本文以逆算法與CFD軟體配合實驗數據探討具渦流產生器之矩形鰭片的熱傳及流體流動特性，並探討改變渦流產生器擺放攻角及高度與風速對結果之影響。由於鰭片上的熱傳係數並非均勻分佈，故將鰭片表面分割成數個子區域並假設各子區域之熱傳係數為常數，再利用有限差分法、最小平方法及實驗溫度量測值之逆算法來預測鰭片上的熱傳係數；本文亦利用CFD軟體求得於實驗系統內之空氣溫度與速度分佈以及鰭片表面之溫度與熱傳係數及出入口邊界之壓力差，為了求出本研究較正確之熱傳及流體流動特性，選用適當的流動模式及網格格點數所求得之鰭片平均熱傳係數，須盡可能分別接近實驗溫度量測值、逆算結果等。結果顯示，流動模式對結果之影響不容忽視，具渦流產生器的鰭片可以有效提升平均熱傳係數，渦流產生器擺放攻角越大，可得到越大之平均熱傳係數，但壓力差也隨之增加；改變渦流產生器高度可造成不同熱傳效果，當高度越高流體進入鰭片速度越快，且伴隨較大之壓力差；當渦流產生器高度為鰭片高度之一半時，流體能以較高的平均速度通過鰭片底部，產生較高的平均熱傳係數。為了驗證本文逆算法預測結果之可靠度，亦與其它相關文獻之經驗公式以及CFD軟體之模擬進行比較。

This study applies inverse method and FLUENT to determine the heat transfer and fluid flow characteristics of plate-fin heat sinks with a pair of vortex generators in a cross flow channel. Using measured data to forecast and analyze the average heat transfer coefficient on the fin in limited space. The inverse method along with the finite difference method and experimental temperature data is applied to determine the heat transfer coefficient. Since the distribution of the heat transfer coefficient on the fin is not uniform, the plate-fin is divided into several sub-fin regions and the heat transfer coefficient in each sub-fin region is assumed to be unknown constant. The effect of the attack angle of the vortex generators, the height of the vortex generators, and the Reynolds number on the thermal-fluid performance of the plate-fin heat sink are elucidated. The results indicate that the heat transfer coefficient increases when install a pair of vortex generators, because the air can easily flow into the heat sink. Regarding the effect of the attack angle of the vortex generators on the thermal performance, the highest average heat transfer coefficient is achieve when the attack angle of the vortex generators is , but the pressure difference also increases with increasing the attack angle of the vortex generators. Regarding the effect of the height of the vortex generators, the pressure difference increases with increasing the height of the vortex generators. In addition, the highest average heat transfer coefficient is achieve when the height of the vortex generators is half of the height of the heat sink. In order to verify the reliability of the inverse method with predicted results of this paper, the present study also in comparison with the empirical correlations and experimental results of other relevant literature and CFD simulation packages.

[1] D.R. Haper and W.B. Brown, “Mathematical equations for heat conduction in the fins of air cooled engines,” N.A.C.A.Rept, pp.158,1922.
[2] T.E. Schmidt, “Heat transfer calculations for extended surfaces,” Refrigerating Engineering, pp.351-3570,1949.
[3] W. Elenbass, ‘‘Heat dissipation of parallel plates by free convection,’’ Physica, vol. 9, No.1 (1942), pp. 2-28.
[4] F. Harahap, H.N. McManus, Jr., “Natural convection heat transfer from horizontal rectangular fin arrays,” ASME J. Heat Transfer, vol. 89 (1967), pp. 32-38.
[5] F. Harahap, D. Setio, “Correlations for heat dissipation and natural convection heat-transfer from horizontally-based, vertically-finned arrays,” Appl. Energy, vol. 69 (2001), pp. 29-38.
[6] F. Harahap, E. Rudianto, IGD. M.E. Pradnyana, ‘‘Measurements of steady-state heat dissipation from miniaturized horizontally-based straight rectangular fin arrays,’’ Heat Mass Transfer, vol. 41 (2005), pp. 280-288.
[7] 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.
[8] S. Baskaya, M. Sivirioglu, M. Ozek, ‘‘Parametric study of natural convection heat transfer from horizontal rectangular fin arrays,’’ Int. J. Therm. Sci., vol. 39 (2000), pp. 797-805.
[9] C.W. Leung, S.D. Probert, M.J. Shilston, “Heat exchanger design: optimum uniform separation between rectangular fins protruding from a vertical rectangular base,” Applied Energy, vol. 19 (1985), pp. 287-299.
[10] E.A.M. Elshafei, Effect of flow bypass on the performance of a shrouded longitudinal fin array, Appl. Thermal Eng. 27 (2009) 2233-2242.
[11] M. Fiebig, Embedded vortices in internal flow：heat transfer and pressure loss enhancement, Int. J. Heat Fluid Flow 16 (1995) 376-388.
