本文以有限差分法、最小平方法之逆算法搭配實驗溫度量測值，藉由改變加熱板位置、矩形外殼之孔洞位置來探討多個加熱板及板型鰭片置放於矩形外殼內的板鰭式熱交換器之熱傳特性與流動特性。由於鰭片上的熱傳係數並非均勻分佈，故將鰭片劃分成數個子區域，再將熱電偶安裝於子區域上以量測不同條件下的子區域溫度，最後反算鰭片之熱傳係數。本文亦使用商用軟體ANSYS進行數值模擬求得於外殼內之速度分佈與空氣溫度以及鰭片表面之溫度與平均熱傳係數。為了求得本研究較正確之熱傳及流體流動特性，探討不同流動模式與網格劃分對於不同物理模型的適用度，再與本文逆運算法所得之逆算值做比較。
結果顯示，流動模式及網格點數目對結果之影響甚大，實驗方面隨著矩形外殼孔洞位置及加熱板擺放位置的變化，空氣流動會有所不同。同時，不同加熱板位置的擺放，會有對應之矩形外殼孔洞位置，以達到增加自然對流的效果，而鰭片上之平均熱傳係數也會隨之增加。但若矩形外殼之上壁面有孔洞，不論加熱板的擺放位置均能大幅的降低空氣溫度並增加鰭片之平均熱傳係數及散熱量。為了驗證本文逆算結果之可靠性及可用性，所求得熱傳係數及散熱量之逆算結果將與先前結果或其他相關文獻之經驗公式相比較。

The present study applies the inverse method to predict the heat transfer and fluid characteristics of plate-finned heat exchanger. By changing the position of the heaters and the holes of the rectangular enclosure to find out transfer characteristics and flow characteristics of the system. Since the heat transfer coefficient on the fin is not uniformly distributed, the fin is divided into several sub-regions, and then thermocouples are installed on the sub-regions to measure the temperature of the sub-regions under different conditions, and finally the heat transfer coefficient of the fin is inverted. The study also uses commercial software ANSYS to perform numerical simulation to obtain the velocity and air temperature distribution in the enclosure, as well as the average temperature and heat transfer coefficient of the fin surface. In order to obtain more accurate heat transfer and fluid flow characteristics, the applicability of different flow models and meshing to different physical models is discussed, and then compared with the inverse method values .
The results show that the flow models and the number of grid points have a great influence on the results. In the experiment, the air flow will be different with the changes in the position of the rectangular enclosure and the placement of the heaters. At the same time, the distance between heaters and the center of bottom wall will have corresponding perforated positions to achieve the effect of increasing natural convection, and the average heat transfer coefficient on the fin will increase accordingly. However, if there are holes on the upper wall, regardless of the placement of the heaters, the air temperature can be greatly decreased, and the average heat transfer coefficient and heat dissipation of the fin can be increased. In order to verify the reliability and usability of the inverse calculation results in the study, the inverse method results of the heat transfer coefficient and heat dissipation will be compared with previous results or empirical formulas in other relevant documents.

[1] E. Bilgen, Natural convection in cavities with a thin fin on the hot wall, International Journal of Heat and Mass Transfer, vol. 48 (2005), pp. 3493-3505
[2] F. Xu, J.C. Patterson, C. Lei, An experimental study of the unsteady thermal flow around a thin fin on a sidewall of a differentially heated cavity, Int. J. Heat Fluid Flow, vol. 29 (2008), pp. 1139-1153
[3] F. Xu, J.C. Patterson, C. Lei, Transition to a periodic flow induced by a thin fin on the sidewall of a differentially heated cavity, Int. J. Heat Mass Transfer, vol. 52 (2009), pp. 620-628
[4] F. Xu, J.C. Patterson, C. Lei, Transient natural convection flows around a thin fin on the sidewall of a differentially heated cavity, J. Fluid Mech., vol. 639 (2009), pp. 261-290
[5] H. Ay, J. 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 (2002), pp. 4069-4078
[6] Hewitt, F. Groffrey, Heat Exchanger Design Handbook, Begell House, Inc., 1998, p. 3340
[7] S. Nada, "Natural convection heat transfer in horizontal and vertical closed narrow enclosures with heated rectangular finned base plate," International Journal of Heat and Mass Transfer, vol. 50 (2007), pp. 667-679
[8] F. Harahap, E. Rudianto, I. M. E. Pradnyana, "Measurements of steady-state heat dissipation from miniaturized horizontally-based straight rectangular fin arrays," International Journal of Heat and Mass Transfer, vol. 41 (2005), pp. 280-288
[9] S.C. Leung, S. Probert, M. Shilston, "Heat exchanger design: optimal uniform separation between rectangular fins protruding from a vertical rectangular base," Applied Energy, vol. 19 (1985), pp. 287-299
[10] T.S. Fisher, K.E. Torrance, Free convection limits for pin-fin cooling, ASME J. Heat Transfer, vol.120 (1998), pp. 699-640
