本文利用數值方法探討三維百葉窗型鰭管式熱交換器之熱流現象。研究參數包含百葉窗起始角度(θi = 20o~28 o)、百葉窗攻角(Δθ = 0o, 1 o, 2 o及3 o)及百葉窗間距(Lp = 0.8 ~ 1.2 mm)，並在不同雷諾數ReFp (以鰭片間距為特徵長度，正向風速為1 ~ 10 m/s )下進行數值運算，進而探討空氣進口速度(Vin)、百葉窗角度(θ)、百葉窗間距(Lp)及百葉窗攻角(Δθ)對熱傳性能之影響。
根據運算結果，發現熱傳因子j、壓降因子f與面積縮減率皆隨百葉窗角度增加而增大。當角度為20o、24o及28o時，面積縮減率(相較於板鰭片)分別為9.60%、19.26%及27.43%。
另外，在固定鰭片角度( θuniform = 20o )下，熱傳及壓降因子皆隨百葉窗間距增加而提升。在ReFp = 320至1636範圍下，百葉窗間距由 0.8 mm增至1.0 mm及1.2 mm會使面積縮減率分別增加5.21%及6.77%。
除此之外亦發現，增加攻角可提升熱傳因子j及面積縮減率，但也同時提高壓降因子f。以起始角度為20o之鰭片為例，採用含攻角(Δθ = 3o)之百葉窗型鰭片可使熱傳因子j增加15.70%、面積縮減率達11.26%，而壓降因子f則提升21.90%。
本文同時以最佳化方法中之簡易共軛梯度法(Simplified conjugate gradient method, SCGM)，搜尋最佳百葉窗間距與百葉窗角度組合 (百葉窗間距約落在0.84 ~ 1.02 mm間，百葉窗角度約介於22.30 o ~ 33.55o) 。與板鰭片相較，採用最佳化設計參數之百葉窗型鰭片可使面積縮減率達到27.64%至36.76%。
最後，本研究根據熱交換器設計理論，發展一套冷卻盤管之電腦輔助設計軟體，幫助使用者方便計算熱交換器相關性能。程式具備功能如下：
(A) 性能評估問題 (Rating problem)
使用者輸入熱交換器尺寸(包括長、寬、高、鰭片間距、厚度、材質等)、空氣及冷媒流量、流體進口溫度等條件，則軟體可自動計算出兩側流體的出口溫度、熱傳量、壓降等性能。
(B) 尺寸計算問題 (Sizing problem)
使用者輸入熱交換器所需之熱傳量及兩側流體進出口溫度，則軟體可自動計算出熱交換器所需之熱傳面積及尺寸(包括長，寬，高，鰭片間距、厚度等)。

A series of 3-D computational fluid dynamics analyses along with the simplified conjugate-gradient method were carried out to study the thermal-hydraulic characteristics for the louver-finned heat exchanger. The effects of different louver angles (θ = 20o to 28o), louver pitches (Lp = 0.8 to 1.2 mm) and angles of attack (Δθ = 0o ~ 3 o) on the heat transfer phenomenon and pressure drop (in terms of Colburn j factor and friction f factor) were investigated in detail. The optimization of the louver angle and louver pitch is carried out by using the simplified conjugate-gradient method. The area reduction ratio using a louver fin relative to the plain surface is the objective function to be maximized.
The numerical results showed that both the f and j factors are increased with the increase of the louver angle; for a given louver angle, increasing the louver pitch (Lp), from 0.8 to 1.2mm, the f and j factors are increased by 2.33% and 4.20%, respectively. The results of optimization analysis revealed that, with inlet frontal velocity ranging from 2 to 10m/s, the optimal values of louver angle and louver pitch are in the range of (22.3o to 33.6o ) and (0.84 to 1.02 mm), respectively. It is also found that, under the optimum conditions, the area reduction ratio could reach up to 28 % to 37%.
It was also found that, as the angle of attack increases, both the f and j factors are increased. In addition, the area reduction ratio could be reached to 21.90% approximately. Finally, the software for computer-aided heat exchanger design was programmed in Visual Basic software, according to the theory of heat exchanger. It can simplify the calculating process and make engineers get the reliable result easily.

[1] Webb, R.L., "Principles of Enhanced Heat Transfer," John Wiley and Sons, ed. Hoboken, USA, 1994.
[2] Bergles, A.E., "Heat transfer enhancement: The encouragement and accommodation of high heat fluxes," ASME Journal of Heat Transfer, vol. 119, pp. 8-19, 1997.
[3] Webb, R.L. and Jung, S.H., "Air side performance of enhanced brazed aluminum heat exchangers," ASHRAE Transactions,, vol. 98, Pt.2, pp. 391-401, 1992.
[4] Wang, C.C., Tao, W.H., and Chang, C.J., "An investigation of the airside performance of the slit fin-and-tube heat exchangers," International Journal of Refrigeration, vol. 22, pp. 595-603, 1999.
[5] Chang, Y.J., Hsu, K.C., Lin, Y.T., and Wang, C.C., "A generalized friction correlation for louver fin geometry," International Journal of Heat and Mass Transfer, vol. 43, pp. 2237-2243, 2000.
