本文使用逆算法以及商用計算流體力學軟體搭配實驗方式量測溫度來探討並列式板鰭管熱交換器之熱傳特性及流體流動性質，並探討鰭片間距、熱交換器鰭片放置於不同高度位置對所得結果之影響。由於先前研究發現鰭片上熱傳係數分布不均，故將鰭片分割成數個子區域，再以實驗設備量測溫度結合有限差分法、最小平方法之逆算法估算鰭片上平均熱傳係數。商用計算流體力學軟體配合適當流動模式和網格數目求解鰭片上對應之量測點溫度以及鰭片平均熱傳係數，其數值盡可能近似實驗溫度量測值及逆算法估算值，結果顯示在自然對流與混合對流中，Zero equation模式所求得結果皆較為準確。本文結果對於不同高度位置，會因為煙囪效應使得高度越高越靠近上開口，其平均熱傳係數隨之降低；而鰭片間距變大，平均熱傳係數會有上升之趨勢。

The present study applies the inverse method and CFD software Icepak in conjunction with the experimental method to predict the heat characteristics of plate-fin and tube heat exchangers. The effects of parameters such as fin pitch and tube location are examined. Since the heat transfer coefficient on the fin is not uniform, the fin is divided into several sub-regions and the heat transfer coefficient in each sub-regions is assumed to be a constant. Later, the inverse method applies finite difference method in conjunction with the least-squares scheme and the experimental data to estimate the heat transfer coefficient on the fins. Furthermore, how to choose the appropriate flow model and the effect of grid points are also investigated. Velocity, temperature and heat transfer coefficient distributions of the fin are determined using the CFD software. More accurate results can be obtained if the heat transfer coefficient is closed to the inverse results and matches the experimental data. The results obtained using the Zero equation turbulence flow model are more accurate for natural convection.

[1]S. Yildiz, H. Yuncu, An experimental investigation on performance of annular fins on a horizontal cylinder in free convection heat transfer, Int. J.Heat Mass Transfer vol.40 (2004) 239-251
[2]N. Kayansayan, Thermal characteristics of fin-and-tube heat exchanger cooled by natural convection, Exp. Therm. Fluid Sci. vol.7 (1993) 177-188.
[3]R. Sajedi, M. Taghilou, M. Jafari, Experimental and numerical study on the optimal fin numbering in an external extended finned tube heat exchanger, Appl. Therm. Eng. vol.83 (2015) 139-146.
[4]Y. Qiu, M. Tian, Z. Guo, Natural convection and radiation heat transfer of an externally-finned tube vertically placed in a chamber, Int. J. Heat Mass Transfer, vol.49 (2013) 405-412.
[5]M. Yaghoubi, M. Mahdavi, An investigation of natural convection heat transfer from a horizontal cooled finned tube, Exp. Heat Transfer vol.26 (2013) 343-359.
[6]A. Kumar, J.B. Joshi, A.K. Nayak, P.K. Vijayan, 3D CFD simulation of air cooled condenser-I: Natural convection over a circular cylinder, Int. J. Heat Mass Transfer, vol.78 (2014) 1265-1283.
[7]A. Kumar, J.B. Joshi, A.K. Nayak, P.K. Vijayan, 3D CFD simulation of air cooled condenser-II: Natural draft around a single finned tube kept in a small chimney, Int. J. Heat Mass Transfer, vol.92 (2016) 507-522.
[8]A.K. Tolpadi, T.H. Kuehn, Conjugate three-dimensional natural convection heat transfer from a horizontal cylinder with long transverse plate fins, Numer. Heat Transfer 7 (1984) 319-341.
[9]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 (1974) 265-272.
[10]T.V. Jones, C.M.B. Russell, Efficiency of rectangular fins, SME/AIChE National Heat Transfer Conference, Orlando, Florida (1980 ) 27-30.
[11]E.C. Rosman, P. Carajilescov, F.E.M. Saboya, Performance of One and Two-row Tube and Plate Fin Heat Exchangers, ASME J. Heat Transfer, vol.106 (1984) 627-632.
[12]R.L. Webb, “Principle of Enhanced Heat Transfer”, Wiley, New York (1994) 125-153.
[13]M.N. Özisik, “Heat Conduction,” second ed., Wiley, New York, Chapter 14, 1993.
[14]K. Kurpisz, A.J. Nowak, “Inverse Thermal Problems,” Computational Mechanics Publications, Southampton, UK, 1995.
[15]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, Int. J. Heat Mass Transfer, vol.46 (2003) 3629-3638.
