本文將矩形鰭片置於水平或垂直加熱板上，而後再將其放置於封閉或具有孔洞之矩形外殼內。本文以有限差分法(Finite difference method)配合最小平方法(Least squares scheme)及實驗溫度量測數據來估算於自然對流環境下之矩形鰭片(Rectangular fin)於等溫條件下之平均熱傳係數(Average heat transfer coefficient)、總熱傳量(Total heat transfer rate)以及鰭片效率(Fin efficiency)。為了欲求得本文之預測值，故將鰭片分割成數個小區域進行逆算分析。於進行逆算之前，先假設每個小區域之熱傳係數為常數，而後再應用本文之逆算法求得本文之預測值。文中並探討鰭片高度及鰭片間距對熱傳特性之預測值的影響。研究結果顯示，在封閉矩形外殼內，矩形鰭片不論在水平或垂直加熱板上，平均熱傳係數會隨著鰭片間距增加而提高，但卻隨鰭片高度增加而減小，而鰭片效率則隨著鰭片間距的增加而減少。若鰭片置於具有孔洞的外殼內，因為煙囪效應(Chimney effect)的使用會增加自然對流效果，因而使得鰭片上之平均熱傳係數及總散熱量皆因而提高。為了驗證本文逆算法之可靠性，本文所估算出於等溫條件下之平均熱傳係數也與課本或其他相關文獻之經驗公式相比較。

The present study applies an inverse method involving the finite difference method in conjunction with the least-squares scheme and experimental temperature measurements to estimate the unknown natural-convection heat transfer coefficient, heat transfer coefficient under the isothermal condition, heat transfer rate and fin efficiency on a rectangular fin mounted on vertical or horizontal plate in closed or open rectangular enclosures. To obtain the present estimates, the whole plate fin is divided into several analytic sub-fin regions before performing the inverse calculation. The heat transfer coefficient on each analytical sub-fin region is assumed as a constant. Later, the present estimates can be obtained using the present inverse scheme. The results show that the average heat transfer coefficient increases with increasing the fin spacing and decreases with increasing the fin height. The fin efficiency decreases with increasing the fin spacing. In the open rectangular enclosure, the chimney effect enhance the natural convection. Thus, the heat transfer coefficient and heat transfer rate are higher than those obtained from the closed rectangular enclosure. In order to evidence the accuracy of the present inverse scheme, the present estimates of the average heat transfer coefficient under the isothermal condition compared with those obtained from the correlation recommended by current textbook and other previous results.

[1]W. Elenbass, “Heat Dissipation of Parallel Plates by Free Convection,” Physica, vol. 9, pp. 2-28, 1942.
[2]E. M. Sparrow, P. A. Bahrami, “Experiments on Natural Convection from Vertical Parallel Plates with Either Open or closed Edges,” ASME J. Heat Transfer, vol. 102, pp.221-227, 1980.
[3]J. R. Bodoia, J. F. Osterle, “The Development of Free Convection Between Heated Vertical Plates,” ASME J. Heat Transfer, vol. 84, pp. 40-44, 1962.
[4]S. Ostrach, “Laminar Natural-Convection Flow and Heat Transfer of Fluids With and Without Heat Sources in Channels With Constant Wall Temperatures,” NACA Tech. Note 2863, 1952.
[5]A. de Lieto Vollaro, S. Grignaffi, F. Gugliermetti, “Opitimum Design of Vertical Rectangular Fin Arrays,” Int. J. Therm. Sci., vol. 38, pp.525-529, 1999.
[6]S. Baskaya, M. Sivirioglu, M. Ozek, “Parametric Study of Natural Convection Heat Transfer from Horizontal Rectangular Fin Arrays,” Int. J. Therm. Sci., vol. 39, pp.797-805, 2000.
[7]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.
[8]F. Harahap, D. Setio, “Correlations for Heat Dissipation and Natural Convection Heat-Transfer from Horinzontally-Based, Vertically-Finned Arrays,” Appl. Energy, vol. 69, pp. 29-38, 2001.
[9]F. Harahap, E. Rudianto, I. G. D. M. E. Pradnyana, “Measurements of Steady-State Heat Dissipation from Horizontally-Based Straight Rectangular Fin Arrays,” Heat Mass Transfer, vol. 41, pp. 280-288, 2005.
[10]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.
[11]A. Güvenç, H. Yüncü, “An Experimental Investigation on Performance of Fins on Horizontal Base in Free Convection Heat Transfer,” Heat Mass Transfer, vol. 37, pp.409-416, 2001.
[12]M. Hasnaoui, P. Vasseur, E. Bilgen, “Natural Convection in Rectangular Enclosures with Adiabatic Fins Attached on the Heated Wall,” Wärme- and Stoffübertragung, vol. 27, pp.357-368, 1992.
[13]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.
[14]E. Yu, Y. K. Joshi, “Heat Transfer in Discretely Heated Side Vented Compact Enclosures by Combined Conduction, Natural Convection, and Radiation,” ASME J. Heat Transfer, vol. 121 pp.1002-1010, 1999.
[15]T. S. Fisher, K. E. Torrance, “Free Convection Limits for Pin-Fin Cooling,” ASME J. Heat Transfer, vol. 120, pp.633-640, 1998.
[16]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.
[17]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.
[18]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.
[19]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.
[20]J. V. Beck, “Calculation of Surface Heat Flux from an Integral Temperature History,” ASME J. Heat Transfer, vol. 62, pp. 46-51, 1962.
[21]J. V. Beck, “Surface Heat Flux Determination Using an Integral Method,” Nucl. Eng. Des., vol. 7, pp. 170-178, 1968.
[22]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.
[23]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,” Heat and Mass Transfer, vol. 31, pp. 127-135, 1996.
[24]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.
[25]V. S. Arpaci, “Introduction to Heat Transfer,” Prentice Hall, New Jersey, pp. 580, 1999.
[26]A. Bejan, “Heat Transfer,” John Wiley & Sons, Inc., New York, pp. 53-62, 1993.
[27]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.
[28]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.
[29]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.
[30]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.
[31]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.
[32]G. D. Raithby, K. G. T. Hollands,“Natural Convection,”Handbook of Heat Transfer Fundamentals, 2nd ed., W. M. Rohsenow , J. P. Hartnett and E. N. Ganic, eds, McGraw-Hill, New York, 1985.
[33]劉立熙，根據實驗溫度量測值估算矩形鰭片上之熱傳特性，國立成功大學機械工程學系，碩士論文，2007。
[34]徐國軒，以逆算法估算自然對流下之垂直矩形鰭片上的熱傳特性，國立成功大學機械工程學系，碩士論文，2008。
[35]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。
[36]劉永智，以逆算法和實驗溫度量測估算CPU上之散熱鰭片的熱傳係數，國立成功大學機械工程學系，碩士論文，2006。
[37]F. Kreith, M. S. Bohn, “Principles of Heat Transfer,” 5th ed., West Publishing Company, Chap. 5, pp. 349-350, 1993.
[38]C. W. Leung, S. D. Probert, “Heat Exchanger Performance: Effect of Orientation,” Appl. Energy, vol. 33, pp.235-252, 1989.
[39]C. W. Leung, S. D. Probert, “Thermal Effectiveness of Short-Protrusion Rectangular Heat Exchanger Fins,” Appl. Energy, vol.34, pp.1-8, 1989.