本文乃以有限差分法（Finite difference method）及拉氏轉換法(Laplace transform method)之混合數值方法，並配合最小平方法(Least-squares method)及溫度量測值來預測板鰭管式熱交換器之鰭片上的暫態平均熱傳係數（Transient average heat transfer coefficient）、暫態熱傳量（Transient heat flux）以及暫態鰭片效率（Transient fin efficiency）。
從先前的研究可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暫態平均熱傳係數、暫態熱傳量及暫態鰭片效率，因此將鰭片分割成數個小分析區域。本文先以模擬問題來驗證本文逆算法的精確性，而後再以所量得之板鰭管式熱交換器之鰭片上的實驗溫度數據來估算鰭片上之暫態熱傳特性。結果顯示，暫態熱傳特性將會隨著時間增加而慢慢地趨向於其所對應之穩定值。因此本文之預估值具有良好的可靠性及正確性。

The present study applies the finite difference method in conjunction with the Laplace transform method, the least-squares method and the experimental temperature data to predict the transient average heat transfer coefficient, transient heat flux and transient fin efficiency on the rectangular vertical fin of one-tube plate finned-tube heat exchangers.
It can be found from the previous study that the heat transfer coefficient on the rectangular fin is very non-uniform. Thus the whole plate fin is divided into several sub-fin regions in order to predict the transient average heat transfer coefficient, transient heat flux and transient fin efficiency on the fin from the knowledge of the experimental fin temperature. In order to validate the accuracy of the present inverse scheme, the present study will simulate this problem. The transient heat-transfer characteristics on the rectangular vertical fin of one-tube plate finned-tube heat exchangers can be predicted using the present inverse scheme in conjunction with the experimental measured temperatures. The results show that the transient heat-transfer characteristics will increase with time and slowly approach its corresponding steady state values. Thus it shows that the estimated results of the present inverse scheme have good reliability and accuracy.

[1] A.D. Kraus, A. Aziz, and J. Welty, “Extended Surface Heat Transfer,” John Wiley and Sons, Inc., 2001.

[2] J.L. Lage, “Tube-to-tube heat transfer degradation effect on finned-tube heat exchangers,” Numerical Heat Transfer Part A, Vol. 39, pp. 321-337, 2001.

[3] G.D. Raithby and K.G.T. Hollands, “Natural Convection,” in Handbook of Heat Transfer Fundamentals, 2nd ed., W.M. Rohsenow, J.P. Hartnett and E.N. Ganic, eds, McGraw-Hill, New York, 1985.

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

[5] 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.

[6] 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.

[7] 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. of Heat and Mass Transfer Vol. 50(2007) 1750-1761.

[8] H.T. Chen, J.C. Chou, H.C. Wang, “Estimation of heat transfer coefficient on the vertical plate fin of finned-tube heat exchangers for various air speeds and fin spacings,” Int. J. of Heat and Mass Transfer Vol. 50(2007) 45-57.

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

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

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

[12] D. Maillet and 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.

[13] J.H. Lin, C.K. Chen, and 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.

[14] C.H. Huang, I.C. Yuan and 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.

[15] 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.

[16] H. Ay, J.Y. Jang and 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.

[17] J. Taler, Poland, Wärme- und Stoffübertragung 23,283-289 (1988).

[18] W. B. Bloem, Ijmuiden, The Netherlands, R. J. van der Linden, C. J. Hoogendoorn, and H. Postma, Delft, The Netherlands, Wärme- und Stoffübertragung 22, 315-323 (1988).

[19] G.R. Warrier, L.C. Witte, “On the application of the hyperbolic heat equation in transient heat flux estimation during flow film boiling, ” Numerical Heat Transfer , Part A, 35:343-359, 1999.

[20] A. Trombe, A. Suleiman, Y. Le Maoult,“Use of an inverse method to determine natural convection heat transfer coefficients in unsteady state, ” Journal of Heat Transfer, DECEMBER 2003, Vol. 125 / 1017.

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

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