[12] K. Torii, K.M. Kwak, K. Nishino, Heat transfer enhancement accompanying pressure-loss reduction with winglet-type vortex generators for fin-tube heat exchangers, Int. J. Heat Mass Transfer 45 (2002) 3795-3801.
[13] S.M. Pesteei, P.M.V. Subbarao, R.S. Agarwal, Experimental study of the effect of winglet location on heat transfer enhancement and pressure drop in fin-tube heat exchangers, Appl. Therm. Eng. 25 (2005) 1684-1696.
[14] M. Henze, J. von Wolfersdorf, B. Weigand, C.F. Dietz, S.O. Neumann, Flow and heat transfer characteristics behind vortex generators- a benchmark dataset, Int. J. Heat Fluid Flow 32 (2011) 318-328.
[15] M. Henze, J. von Wolfersdorf, Influence of approach flow conditions on heat transfer behind vortex generators, Int. J. Heat Mass Transfer 54 (2011) 279-287.
[16] H.E. Ahmed, H.A. Mohammed, M.Z. Yusoff, An overview on heat transfer augmentation using vortex generators and nanofluids: approaches and applications, Renew. Sustain. Energy Rev. 16 (2012) 5951-5993.
[17] A. Sinha, K.A. Raman, H. Chattopadhyay, G. Biswas, Effects of different orientations of winglet arrays on the performance of plate-fin heat exchangers, Int. J. Heat Mass Transfer 57 (2013) 202-214.
[18] H.Y. Li, C.L. Chen, S.M. Chao, G.F. Liang ‘‘Enhancing heat transfer in a plate-fin heat sink using delta winglet vortex generators,’’Int. J. Heat Mass Transfer, vol. 67 (2013), pp. 666-677.
[19] J.V. Beck, “Calculation of surface heat flux from an integral temperature history,” ASME J. Heat Transfer, vol. 62 (1962), pp. 46-51.
[20] J.V. Beck, “Surface heat flux determination using an integral method,” Nuclear Engineering Design, vol. 7 (1968), pp. 170-178.
[21] J.V. Beck, B. Litkouhi, C.R. Stclair, “Efficient sequential solution of nonlinear inverse heat-conduction problem,” Numer. Heat Transfer, vol. 5 (1982), pp. 275-286.
[22] E.M. Sparrow, A. Haji-Sheikh, T.S. Lundgren, ‘‘The inverse problem in transient heat conduction,’’ J. Appl. Mech., vol. 31 (1964), pp. 369-375.
[23] N.M. Alnajem, M.N. Özişik, ‘‘A direct analytical approach for solving linear inverse heat conduction problems,’’ ASME J. Heat Transfer, vol 107 (1985), pp. 700-703.
[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 (2005), pp. 80-91.
[25] 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), pp. 2697-2707.
[26] 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), pp. 1750-1761.
[27] H.T. Chen, S.T. Lai, L.Y. Haung, ‘‘Investigation of heat transfer characteristics in plate-fin heat sink,’’ App. Thermal Engineering, vol. 50 (2013), pp. 352-360.
[28] H.T. Chen, S.K. Lee, “Estimation of heat-transfer characteristics on the hot surface of glass pane with down-flowing water film,”Building and Environment, vol. 45 (2010), pp. 2089-2099.
[29] V.S. Arpaci, ‘‘Introduction to heat transfer,’’ Prentice Hall, New Jersey (1999), pp. 580.
[30] A. Bejan, ‘‘Heat transfer,’’ John Wiley & Sons, Inc., New York (1993), pp. 53-62.
[31] 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.
[32] 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), pp. 265-272.
[33] 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 (1993), pp. 3034-3044.
[34] Q. Chen, W. Xu, ‘‘A zero-equation turbulence model for indoor airflow simulation,’’ energy & buildings, vol 28 (1998), pp. 137-144.
[35] B.E. Launder, D. Spalding, ‘‘The numerical computation of turbulent flows,’’ Computer Methods in Applied Mechanics and Engineering, vol. 3 (1974), pp. 269-289.
[36] 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 Fluids A, vol. 4 (1992), pp 1510-1520.
[37] F.P. Icropera , D.P. Dewitt, T.L. Bergman, A.S. Lavine, ‘‘Principles of Heat and Mass Transfer,” 7th ed., John Wiley & Sons, pp. 519, 2013.
[38] 賴詩婷，矩行鰭片陣列於具開孔矩形外殼內之熱傳特性研究，國立成攻大學機械工程學系，碩士論文，2012。
[39] 賴仲豪，板鰭式熱沉於封閉外殼內之自然對流熱傳特性的實驗與數值研究，國立成攻大學機械工程學系，碩士論文，2014。
[40] 陳韋志，預測傾斜矩形平板上之自然對流熱傳特性，國立成攻大學機械工程學系，碩士論文，2009。
[41] FLUENT Dynamic Software, FLUENT, Lehanon, NH (2010).