Wärme- und Stoffübertragung, vol. 27, pp. 357-368, 1992.
[16] J. V. Beck, “Calculation of surface heat flux from an integral temperature history,” ASME J. Heat Transfer, vol. 62, pp. 46-51, 1962.
[17] J. V. Beck, “Surface heat flux determination using an integral method,” Nuclear Engineering Design, vol. 7, pp. 170-178, 1968.
[18] J. V. Beck, B. Litkouhi, C. R. Stclair, “Efficient numerical-solution of nonlinear inverse heat-conduction problem,” Mech. Eng., vol. 102, pp. 96-96, 1980.
[19] E. M. Sparrow, A. Haji-Sheikh and T. S. Lundgern, “The inverse problem in transient heat conduction,” J. Appl. Mech., vol. 86, pp. 369-375, 1964.
[20] N. M. Alnajem, M. N. Özisik, “A direct analytical approach for solving linear inverse heat conduction problems,” ASME J. Heat Transfer, vol. 107, pp. 700-703, 1985.
[21] S. Sunil, J. R. N. Reddy, C. B. Sobhan, “Natural convection heat transfer from a thin rectangular fin with a line source at the base – a finite difference solution,” Int. J. Heat Mass Transfer, vol. 31, pp. 127-135, 1996.
[22] E. Velayati, M. Yaghoubi, “Numerical study of convection heat transfer from an array of parallel bluff plates,” Int. J. Heat Fluid Flow, vol. 26, pp. 80-91, 2005.
[23] H. T. Chen, J. P. Song, Y. T. Wang, “Prediction of heat transfer coefficient on the fin inside one-tube plate finned-tube heat exchangers,” Int. J. Heat Mass Transfer, vol. 48, pp. 2697-2707, 2005.
[24] H. T. Chen, J. C. Chou, “Investigation of natural-convection heat transfer coefficient from the vertical fin of finned-tube heat exchangers,” Int. J. Heat Mass Transfer, vol. 49, pp. 3034-3044, 1993.
[25] H. T. Chen, W. L. Hsu, “Estimation of heat transfer coefficient on the fin of annular finned-tube heat exchangers in natural convection for various fin spacings,” Int. J. Heat Mass Transfer, vol. 50, pp. 1750-1761, 2007.
[26] V. S. Arpaci, “Introduction to Heat Transfer,” Prentice Hall, New Jersey, pp. 580, 1999.
[27] A. Bejan, “Heat Transfer,” John Wiley & Sons, Inc., New York, pp. 53-62, 1993.
[28] C. D. Jones, L. F. Smith, “Optimum arrangement of rectangular fins on horizontal surfaces for free-convection heat transfer,”ASME J. Heat Transfer, pp. 6-10, 1970.
[29] F. E. M. Saboya, E. M. Sparrow, “Local and average heat transfer coefficients for one-row plate fin and tube heat exchanger configurations,” ASME J. Heat Transfer, vol. 96, pp. 265-272, 1974.
[30] H. G. Yalcin, S. Baskaya, M. Sivrioglu, “Numerical analysis of natural convection heat transfer from rectangular shrouded fin arrays on a horizontal surface,” Int. Comm. Heat Mass Transfer, vol. 35, pp. 299-311, 2008.
[31] FLUENT Dynamic software, FLUENT, Lehanon, NH, 2010.
[32] V. Yakhot, S. A. Orszag, S. Thangam, T. B. Gatski, C. G. Speziale, “Development of turbulence models for shear flows by a double expansion technique,” Physics of Fluids A, vol. 4, pp. 1510-1520, 1992.
[33] Han-Taw Chen, Chung-Hou Lai, Tzu-Hsiang Lin, Ge-Jang He, “Estimation of natural convection heat transfer from plate-fin heat sinks in a closed enclosure,” International Conference on Mechanical, Aeronautical and Manufacturing Engineering, 2014.
[34] C. Min, C. Qi, X. Kong, J. Dong, “Experimental study of rectangular channel with modified rectangular longitudinal vortex generators,” Int. J. Heat Mass Transfer, vol. 53, pp. 3023-3029, 2010.
[35] B. T. Van Lear, E. M. Sparrow, “Enhancement of natural convection fins by high-frequency forced oscillations,” Int. J. Heat Mass Transfer, vol. 53, pp. 1570-1574, 2010.
[36] 陳韋志，預測傾斜矩形平板上之自然對流熱傳特性，國立成功大學機械工程學系，碩士論文，2009。
[37] 賴詩婷，矩行鰭片陣列於具開孔矩形外殼內之熱傳特性研究，國立成功大學機械工程學系，碩士論文，2012。
[38] 曾鈴如，矩行鰭片陣列於不同矩形外殼內之熱傳特性的實驗與數值研究，國立成功大學機械工程學系，碩士論文，2013。
[39] B. E. Launder, D. B. Spalding, “The numerical computation of turbulent flows”, Computer Methods in Applied Mechanics and Engineering, vol. 3, pp. 269-289, 1972.