本文以數值方法探討空氣式冷擬器之熱交換器鰭片熱傳現象，主要探討三種不同長短軸比的橢圓鰭管，其長短軸比(Ar)分別為2.5、2.8及3.1，與其相同管徑(27mm)的圓鰭管做比較。以三維延伸κ-ε (extended κ-εmodel)紊流模式並考慮共軛熱傳效應(有限熱導度)，在管壁溫度上考慮為定溫，探討在不同正向風速下(1 ~ 5 m/s)，三維熱流場通道內溫度、壓力及鰭片表面紐賽數、壓降係數的變化，同時與等溫鰭片(無限熱導度)做比較，最後比較三個測試本體間的性能差異。
　　由數值分析的結果得知，圓鰭管式熱交換無論是在壓降上(約為3倍)或熱傳上(約為1.1倍)都大於橢圓鰭管式熱交換器，而比較三種長短軸比上，在單位壓降的熱傳係數上的比較上，以橢圓鰭管長短軸比(Ar = 3.1)約大於長短軸比(Ar =2.8)為1.08倍，大於長短軸比(Ar =2.5)為1.24倍及大於圓鰭管2.6倍。

　　The numerical analysis was carried out to study the 3- D heat transfer and flow in finned tube heat exchanger of Air-cooled condenser. Three kinds of major/mirror axis ratios (2.5、2.8 and 3) are examined for the elliptic finned-tube heat exchangers and the results are also compared with the corresponding circular finned-tube having the same perimeter. Numerical simulation was performed by 3-D turbulence analysis with conjugated heat transfer and fluid flow. The numerical results for the temperature、pressure 、Nusselt number and fanning friction factor at various inlet frontal velocities(1~5 m/s) are shown and compared with the available experimental data.
　　The numerical result indicated that the pressure drop of circular finned-tube heat exchanger is 3 times of elliptic finned-tube heat exchanger, while the heat transfer coefficient of circular finned-tube is 1.1 times of elliptic finned-tube. The heat transfer coefficient per unit of pressure drop for elliptic finned-tube(Ar = 3.1) is 1.08 times of elliptic finned-tube(Ar = 2.8) 、1.24 times of elliptic finned-tube(Ar = 2.5) and 2.6 times of circular finned-tube.

1. Saboya, F.E.M, Sparrow, E.M., “Local and average transfer coefficients for one-row plate fin and tube heat exchanger configurations”, J. fo Heat Transfer (ASME), Vol.96, pp.265-272, 1974.
2. Saboya, F.E.M, Sparrow, E.M., “Transfer characteristics of two-row plate fin and tube heat exchanger configurations”, Int. J. Heat Mass Transfer, Vol.19, pp.41-49, 1976.
3. Webb, P. L. and Trauger, P., 1991, “Flow structure in the louvered fin heat exchanger geometry”, Experimental Thermal and Fluid Science, Vol. 4, PP.205-217.
4. Atkinson , K. N., Drakulic , R., Heikal, M. R., and Cowell, T. A., 1998, “Two-and three-dimensional numerical models of flow and heat transfer over louver fin arrays in compact heat exchangers”, International Journal of Heat and Mass Transfer, Vol. 41, PP. 4063-4080.
5. Liu, M. S, Leu, J. S, Liaw, J. S and Wang, C. C., 2000,”3-D simulation of the thermal-hydraulic characteristics of louvered fin-and-tube heat exchangers with oval tubes”, 2000 ASHRAE Annual Meeting, Minneapolis, MN, U. S. A.
6. Wang, C. C. and Chang, Y. J., 1997, “A generalized heat transfer correlation for louver fin geometry”, International Journal Heat Mass Transfer, Vol.40, No.3, PP. 533-544.
7. Wang, C. C., Chi, K. Y., and Chang, Y. J., 1998, “An experimental study of heat transfer and friction characteristics of typical louver fin-and-tube heat exchangers”, International Journal of Heat Mass Transfer, Vol.41, PP. 817-822.
8. Wang, C. C., Cahng, Y. P., Chi, K. Y. and Chang, Y. J., 1998, ”Al study of non-redirection louver fin-and tube heat exchangers”, Proc. Instn. Mech. Engrs, Vol.212, part C, PP. 1-13.
9. Wang, C. C., Chen, P. Y. and Jang, J. Y., 1996, “Heat transfer and friction characteristics of convex-louver fin-and-tube heat exchangers”, Experimental Heat Transfer, Vol. 9, PP. 61-78.
10. Jang, J.Y. and Lin, C. N. and Shien, K. P., 2001, “3-D thermal-hydraulic analysis in convex louver finned -tube heat exchangers”, accepted for publication in 2001 American Society of Heating, Refrigeration and Air-conditioning Engineers Annual Meeting, Cincinnati , OH, U.S. A., June 22-27.
