本文主要是以有限差分法（Finite difference method）的數值方法，並配合最小平方法（Least-squares scheme）及溫度量測值來預測板鰭管式熱交換器之矩形垂直鰭片上的平均熱傳係數（Average heat transfer coefficient）和鰭片效率（Fin efficiency）。從先前的研究可以發現鰭片上的熱傳係數是非常不均勻的。為了利用鰭片上的溫度實驗値來預測鰭片上的熱傳係數及鰭片效率，因此將鰭片分割成數個小區塊。本文將以自行設計的板鰭管式蒸發器之鰭片組並配合相關實驗設備以量取於穩態下之鰭片溫度與管壁溫度。根據這些數據，再配合數值反算法來估算鰭片上之熱傳係數。結果顯示，於混合對流（Mixed convection）之環境下，迎風面的熱傳係數會大於背風面的熱傳係數，於自然對流（Free convection）之環境下，若鰭片間距（Fin spacing）大於0.002m時，鰭片上之平均熱傳係數將會漸趨近於一固定值。所估算之平均熱傳係數與一般熱傳課本內之經驗公式相比較，以驗證本文反算方法之準確性及先前經驗公式之合理性。

　The present study applies the finite difference method in conjunction with the least-squares scheme and the experimental temperature data to predict the average convection heat transfer coefficient and the fin efficiency on the rectangular vertical fin of one-tube plate finned-tube heat exchangers. The heat transfer coefficient on this rectangular fin is very non-uniform. Thus the whole plate fin is divided into several sub-fin regions in order to predict the average heat transfer coefficient and the fin efficiency on the fin from the knowledge of the experimental fin temperature. A plate finned-tube evaporator and some relative experimental equipments and set up in order to measure the fin temperature. The heat transfer coefficient can be predicted by using the present inverse scheme according to the temperature measurements on the fin. The results show that the heat transfer coefficient on the upstream region of the fin can be markedly higher than that on the downstream region in mixed convection. However, the average heat transfer coefficient will approach a fixed value under the free convection provided the fin spacing is larger than 0.002m. In order to evidence the accuracy of the present inverse scheme and the reliability of the some experimental formulas, a comparison of the average heat transfer coefficient between the present predicated results and the previous results in Heat Transfer Textbook is made.

[1] T.V. Jones, C.M.B. Russell, “Efficiency of rectangular fins,” ASME/AIChE National Heat Transfer Conference, Orlando, Florida, pp. 27-30, 1980.

[2] F.E.M. Saboya, E.M. Sparrow, “Local and average heat transfer coefficients for one-row plate fin and tube heat exchanger configurations,” ASME Journal of Heat Transfer Vol.96, pp.265-272, 1974.

[3] E.C. Rosman, P. Carajilescov, F.E.M. Saboya, “Performance of one- and two-row tube and plate fin heat exchangers,” ASME Journal of Heat Transfer Vol.106, pp.627-632, 1984.

[4] H. Ay, J.Y. Jang, J.N. Yeh, “Local heat transfer measurements of plate finned-tube heat exchangers by infrared thermography,” International Journal of Heat and Mass Transfer Vol.45, pp.4069-4078, 2002.

[5] R.L. Webb, “Principles of Enhanced Heat Transfer,” Wiley, New York, pp.125-153, 1994.

[6] M.N. Özisik, “Heat Conduction,” second ed., Wiley, New York, Chapter 14, 1993.

[7] K. Kurpisz, A.J. Nowak, “Inverse Thermal Problems,” Computational Mechanics Publications, Southampton, UK, 1995.

[8] D. Maillet, A. Degiovanni, R. Pasquetti, “Inverse heat conduction applied to the measurement of heat transfer coefficient on a cylinder: Comparison between an analytical and a boundary element technique,” ASME Journal of Heat Transfer Vol.113, pp.549-557, 1991.

[9] J.H Lin, C.K. Chen, Y.T. Yang, “An inverse estimation of the thermal boundary behavior of a heated cylinder normal to a laminar air stream,” International Journal of Heat and Mass Transfer Vol.43, pp. 3991-4001, 2000.

[10] J.H. Lin, C.K. Chen, Y.T. Yang, “An inverse method for simultaneous estimation of the center and surface thermal behavior of a heated cylinder normal to a turbulent air stream,” ASME Journal of Heat Transfer Vol.124, pp.601-608, 2000.

[11] C.H. Huang, I.C. Yuan, H. Ay, “A three-dimensional inverse problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers,” International Journal of Heat and Mass Transfer Vol.46, pp. 3629-3638, 2003.

[12] D.R. Haper, W.B. Brown, “Mathematical Equations for Heat Conduction in the Fins of Air cooled Engines,” N. A. C. A. Rept, pp.158, 1922.

[13] K.A. Gardner, “Efficiency of Extend Surface,” Teans. ASME, Vol. 67, pp.621-631, 1945.

[14] T.E. Schmidt, “Heat transfer calculations for extended surfaces,” Refrigerating Engineering, pp.351-357, 1949.

[15] H. Zabronsky, “Efficiency of a Heat Exchanger Using Square Fins on Round Tubes,” Carbide and Carbon Chemical Company, K-25 Plant Oak Ridge, Tennessee. August 15, 1952.

[16] W. Elenbaas, “Heat Dissipation of Parallel Plates by Free Convection,” Physica, Vol.IX, No.1, pp.2-28, 1942.

[17] E.M. Sparrow, P.A. Bahrani, “Experiments on Natural Convection from Vertical Parallel Plates with Either Open or Closed Edges,” ASME J. Heat Transfer, Vol.102, pp.221-227, 1980.

[18] L. Buzzoni, R. Dall’Olio, M. Spiga, “Efficiency of the Unit Cell in Rectangular Finned Tube Arrangement,” Applied Thermal Engineering, Vol.19, Issue11, pp.1147-1156, 1999.

[19] 許永毅, “根據實驗數據預測結霜時雙管型板鰭管式熱交換器之鰭片上熱傳遞係數,” 成功大學機械工程研究所碩士論文, 2002.

[20] 吳國文, “利用逆算法配合實驗數據預測橢圓鰭管式熱交換器之鰭片於結霜狀態下的熱傳遞係數,” 成功大學機械工程研究所碩士論文, 2003.

[21] 王益彤, “利用逆算法配合實驗數據預測單橢圓管式之管鰭片蒸發器於結霜狀態下之熱傳遞係數,” 成功大學機械工程研究所碩士論文, 2004.

[22] 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 and Mass Transfer, Vol.48, pp.2697-2707, 2005.

[23] F. Kreith, M.S. Bohn, “Principles of Heat Transfer,” fifth ed, West Publishing Company, Chapter5, pp.347-348, 1993.

[24] V.S. Arpaci, S.H. Kao, A. Selamet, “Introduction to Heat Transfer,” Prentice-Hall, pp.588, 1999.

[25] W.M. Rohsenow, J.P. Hartnett, E.N. Ganic, “Handbook of Heat Transfer Fundamentals,” second ed., McGraw-Hill Book Company, Chapter6, 1985.

[26] A. Bejan, “Heat Transfer,” John Wiley & Sons, Inc., New York, pp. 53-62, 1993.

[27] F.P. Incropera, D.P. Dewitt, “Introduction to Heat Transfer,” third ed., John Wiley & Sons, table1.1 pp.8, 1996.