[6] Kays, W.M., and London, A.L., "Heat transfer and flow friction characteristics of some compact heat exchanger surfaces-Part I: Test system and procedure," ASME Journal of Heat Transfer, vol. 72, pp. 1075-1085, 1950.
[7] Beauvais, F.N., "An aerodynamic look at automotive radiators," SAE paper No.650470, 1965.
[8] Davenport, C.J., Heat Transfer and Fluid Flow in Louvred Triangular Ducts, Ph.D. thesis, CNAA, Lanchester Polytechnic, 1980.
[9] Davenport, C.L., "Correlations for heat transfer and flow friction characteristics of louvred fin," AIChE Symposium Series, vol. 79, pp. 19-27, 1983.
[10] Achaichia, A., and Cowell, T.A., "Heat transfer and pressure drop characteristics of flat tube and louvered plate fin surfaces," Experimental Thermal and Fluid Science, vol. 1, pp. 147-157, 1988.
[11] Webb, R.L., and Trauger, P., "Flow structure in the louvered fin heat exchanger geometry," Experimental Thermal and Fluid Science, vol. 4, pp. 205-217, 1991.
[12] Sahnoun, A. and Webb, R.L., "Prediction of heat transfer and friction for the louver fin geometry," Journal of Heat Transfer, vol. 114, pp. 893-900, 1992.
[13] Rugh, J.P., Pearson, J.T., and Ramadhyani, S., "A Study of a Very Compact Heat Exchanger Used for Passenger Compartment Heating in Automobiles," ASME Symposium Series, vol. 201, pp. 15-24, 1992.
[14] Sunden, B., and Svantesson, J., "Thermal hydraulic performance of new multilouvered fins," Proceedings of the 9th International Heat Transfer Conference, vol. 14-HX-16, pp. 91-96, 1990.
[15] Sunden, B., and Svantesson, J., "Correlation of j- and f-factors for multi louvered heat transfer surfaces," Proceedings of the 3rd UK National Heat Transfer Conference, pp. 805-811, Rugby, UK, 1992.
[16] Chang, Y.J., Wang, C.C., and Chang, W.R., "Heat transfer and flow characteristics of automotive brazed aluminum heat exchangers," ASHRAE Transactions,, vol. 100, Pt.2, pp. 643-652, 1994.
[17] Webb, R.L., Chang, Y.J., and Wang, C.C., "Heat transfer and friction correlation for the louver fin geometry," International journal heat and mass transfer, vol. 2, pp. 533-541, 1995.
[18] Chang, Y.J., and Wang, C.C., "Air Side Performance of Brazed Aluminum Heat Exchangers," vol. 3, pp. 15-28, 1996.
[19] Chang, Y.J., and Wang, C.C., "A generalized heat transfer correlation for Iouver fin geometry," International Journal of Heat and Mass Transfer, vol. 40, pp. 533-544, 1997.
[20] Wang, C.C., Chi, K.Y., Chang, Y.J., and Chang, Y.P., "An experimental study of heat transfer and friction characteristics of typical louver fin-and-tube heat exchangers," International Journal of Heat and Mass Transfer, vol. 41, pp. 817-822, 1998.
[21] Wang, C.C., Chang, Y.P., Chi, K.Y., and Chang, Y.J., "A study of non-redirection louvre fin-and-tube heat exchangers," Journal of Mechanical Engineering Science, vol. 212, pp. 1-14, 1998.
[22] Wang, C.C., Lin, Y.T., and Lee, C.J., "Heat and momentum transfer for compact louvered fin-and-tube heat exchangers in wet conditions," International Journal of Heat and Mass Transfer, vol. 43, pp. 3443-3452, 2000.
[23] Wang, C.C., Lee, W.S., and Sheu, W.J., "A comparative study of compact enhanced fin-and-tube heat exchangers," International Journal of Heat and Mass Transfer, vol. 44, pp. 3565-3573, 2001.
[24] Wang, C.C., Lee, C.J., Chang, C.T., and Lin, S.P., "Heat transfer and friction correlation for compact louvered fin-and-tube heat exchangers," International Journal of Heat and Mass Transfer, vol. 42, pp. 1945-1956, 1998.
[25] Suga, K., Aoki, H., and Shinagawa, T., "Numerical Analysis on Two-Dimensional Flow and Heat Transfer of Louvered Fins Using Overlaid Grids," JSME international journal. Ser. 2, Fluids engineering, heat transfer, power, combustion, thermophysical properties, vol. 33, pp. 122-127, 1990.
[26] Suga, K. and Aoki, H., "Numerical Study on Heat Transfer and Pressure Drop in Multilouvered Fins," vol. 2, pp. 231-238, 1995.
[27] Hiramatsu, M., Ishimaru, T., and Matsuzaki, K., "Research on fins for air conditioning heat exchangers," JSME international journal series Ⅱ, vol. 33, pp. 749-756, 1990.
[28] Ikuta, S., Sasaki, Y., Tanaka, K., Takagi, M., and Himeno, R., "Numerical analysis of heat transfer around louver assemblies," SAE paper No.900081, 1990.