11. Briggs, D. E. and Young, E. H., “Convection heat transfer and pressure drop of air flowing across triangular pitch banks of finned tubes”, Chem. Eng. Prog. Symp. Ser., Vol.59, No.41, PP.1-10, 1963.
12. Robinson, K. K. and Briggs, D. E., “Pressure drop of air flowing across triangular pitch banks of finned tubes”, Chem. Eng. Prog. Symp. Ser Vol.62, No.64, PP.177-184, 1966.
13. Rich, D. G., “The effect of the number of tube rows on the heat transfer performance of smooth plate and fin-and-tube heat exchangers”, ASHRAE Trans., Vol.81, Pt.l, PP.307-317, 1975.
14. Idem, S. A. and Jacobi, A.M. and Goldchmidt, V. W., “Heat transfer characterization of a finned-tube heat exchanger (with and without condensation)”, Transaction of the ASME, Vol.112, PP.64-70, 1990.
15. Le Feuvre, R. F., “Laminar and turbulent forced convection processes through in-line tube banks”, Imperial College London, Mechanical Engineering Department, HTS/74/5, 1973.
16. Launder, B.E. and Massey, T.H., “The numerical prediction of viscous flow and heat transfer in tube banks", J. Heat Transfer (ASME), Vol.100, PP.565-571, 1978.
17. Fujii, M., Fujii, T., and Nagata, T,. “A numerical analysis of laminar flow and heat transfer of air in an in-line tube bank”, Numerical Heat Tranfer, Vol.7,PP.89-102, 1984.
18. Farouk, B., Güceri, Sí., “Natural convection from horizontal cylinders in interacting flow fields”, Int. J. Heat Mass Transfer, Vol.26, PP.231-243, 1983.
19. Wung, T. S. and Chen, C. J., “Finite analytic solution of convective heat transfer for tube arrays in crossflow：part 1--flow field analysis”, J. of Heat Transfer (ASME), Vol.111, PP.633-640, 1989.
20. Wung, T. S. and Chen, C. J., “Finite analytic solution of convective heat transfer for tube arrays in crossflow：part 2--heat transfer analysis”, J. of Heat Transfer (ASME), Vol.111, PP.641-648, 1989.
21. Faghri, M. and Rao, N., “Numerical computation of flow and heat transfer in finned and unfinned tube banks”, International J. of Heat and Mass Transfer, Vol.30, No.2, PP.363-372, 1987.
22. Bejan A., Fowler A. J., “The optimal spacing between horizontal cylinders in a fixed volume cooled by natural convection”, Int. J.Heat Mass Transfer., Vol.38, No.11, PP.2047-2055, 1995.
23. Dunwoody, N.T,,” Thermal results for forced heat convection through elliptical ducts”, J. of Applied Mech., Vol.29, PP.l65-170, 1962.
24. Brauer, H.,”Compact heat exchangers”, Chem. & Process Engineering, London, Vol.45, No.8, PP.451-460, 1964.
25. Schenk, J. and Han, B.S., “Heat transfer from laminar flow in ducts with elliptic cross section”, Appl. Sci. Res., Vol.17, PP.96-114, 1967.
26. Ota, T., Aiba, S., Tsuruta, T., and Kaga, M., “Forced convection heat transfer from an elliptic cylinder of axis ratio 1 : 2”, Int. J. Heat Mass Transfer, Vol.27, No.10, PP.1771-1779, 1984.
27. Abdel-Wahed, R. M., Attia, A. E., and Hifni, M. A. “Experiments on lamiar flow and heat transfer in an elliptical duct”, Int. J. Heat Mass Transfer, Vol.27, No.12, PP.466-472, 1961
28. Toa L. N., “On some laminar forced-convection problems”, ASME J. Heat Trans., Vol.83, PP.466-472, 1961.
29. Javeri, V., “Analysis of laminar thermal entrance region of elliptic and rectangular channels with the Kantorowich method”, Warme Sto-ffubert., Vol.9, PP.85-98, 1976.
30. Merkin, J. H., “Free convection boundary layers on cylinders of elliptic cross section”, J. Heat Transfer , Vol.99, No.3, PP.453-457, 1977.
31. Chao, B. T., and Lin, F. N., “Local similarity solutions for free con- vection boundary layer flows”, J. Heat Transfer, Vol.97, P.294.
32. Facas, G. N., “Natural convection from an elliptic heat source buried in a semiinfinite, saturated, porous medium”, ASME/JSME Thermal Engi- neering Conference, Vol.3, PP.423-430, 1995.
