本文探討強制對流牛頓流體流經波形渠道之熱傳遞分析，波形渠道上下壁面為一個正弦函數的組合波，分別為基本波頻及其諧波組成，波頻率相差兩倍。相較於單一的正弦波形的流體運動情況來的複雜。本文利用座標轉換，求解不規則曲面之問題，將複雜的波形轉換到一規則之平面。藉由改變複雜波形之熱傳問題是一個增加熱傳增益方法之一，複雜波形曲面能反應出更多真實之物理現象，因此常被使用在增加熱傳傳遞的強化過程。複雜波形壁面在熱傳遞過程中更有效率之原因在於促進壁面附近複雜的流動現象。若渠道壁面由兩個或更多個正弦函數合成，預計可得到更好的熱傳增益相較於單一波形壁面。本文數值結果證明增加諧波於壁面，對流場及溫度場有大幅的變化，總熱傳效率較平板或單一波形壁面大。但由於複雜曲面之流體流動較平板複雜，因此其能量損好也是不可或缺之問題之一，因此本文亦引進熵增(Entropy generation)之概念來探討波形渠道之不可用能之變化。

In this study, forced-convection through the complex wavy-wall channel had been discussion. The surface wall with two sinusoidal functions is composed of a fundamental wave and its first harmonic whose frequency is twice than fundamental wave. The complex wavy-wall channel is more complex than single sinusoidal wave-wall channel extensively studied in the past two decades. We used the method of transformed coordinates to solve the irregular surface. It is one of the methods to increase heat-transfer problem of many kinds. Compared with flat-wall channel, complex wavy-wall channel is more real in our life. This is one of the reasons that we choose. And the other reason is that it makes more complex disturbance flow near the surface when the heat-transfer process, cause the efficiency greater. So we get it if the surface is compose of more and more sinusoidal wavy, it will promote the efficiency better. In the study, we got the truth. But it will makes up the irreversible produce and useful energy reduce. So we also used the entropy generation to discussion the heat-transfer process.

參考文獻

Agarwal, R.S., Dhanapal, C., ”Flow and Heat Transfer in a Micropolar Fluid Past a Flat Plate with Suction and Heat Sources,” Int.J.Engng.Sci., Vol.26, pp.1257-1266, 1988.

Ahlbrg, J. H., Nilson, E. N., and Walsh, J. L., “The theory of splines and their application,” Academic Press, 1967.

Ahmadi, G., ”Self-Similar Solution of Incompressible Micro-polar Boundary Layer Flow Over a Semi-Infinite Plate,” Int.J.Engng.Sci., Vol.14, pp.639-646, 1976.

Albasiny, E. L. and Hoskins, W. D., “Increase Accuracy cubic spline solutions to two-point boundary value problems,” J. Inst. Math. Applic., Vol.9, pp. 47-55, 1972.

Arimanb, T., Turk, M. A. and Sylvester, N. D., “On steady and pulsatile flow of blood,” J. Appl. Mech., Vol. 41, pp. 1-7, 1974.

Ariman, T., Turk, M.A., Sylvester, N.D., ”Microcontinuum Fluid Mechanics A Review,” Int.J.Engng.Sci., Vol.11, pp. 905-930, 1973.

Ariman, T., Turk, M.A., Sylvester, N.D., ”Applications of Microcontinuum Fluid Mechanics,” Int.J.Engng Sci. Vol.12, pp.273-293, 1974.

Burns, J. C. and Parks, T., “Peristaltie motion,” Journal of Fluid mechanical, Vol. 29, No. 3, pp.405-416, 1967.

Char, M. I., Chen, C. K., “Temperature field in non-Newtonian flow over a stretching plate with variable heat flux.” Int. J. Heat Mass Transfer Vol.31, pp. 917-921, 1988.

Chawla, T. C., Leaf, G., Chen, W. L., and Grolmes, M. A., “The application of the collocation method using hermite cubic spline to nonlinear transient one-dimensional heat conduction problem,” ASME Journal of Heat Transfer, pp.562-569, 1975.