[29] Achaichia, A., Heikal, M.R., Sulaiman, Y., and Cowell, T.A., "Numerical investigation of flow and friction in louvered fin arrays," in Proceedings of the Tenth International Heat Transfer Conf., Brighton, 1994.
[30] Hsieh, C.T. and Jang, J.Y., "3-D thermal-hydraulic analysis for louver fin heat exchangers with variable louver angle," Applied Thermal Engineering, vol. 26, pp. 1629-1639, 2006.
[31] Jang, J.Y., Wu, M.C., and Chang, W.J., "Numerical and experimental studies of threedimensional plate-fin and tube heat exchangers," International Journal of Heat and Mass Transfer, vol. 39, pp. 3057-3066, 1996.
[32] Jang, J.Y. and Chen, L.K., "Numerical analysis of heat transfer and fluid flow in a three-dimensional wavy-fin and tube heat exchanger," International Journal of Heat and Mass Transfer, vol. 40, pp. 3981-3990, 1997.
[33] Atkinsona, K.N., Drakulic, R., Heikal, M.R., and Cowell, T.A., "Two- and three-dimensional numerical models of flow and heat transfer over louvred fin arrays in compact heat exchangers," International Journal of Heat and Mass Transfer, vol. 41, pp. 4063-4080, 1998.
[34] Jang, J.Y., Shieh, K.P., and Ay, H., "3-D thermal-hydraulic analysis in convex louver finned -tube heat exchangers," ASHRAE Annual Meeting, Cincinnati, OH, U.S. A., June 22-27, vol. Vol.107 Pt.2, pp. 501-509, 2001.
[35] Tayal, M.C., Fu, Y., and Diwekar, U.M., "Optimal Design of Heat Exchangers: A Genetic Algorithm Framework," Industrial & Engineering Chemistry Research, vol. 38, pp. 456-467, 1998.
[36] Fabbri, G., "Heat transfer optimization in corrugated wall channels," International Journal of Heat and Mass Transfer, vol. 43, pp. 4299-4310, 2000.
[37] Guo, L., Qin, F., Chen, J., Chen, Z., and Zhou, Y., "Influence of geometrical factors and pressing mould wear on thermal-hydraulic characteristics for steel offset strip fins at low Reynolds number," International Journal of Thermal Sciences, vol. 46, pp. 1285-1296, 2007.
[38] Lihua, G., Jiangping, C., Feng, Q., and Zhijiu, C., "Geometrical optimization and mould wear effect on HPD type steel offset strip fin performance," Energy Conversion and Management, vol. 48, pp. 2473-2480, 2007.
[39] Hsieh, C.T., and Jang, J.Y., "Parametric study and optimization of louver finned-tube heat exchangers by Taguchi method," Applied Thermal Engineering, vol. 42, pp. 101-110, 2012.
[40] Jang, J.Y. and Tsai, Y.C., "Optimum louver angle design for a louvered fin heat exchanger," International Journal of the Physical Sciences vol. 6, pp. 6422-6438, 2011.
[41] 許玲芳, "渦流產生器增強技術應用於鰭管式熱交換器之最佳化性能研究," 機械工程研究所, 國立成功大學, 2012.
[42] 王啟川, 熱交換器設計: 五南出版社, 2005.
[43] Hermes, C.J.L., Silva, W.de Lima e Jr, and de Castro, F.A.G., "Thermal-hydraulic design of fan-supplied tube-fin condensers for refrigeration cassettes aimed at minimum entropy generation," Applied Thermal Engineering, vol. 36, pp. 307-313, 2012.
[44] Launder, B.E., and Spalding, D.B., Mathematical Models of Turbulence, ed. London: Academic Press, pp. 99-100, 1972.
[45] Van Doormaal, J.P., and Raithby, G.D., "Enhancements of The Simple Method For Predicting Incompressible Fluid Flows," Numerical Heat Transfer, vol. 7, pp. 147-163, 1984.
[46] Patankar, S.V., Numerical heat transfer and fluid flow: Hemisphere Publishing Company, 1980.
[47] Cheng , C.H., and Chang, M.H., "A Simplified Conjugate-gradient Method for Shape Identification Based On Thermal Data," Numerical Heat Transfer, Part B: Fundamentals, vol. 43, pp. 489-507, 2003.
[48] Gnielinski, V., "New Equation for Heat and Mass Transfer in Turbulent Pipe and Channel Flow," Industrial and Eng. Chemistry, vol. 16, pp. 359-368, 1976.
[49] Kandlikar, S.G., "A General Correlation for Saturated Two-Phase Flow Boiling Heat Transfer Inside Horizontal and Vertical Tubes," ASME Journal of Heat Transfer, vol. 112, pp. 219-228, 1990.
[50] Friedel, L., "New Friction Pressure Drop Correlations for Upward, Horizontal and Downward Two-Phase Pipe Flow," Presented at the HTFS Symposium, Oxford. (Hoechst AG Reference 372217/24 698), 1979.
[51] Hewitt, G.F., Shires, G.L., and Bott, T.R., "Process Heat Transfer," Ch14,CRC Press, 1994.