33. Badr, H. M., “Mixed convection from a straight isothermal tube of elliptic cross section”, Int. J. Heat Mass Transfer, Vol.37, No.15, PP.2343-2365, 1994.
34. Ebadian, M. A., Topakoglu, H. C. and Arnas, O. A., “The effect of heat generation on the convection heat transfer in a tube of elliptical cross section maintained under constant wall temperature”, ASME J. Heat Trans. Vol.110, PP.1101-1104, 1988.
35. Tsareva, E. A., Galin, N.M., and Dem’Yanenko, V Y., “Hydrodynamics and local heat transfer to a turbulent flow in tubes of elliptical cross section”,Teploenergetika, Vol.38 ,PP.623-626, 1991.
36. Shintani, K., Umemura, A., Takano A., “Low-reynolds-number flow past an elliptic cylinder”, J. Fluid Mech., Vol.136, PP.277-289, 1983.
37. Yamashita, H., Kushida, G., Izumi, R., “Fluid flow and heat transfer in a plate-fin and tube heat exchanger (analysis of fluid flow around a square cylinder situated between parallel plates)”, Bulletin of JSME, Vol.29, No.254, PP.2562-2569, 1986.
38. Yamashita, H., Kushida, G., Izumi, R., "Fluid flow and heat transfer in a plate-fin and tube heat exchanger (analysis of fluid flow around a square cylinder situated between parallel plates)”, Bulletin of JSME, Vol.29, No.258, PP.4185-4191, 1986.
39. Bastani, A., Fiebig, M., Mitra, N. K., “Numerical studies of a compact fin-tube heat exchanger”, Proceedings of the EUROTHERM Seminar No.18, Design and Operation of Heat Exchangers, Feb.27 - Mar. 1, Hamburg, Germany, PP.154-163, 1991.
40. Zdravistch, F., Fletcher, C. A. J. and Behnia, M., “Laminar and turbulent heat transfer predictions in tube banks in cross flow”, Int. Conference on Fluid and Thermal Energy Conversion, Dec. 12-15, Kutta-Denpasar, Indonesia, PP.29-34, 1994.
41. Jang, J. Y., Wu, M. C. and Chang, W. J., “Numerical and experimental studies of three-dimensional plate-fin and tube heat exchangers”, Int. J. Heat Mass Transfer, Vo1.39, PP.3057-3066, 1996.
42. Barozzi, G. S., and Pagliarin, G., “A method to solve conjugate heat transfer problem : The case of fully developed laminar flow in a pipe”, ASME Journal of Heat Transfer, Vol.27, PP.77-83, 1985.
43. Pagliarin G., “Conjugate heat transfer for simultaneously developing laminar flow in a circular tube”, ASME Journal of Heat Transfer, Vol.113, PP.763-766, 1991.
44. Fiebig, M., Chen, Y., Grosse-Gorgemann, A., and Mitra, N.K, “Conjufate heat transfer of a finned tube part A : Heat transfer behavior and occurrence of heat transfer reversal”, Numerical Heat Transfer, Part A, Vol.28, PP.113-146, 1995.
45. Fiebig, M., Chen, Y., Grosse-Gorgemann, A., and Mitra, N.K., “Conjufate heat transfer of a finned tube part B：Heat transfer augmentation and avoidance of heat transfer reversal by longitudinal vortex generators”, Numerical Heat Transfer, Part A, Vol.28, PP.147-155, 1995.
46. Chio, C. Y., and Kim, S. J., “Conjugate mixed convection in a channel : Modified five percent deviation rule”, Int. J. Heat Mass Transfer, Vol.39, No.6, PP.1223-1234, 1996.
47. Launder, B. E. and Spalding, A. D., Mathematical models of turbulence, PP.90-100, Academic, London, 1972.
48. Chen, Y. S., Kim, S. W., Computation of turbulent flow using an extend k-��nturbulence closure model, NASA CR-179204, Oct, 1987.
49. Wang, T. S., Chen, Y. S., Unified navier-stokes flow field and performance analysis of liquid rocket engines, AIAA Journal, Vol.22, PP.844-846, 1984.
50. Thompson, J. F., Thames, F. C. and Mastin, C. W., Automatic numerical generation of body-fitted curvilinear coordinate system for fields containing any number of arbitrary two-dimensional bodies, Journal of Computational Physics, Vol.15, PP.299-310, 1974.
51. Thompson, J. F., Warsi, Z. U. A. and Mastin, C. W., Numerical grid generation foundations and applications, North Holland, 1985.
52. STAR CD V.3.15A, Simulation of turbulent flow in arbitrary regions, computational dynamics Limited, UK, 2003.