Chen, C. K.,“Application of cubic spline collocation method to solve transient heat transfer problem,” Heat Transfer in Thermal Systems Seminar-phase, pp. 167-182, 1986.

Chiu, P. and Chou, H. M., “Free Convection in the Boundary Layer Flow of a Micropolar Fluid along a Vertical Wavy Surface”, Acta Mechanical. Vol. 101, pp.161-174, 1993.

Chiu, C. P. and Chou, H. M., “Transient analysis of natural convection along a vertical wavy surface in micropolar fluids,” International Journal of Engineering Science, Vol. 32, pp.19-33, 1994.

Eringen, A. C., “Simple microfluids,” Int. J. Engng. Sci., Vol. 2, pp.205-217, 1964.

Eringen, A. C., ”Theory of micropolar fluids,” Journal of Mathematical Mechanics, Vol. 16, No.1, pp.1-16, 1966.

Eringen, A. C., “Theory of thermomicro fluids,” Journal of Mathematical Analysis and Application, Vol. 38, No.9, pp.480-490, 1972.

Eringen, A. C., “Assessment of director and micropolar theories of liquid crystals,” International Journal of Engineering Science, Vol. 31, No.4, pp. 605-616, 1993.

Ericksen, J. L., “Theory of anisotropic fluids,” Transactions Society of Rheology, Vol. 4, pp.29-39, 1960.

Fyfe, D. J., “The use of cubic splines in the solution of two-point boundary value problems,” Computer Journal, Vol. 12, pp.188-192, 1969.

Goldstein, L. J. and Sparrow, E. M., “Heat/mass transfer characteristics for flow in a corrugated wall channel,” ASME Journal of Heat Transfer, Vol. 99, No.2, pp.187-195, 1977.

Gorla, R. S., Pender, R., Eppich, J., ”Heat Transfer in Micro-polar Boundary Layer Flow Over a Flat Plate,” Int.J. Engng.Sci., Vol. 21, pp.791-798, 1983.

Hudimoto, B. and Tokuoka, T., “Two-dimensional shear flows of linear micropolar fluids,” International J. of Engineering Science, Vol. 7, pp.515-522. 1969.

Jeffery, G. B., “The motion of ellipsoidal particies immersed in a viscous fluid,” Proceedings of the Royal Society of London, Series A, Vol.102, pp. 161-179, 1922.

Khonsari, M. M., “On the self-excited whirl orbits of a journal in a sleeve bearing lubricated with micropolar fluids,” Acta Mechanica, Vol. 81,No.3-4, pp.235-244, 1990.

Khonsari, M. M. and Brewe, D. E., “On the performance of finite journal bearings lubricated with micropolar fluids,” STLE Tribology Transactions, Vol.32, No.2, pp.155-160, 1989.

Kolpashchikov, V. L., Migun, N. P. and Prokhorenko, P. P., “Experimental determination of material micropolar fluid constants,” International Journal of Engineering Science, Vol.21, No.4, pp.405-411, 1983.

Lee, J. D. and Eringen, A. C., “Boundary effects of orientation of nematic liquid crystals,” J. Chem. Phys., Vol. 55, pp.4509-4512, 1971.

Lien, F. S., Chen, C.K., Cleaver, J.W., ”Analysis of Natural Convection Flow of Micropolar Fluid about a sphere with Blowing and Suction,” ASME J.Heat Transfer, Vol.108, pp.967-970., 1986.

Lien, F. S., Chen, T.M., Chen, C.K., ”Analysis of a Free-Convection Micro -polar Boundary Layer about a Horizontal Permeable Cylinder at a Non -uniform Thermal Condition,” ASME J.Heat Transfer, Vol.112, pp.504-506, 1990.

