本文討論以CFD商業軟體之Ansys中Fluent軟體進行數值模擬，研究以非牛頓流體中的冪次律流體在流過曲面邊界上層流之凝結分析，得到表面摩擦力、局部熱通量以及凝結厚度…等數據後，並進一步討論在曲面幾何邊界流場下速度與溫度的關係跟趨勢。首先，將本次重點放在流場之幾何曲率半徑以及流動特性指數(n)上，分別討論不同的曲率半徑對流場的影響，其中討論薄膜厚度和薄膜內溫度分布，以及不同的流動特性指數(n)所造成的影響，其中包括凝結液膜厚度、局部紐賽數、壁面剪應力和液膜內速度跟溫度的分布。除了上述討論兩種主題之外，也討論流場的雷諾數和流體的普朗特數對流場的影響。最後，可以得出以下結論:
1.薄膜厚度與雷諾數、普朗特數成反比關係，與流動特性指數成正比關係。在曲率半徑上，對於擬塑性流體而言亦成反比關係，對於膨脹性流體則成正比關係。
2.局部紐賽數以及平均紐賽數與普朗特數和流動特性指數成正比。
3.壁面剪應力和流動特性指數成正比。
4.薄膜內溫度分布的部分，普朗特數以及流動特性指數皆與溫度梯度和溫度極值成正比。當流體為擬塑性流體則溫度梯度和溫度極值和曲率半徑成反比，膨脹性流體則成正比。薄膜內速度分布的部分，流動特性指數和速度梯度、速度成反比。

In this paper, numerical simulation had been conducted in order to study the condensation behavior of the power-law non-Newtonian fluid on the curved surface. After obtaining data of surface friction, local heat flux, condensation thickness, and etc., then further discuss the relation between velocity and temperature under different geometry. First of all, the main focus is curvature and power-law index. Then the effect of curvature on the flowing behavior, thin film thickness and temperature distribution is discussed. Furthermore, the influence of power-law index is discussed. Besides the two topic mentioned above, Reynolds number and Prandtl number are discussed as well.
With the simulation results, following conclusion can be made:
1. Thin film thickness is inversely correlated to Reynolds number and Prandtl number, but correlated to power-law index. As for the curvature, pseudo plastic fluid is inversely correlated but dilatant fluid is correlated.
2. Local Nusselt number, average Nusselt number and Prandtl number are proportional to power-law index.
3. Surface shearing stress is correlated to power-law index.
4. As for the temperature profile within the thin film, Prandtl number and power-law index are correlated to temperature gradient and maximum temperature. If the fluid is pseudo plastic, then temperature gradient and maximum temperature are in an anti-correlation with curvature. The results is completely the opposite if it is dilatant fluid. As for the velocity distribution, power-law index is inversely correlated to velocity gradient and velocity.

【1】 Sang, II Lee., and Hee, Cheon No., 1998, “Improvement of direct contact condensation model of relap5/mod3.1 for passive high-pressure injection system,” Annals of Nuclear Energy, Vol. 25, pp. 677-688.
【2】 Hun Ju, Seong, Cheon No, Hee, and Mayinger, Franz., 2000, “Measurement of heat transfer coefficients for direct contact
condensation in core makeup tanks using holographic interferometer,” Nuclear Engineering and Design, Vol. 199, pp. 75-83.
【3】 Brown, G., 1951, “Heat transmission by condensation of steam on a spray of water drops,” Inst. Mech. Engers. Proc. Discussion on Heat Transfer, pp.49-52.
【4】 Brouwers H. J. H., 1992, “Film models for transport phenomena with fog formation: The fog film model,” Int. Heat and Mass Transfer, Vol. 35, pp. 13-28.
【5】 Brouwers, H. J. H., Van Der Geld, and C. W. M., 1996, “Heat transfer, condensation and fog formation in crossflow plastic heat exchangers,” Int. J. Heat and Mass Transfer, Vol. 39, pp. 391-405.
【6】Rose, J. W., 2001, “Dropwise condensation theory and experiment: A Review,” Imeche. J. Power and Energy, Vol. 216. pp. 115-127.
【7】 Wodruff, D. W. and Westwater, J.W., 1981, “Steam condensation on various gold surfaces,” J. Heat Transfer,” Vol. 103, pp. 685-692
【8】 O’Nell, G. A. and Westwater, J. W. 1984, “Dropwise condensation of
steam on electroplated silver surfaces,” Int. J. Heat and Mass Transfer, Vol. 27,
pp. 1539-1549.
【9】 Nash, C. A. and Westwater, J. W., 1987, “A study of novel surfaces for dropwise condensation,” Proc. ASME-JSME Thermal Eng. Conf. Honolulu, 2, pp. 485-491.
【10】 Nusselt, W., 1916, “Die oberflachenkondensation des wasserdampfes,” Zeitschr. Ver Deutsch. Ing. 60, pp. 541-569.
【11】 Gregorig, R., Kern, J. and Turek, 1974, ”Improved correlation of film condensation data based on or more rigorous application of similarity parameters,” Warme-und Stoffubertragung, Vol.7, pp.1-13.