[11] E. Yu, Y. Joshi, Heat transfer enhancement from enclosed discrete components using pin-fin heat sinks, International Journal of Heat and Mass Transfer, vol. 45 (2002), pp. 4957-4966
[12] A. Kumar, J. B. Joshi, A. K. Nayak, P. K. Vijayan, "3D CFD simulations of air cooled condenser-II: Natural draft around a single finned tube kept in a small chimney," International Journal of Heat and Mass Transfer, vol. 92 (2016), pp. 507-522
[13] A. Elatar, M. A. Teamah, M. A. Hassab, "Numerical study of laminar natural convection inside square enclosure with single horizontal fin," International Journal of Thermal Sciences, vol. 99 (2016), pp. 41-51
[14] S. Baskaya, M. Sivrioglu, M. Ozek, "Parametric study of natural convection heat transfer from horizontal rectangular fin arrays," International Journal of Thermal Sciences, vol. 39 (2000), pp. 797-805
[15] R.A. Wirtz, Effect of flow bypass on the performance of longitudinal fin heat sinks, ASME Journal of Electronic Packaging 116 (1994) pp. 206-212
[16] E.A.M. Elshafei, Effect of flow bypass on the performance of a shrouded longitudinal fin array, Applied Thermal Engineering (2007) pp. 2233-2242
[17] S. Acharya, S.V. Patankar, Laminar mixed convection in a shrouded fin array, ASME. J. Heat Transfer, vol. 103 (1981), pp. 559-565
[18] J.V. Beck, Calculation of surface heat flux from an integral temperature history, ASME J. Heat Transfer, vol. 62 (1962), pp. 46-51
[19] J.V. Beck, Surface heat flux determination using an integral method, Nuclear Engineering Design, vol. 7 (1968), pp. 170-178
[20] E. Sparrow, A. Haji-Sheikh, and T. Lundgren, "The inverse problem in transient heat conduction," Journal of Applied Mechanics, vol. 31 (1964), pp. 369-375
[21] N. Ainajem, M. Ozisik, "A direct analytical approach for solving linear inverse heat conduction problems," ASME Transactions Journal of Heat Transfer, vol. 107 (1985), pp. 700-706
[22] J. V. Beck, B. Litkouhi, C. S. Clair Jr, "Efficient sequential solution of the nonlinear inverse heat conduction problem," Numerical Heat Transfer, Part A Applications, vol. 5 (1982), pp. 275-286
[23] S. Sunli, 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, International Journal of Heat and Mass Transfer, vol. 31 (1996), pp. 127-135
[24] Piotr Duda, Konieczny, Solution of an inverse transient heat conduction problem in a part of a complex domain, International Journal of Heat and Mass Transfer vol. 127 (2018), pp. 821-832
[25] H.T. Chen, S.T. Lai, L.Y. Huang, Investigation of heat transfer characteristics in plate-fin sinks, International Journal of Heat Mass Transfer vol. 50 (2013), pp. 352-360
[26] H.T. Chen, H.C. Tseng, S.W. Jhu, J.R. Chang, Numerical and experimental study of mixed convection heat transfer and fluid flow characteristics of plate-fin sinks , International Journal of Heat Mass Transfer vol. 111 (2017), pp. 1050-1062
[27] M.N. Özişik, H.R.B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor & Francis, New York, (2000)
[28] A.N. Tikhonov, V.Y. Arsenin, Solution of Ill-posed Problems, V.H. Winston & Sons, Washington, DC, (1977)
[29] O.M. Alifanov, Inverse Heat Transfer Problem, Springer-Verlag, Berlin, (1994)
[30] J.V. Beck, B. Blackwell, C.R. St. Clair, Inverse Heat Conduction: Ill-Posed Problems, Wiley Interscience, New York, (1985)
[31] V.S Arpaci, Introduction to Heat Transfer, Prentice Hall, New Jersey, (1999), p. 580
[32] A. BeJan, Heat Transfer, John Wiley & Sons, Inc., New York, (1993), pp. 53-62
[33] C.D. Jones, L.F. Smith, Optimum arrangement of rectangular fins on horizontal surfaces for free-convection heat transfer, ASME J. Heat Transfer, (1970), pp. 6-10
[34] F.E.M. Saboya, E.M. Sparrow, Local and average heat transfer coefficient for one-row plate fin and tube heat exchanger configurations, ASME J. Heat Transfer, vol. 96 (1974), pp. 265-272
[35] Q. Chen, W. Xu, A zero-equation turbulence model for indoor airflow simulation, Energy and Buildings, vol. 28 (1998), pp. 137-144
[36] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flows, Computer Methods in Applied Mechanics Eng., vol. 3(1974), pp. 269-289
[37] 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 Fluid A, vol. 4(1992), pp. 1510-1520
[38] 賴詩婷，矩形鰭片陣列於具開孔矩形外殼內之熱傳特性研究，碩士論文，國立成功大學機械工程學系，2012
[39] 曾鈴如，矩形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，碩士論文，國立成功大學機械工程學系，2013
[40] 林子祥，預測板鰭式熱沉於各種矩形外殼內之熱傳特性，碩士論文，國立成功大學機械工程學系，2015
[41] 朱釋唯，矩形鰭片置於具兩開孔之矩形外殼內之自然對流熱傳特性研究，碩士論文，國立成功大學機械工程學系，2017