Lockwood, F. E., Benchaita, M. T. and Friberg, S. E., “Study of lyotropic liquid crystals in viscometric flow and elastohydrodynamic contact,” ASLE Tribology Transactions, Vol. 30, No. 4, pp.539-548, 1987.

Napolitano, M., “Efficient ADI and spline ADI Methods for the steady-state Navior-Stokes equations,” International Journal for Numerical Methods in Fluids, Vol. 4, pp.1101-1115, 1984.

O’Brien, J. E. and Sparrow, E. M., “Corrugated-duct heat transfer, pressure drop, and flow visualization, ”ASME Journal of Heat Transfer, Vol.104, No.3, pp.410-416, 1982
Prager, S., “Stress strain relations in a suspension of dumbbells,” Transactions Society of Rheology, Vol. 1, pp.53-62, 1957.

Raggett, G. F., Stone, J. A. R., and Wisher, S. J., “The cubic spline solution of practical problems modeled by hyperbolic partial differential equations,” Computer Methods in Applied Mechanics and Engineering, Vol.8, pp. 139-151, 1976.

Ramachandran, P. S., Mathur, M. N., Ojha, S. K., ”Heat Transfer in Boundary Layer Flow of a Micropolar Fluid Past a Curved Surface with Suction and Injection,” Int.J.Engng.Sci., Vol.17, pp.625, 1979.

Rohsenow, W. M., “Heat transfer and temperature distribution in laminar film condensation on a horizontal tube,” International Journal of Heat and Mass Transfer, Vol.27, pp.39-47, 1956.

Rubin, S. G. and Graves, R. A., “Viscous flow solution with a cubic spline approximation,” Computers and Fluids, Vol. 1, No.5, pp. 1-36, 1975.

Rubin, S. G. and Khosla, P. K., “Higher-order numerical solution using cubic splines,” AIAA Journal, Vol.14, pp.851-858, 1976.

Rubin, S. G. and Khosla, P. K., “Polynomial interpolation methods for viscous flow calculation,” Journal of Computational Physics, Vol.24, pp.217-244, 1977.

Saniei, N. and Dini, S., ”Heat transfer characteristics in a wavy-walled Channel,” ASME Journal of Heat Transfer, Vol.115, No.3, pp.788-792, 1993.

Wang, G. and Vanka, P.,”Convective heat transfer in periodic wavy passages,” International Journal of Heat and Mass Transfer. Vol. 38, No. 17, pp. 3219-3230, 1995.

Wang, P., Kahawita, R., “Numerical interration of patial differential equations using cubic spline.” Int. J. Computer Math., Vol.13, pp.271-286, 1983.

Wang, P., Lin, S., and Kahawita, R., “The cubic spline integration technique for solving fusion welding problems,” Journal of Heat Transfer, Vol. 107, pp. 485-489, 1985.

Yang, Y. T., Chen, C. K., Lin, M. T., “Natural convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect,” International Journal of Heat and Mass Transfer, Vol. 39, No. 13, pp.2831 -2842, 1996.

Yao, L. S., ”Natural convection along a Vertical Wavy Surface,” ASME J.Heat Transfer, Vol.105, pp.464-468, 1983.

Bejan, A., ‘‘Entropy Generation Through Heat and Fluid Flow,’’ Wily, New York, pp.109-114,1982

Bejan, A., Tsatsaronis, G. and Moran, M., ‘‘Thermal Design and Optimization,’’ Wiley, New York, NY, USA,1996.

Bejan, A., ‘‘A study of entropy generation in fundamental convective heat transfer,’’ ASME J. Heat Transfer, Vol.101, pp.718-725,1979.

Mahmud, S. and Fraser, R.A., ‘‘The second law analysis in fundamental convective heat transfer problems,’’ International Journal of Thermal Sciences, Vol.42, pp.177-186,2003.

Narusawa, U., ‘‘The Second-law analysis of mixed convection in rectangular ducts,’’ Heat Mass Transfer, vol.37, pp.1125-1129,2008.