【12】 Rohsenow, W. M., 1956, “Heat transfer and temperature distribution in laminar-film condensation,” Trans. ASME, Vol. 78, pp. 1645-1648.
【13】 Sparrow, E. M. and Gregg, J.L., 1959, “A boundary-layer treatment of laminar film condensation,” Trans. ASME, J. Heat Transfer, Vol.81, pp.13-18.
【14】 Chen, M. M., 1961, “An analytical study of laminar film condensation: part 1-flat plates,” Trans. ASME, J. Heat Transfer, Vol.83, pp.48-54.
【15】 Koh, J. C. Y., 1961, “An integral treatment of two-phase boundary layer in film condensation,” Trans. ASME, J. Heat Transfer, Vol.83, pp.359-362.
【16】Sugawara, S., Michiyoshi, I. and Minamiyama, T., 1956, “The condensation of vapour flowing normal to a horizontal pipe,” Proc. 6th Jap. Nat. Cong. App. Mech, Paper 3-4, pp.385.
【17】 Le Fevre, E. J. and Mandelsweig, S. I., 1960, “The effect of vertically downward velocity on the heat transfer from stream-nitrogen mixtures condensing on a horizontal cylinder,” MSc Thesis, Univ. London.
【18】 Mayhew, Y. R. and Aggarwal, J. K., 1973, “Laminar film condensation with vapour drag on a flat surface,” Int. J. Heat Mass Transfer, Vol.16, pp.1944-1949.
【19】 Nicol, A. A. and Wallace, D. J., 1974, “The influence of vapour shear force on condensation on a cylinder,” Inst. Chem. Eng. Symp., Ser.38, p.1
【20】 Nobbs, D. W., 1975, “The effect of downward vapour velocity and inundation on the condensation rates on horizontal tube banks,” PhD Thesis Univ. of Bristol, U.K.
【21】 Asano, K., Nakano, Y. and Inaba, M., 1979, “Forced convection film condensation of vapours in the presence of noncondensable gas on a small vertical fiat plate,” J. Chem. Eng. Jpn., Vol.12, No.3, pp.196.
【22】 South, V. and Denny, V. E., 1972, “The vapor shear boundary condition for laminar film condensation,” Trans. ASME. J. Heat Transfer., Vol.94, pp.248-249.
【23】 Cess, R. D., 1960, “Laminar-film condensation on a flat plate in the absence of a body force,” Zeitschrift fur Angewandte und Physik, Vol.11, pp.426-433.
【24】 Koh, J. C. Y., 1962, “Film condensation in a forced convection boundary layer flow,” Int. J. Heat Mass Transfer, Vol.5, pp.941-954.
【25】 Shekriladze, I. G. and Gomelauri, V. I., 1966, “Theoretical study of laminar film condensation of a flowing vapour,” Int. J. Heat Mass Transfer, Vol.9, pp.581-591.
【26】 Denny, V. E. and Mills, A. F., 1969, “Laminar film condensation of a flowing vapor on a horizontal cylinder at normal gravity,” Trans. ASME J. Heat Transfer, Vol.91, pp.495.
【27】 Jacobs, H. R., 1966, “An integral treatment of combined body force and forced convection in laminar film condensation,” Int. J. Heat Mass Transfer, Vol.9, pp.637-648.
【28】 Fujii, T. and Uehara, H., 1972, “Laminar film condensation on a vertical surface,” Int. J. Heat Mass Transfer,” Vol.15, pp.217-233.
【29】 Gaddis, E. S., 1979, “Solution of the two phase boundary layer equations for laminar film condensation of vapour flowing perpendicular to a horizontal cylinder,” Int. J. Heat Mass Transfer, Vol.22, pp.371.
【30】 Fujii, T., Honda, H. and Oda, K., 1979, “Condensation of steam on a horizontal tube-the influence of on coming velocity and thermal condition at the tube wall,” Condensation Heat Transfer, Proc. 18th Nat. Heat Transfer. Conf. ASME, pp.35-43.
【31】 Lee, W. C. and Rose, J. W., 1982, “Film condensation on a horizontal tube-effect of vapour velocity,” Proc. 7th , Int. Heat Transfer Conf., Munich, Vol.5, pp.101-106.
【32】Truckenbrodt, E., 1956, “Ein einfaches naherungsverfahrenzum berechnen der laminaren riebungsicht mit absangung,” Forschung Ing.
【33】 Wang, C. C. and Chen, C. K., 2002, “Combined free and forced convection film condensation on a finite-size horizontal wavy plate,”ASME J. Heat Transfer, Vol. 124, pp. 573-576.
【34】 Yang, S. A. and Chen, C. K., 1993, “Laminar film condensation on a horizontal elliptical tube with iniform surface heat flux and suction at the porous wall,” J. of the Chinese Society of Mechanical Engineers, Vol. 14, No. 1, pp. 93-100.
【35】 Yang, S. A. and Chen, C. K., 1994, “Filmwise condensation on a horizontal elliptical tube embedded in porous media,”Chemical Engineering
Communications, Vol. 127, pp. 125-135.
【36】 Yang, S. A. and Chen, C. K., 1997, “Filmwise condensation on a vertical porous ellipsoid with uniform suction velocity,”Chemical Engineering Communications, Vol. 160, pp. 123-135.