[16]C.H. Huang, I.C. Yuan, H. Ay, An experimental study in determining the local heat transfer coefficients for the plate finned-tube heat exchangers, Int. J. Heat Mass Transfer, vol.52 (2009) 3057-3066.
[17]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 (2005) 2697-2707.
[18]H.T. Chen, J.C. Chou, Investigation of natural-convection heat transfer coefficient on a vertical square fin of finned-tube heat exchangers, Int. J. Heat Mass Transfer, vol.49 (2006) 3034-3044.
[19]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 (2007) 1750-1761.
[20]H.T. Chen, J.R. Lai, Study of heat-transfer characteristics on the fin of two-row plate finned-tube heat exchangers, Int. J. Heat Mass Transfer, vol.50 (2012) 45-57.
[21]G.D. Raithby, K.G.T. Hollands, Natural convection, Chap. 4, in: W.M. Rohsenow, J.P. Hartnett, Y.I. Cho (Eds.), Handbook of Heat Transfer, third ed., McGraw-Hill, 1998. Chap. 4.
[22]H.T. Chen, C.H. Lu, Y.S. Huang, K.C. Liu, Estimation of fluid flow and heat transfer characteristics for two-row plate-finned tube heat exchangers with experimental data, Int. J. Heat Mass Transfer, vol.52 (2016) 969-979.
[23]H.T. Chen, Y.S, Lin, P.C. Chen, J.R. Chang, Numerical and experimental study of natural convection heat transfer characteristics for vertical plate fin and tube heat exchangers with various tube diameters, Int. J. Heat Mass Transfer, vol.100 (2016) 320-331.
[24]H.T. Chen, Y.L, Chang, P.Y. Lin, Y.J, Chui, J.R. Chang, Numerical study of mixed convection heat transfer for vertical annular finned tube heat exchanger with experimental data and different tube diameters, Int. J. Heat Mass Transfer, vol.118 (2018) 931-947.
[25]Fluid Dynamics Software, FLUENT 4, Lebanon, NH-USA, 2002.
[26]Fluid Dynamics Software, FLUENT 15, Lebanon, NH-USA, 2013.
[27]L.A.O. Rocha, F.E.M. Saboya, J.V.C. Vargas, “A comparative study of elliptical and circular sections in one- and two-row tubes and plate fin heat exchangers”, Int. J. Heat and Fluid Flow, vol.18 (1997) 247-252.
[28]S.M. Saboya, F.E.M. Saboya, “Experiments on elliptic sections in one- and two-row arrangements of plate fin and tube heat exchangers”, Experimental Thermal and Fluid Science, vol.24 (2001) 67-75.
[29]J.Y. Jang, M.C. Wu, W. J. Chang, “Numerical and experimental studies of three-dimensional plate-fin and tube heat exchangers”, Int. J. Heat Mass Transfer, vol.39 (1995) 3057-3066.
[30]H. Ay, J.Y. Jang, J.N. Yeh, “Local heat transfer measurements of plate finned-tube heat exchangers by infrared thermography”, Int. J. Heat Mass Transfer, vol.45 (2002) 4069-4078.
[31]R.S. Matos, J.V.C. Vargas, T.A. Laursen, A. Bejan, “Optimally staggered finned circular and elliptic tubes in forced convection”, Int. J. Heat Mass Transfer, vol.47 (2004) 1347-1359.
[32]C.W. Lu, J. M. Huang, W.C. Nien, C.C. Wang, “A numerical investigation of the geometric effects on the performance of plate finned-tube heat exchanger”, Energy. C. M., vol.52 (2011)1638-1643.
[33]J.Y. Kim, T.H. Song, “Effect of tube alignment on the heat/mass transfer from a plate fin and two-tube assembly: naphthalene sublimation results”, Int. J. Heat Mass Transfer, vol.46 (2003) 3051-3059.
[34]A. Bejan, “Heat Transfer”, John Wiley & Sons, New York (1993) 53-62.
[35]B.E. Launder, D.B. Spalding, “Mathematical Method of Turbulence”, Academic, London (1972) 3-51.
[36]V. Yakhot, S.A. Orszag, “Renormalization group analysis of turbulence”, Journal of Scientific Computing, vol.1 (1986) 3-51.
[37]于承廷，並列式板鰭管式熱交換器之熱傳特性預測，國立成功大學機械工程學系，碩士論文，2010。
[38]賴健榮，四圓管板鰭管式熱交換器之熱傳特性研究，國立成功大學機械工程學系，碩士論文，2011。
[39]陳品君，具各種圓管排列之板鰭管式熱交換器的熱傳特性研究， 國立成功大學機械工程學系，碩士論文，2015。