本文探討強制對流下牛頓流體流經複雜波形渠道之熱傳遞分析。渠道之幾何模型為上下對稱的複雜波形壁面，壁面由兩個不同頻率的正弦函數合成，分別是基本頻波(fundamental wave)及其諧波(harmonic wave)，波頻率相差兩倍。相較於單一正弦函數，複雜波形壁面的流體運動情形更為複雜。本文運用座標轉換理論，求解各種不規則波形壁面的熱傳問題，將各種不規則邊界展開成一規則平面。藉由改變壁面幾何形狀增加熱傳增益是相當受人重視的主題，複雜的幾何壁面可透漏出更多真實的物理現象，因此經常應用於熱傳遞的強化過程。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。

A forced-convection through a complex wavy-wall channel has been investigated. The geometry model considered is an asymmetric complex wall channel, whose surface is described by two sinusoidal functions, a fundamental wave and its first harmonic. It is more complex than the single sinusoidal surface extensively studied in the past two decades. The method of transformed coordinates was used as a tool to solve heat-transfer problems in the presence of irregular surfaces of all kinds. The problem of forced convection along a complex surface has received considerable attention due to its relevance to real geometries and it occurs often in problems involving the enhancement of heat transfer. One of the reasons why a complex-wavy wall is more efficient in heat transfer is its capability to promote a correspondingly complicated fluid motion near the surface; in this way a complex-wavy surface, a sum of two or more sinusoidal surfaces, is expected to promote a larger heat-transfer rate than a single sinusoidal surface. The numerical results demonstrate that the additional harmonic substantially alters the flow field and temperature distribution. Moreover, the total heat-transfer rate for a complex-wavy wall channel is greater than that for a corresponding flat plate or for a single sinusoidal surface.

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.