本論文為分析微極流體在磁場及化學反應下通過波形渠道的熱質傳現象。微極流體是採用Eringen所推導的理論，化學反應則是以Anjalidevi所使用的化學反應參數，而統御方程式是以完整的Navier-Stokes方程式推導完成，無因次化後再對波形表面做座標轉換，數值方法則是以三次樣線交換方向定置法( SADI )來求其數值解。
分析結果顯示，雷諾數對於在波形渠道中的熱質傳依然有很大的影響力，雖然微極流體的渦漩黏度、旋轉梯度黏度及微慣量使得渦漩度下降，但由於微極流體有較牛頓流體為高的黏滯性，因此會增加阻力及降低熱質傳。波形表面會使得表面積增加進而提高熱質傳率，但也會使迴流區擴大進而降低此區的效率，也就是俗稱的”死水區”，但加入磁場效應之後會使得渠道中心流速變慢，接近壁面的流速加快，熱質傳率便會大增，但所付出的代價就是要增加驅動力。因溫度差及濃度差產生的浮力效應會使流速加快，摩擦係數、Nusselt數、Sherwood數也都會上升，迴流區則會變小甚至消失。化學反應在混合對流時，比較不會有使濃度逆傳遞的現象產生，且只會對質傳效果產生比較大的影響。

The micropolar fluids pass through a wavy-wall channel whit magnetic field effect and chemical reaction has been analyzed. We used the theory of micropolar fluid that derived by Erigen and took the chemical parameter that used by Anjalidev. The governing equations of system are derived from complete Navier-Stokes equations with theories of micropolar fluid and chemical reaction parameter. After dimensionless, we used a coordinate transformation method to expand the irregular boundary into a calculable regular and spline alternating- direction implicit (SADI) method to solve the equation.
Numerical results show that, heat and mass transfer rate will increase when rise the Reynolds number. In micropolar fluid, though, the characteristics of effects of vortex viscosity, spin-gradient viscosity and micro-inertia density will increase the vorticity, the drag force and transfer rate will get rise and down respectively because of that micropolar fluids has higher viscosity than Newtonian fluid. Use the model of wavy channel will increase the quantity of heat transfer area but it will arise the area of vortex called “dead water”. Including the magnetic field effect can decrease the velocity in the middle of the channel and increase near the wavy surface, and the heat transfer rate will get better. Furthermore, it should be noted that adding in heat transfer rate usually implies the increase in skin-friction coefficient. This would make a penalty in pumping power required for wavy channels. When including the buoyancy force effects cause by temperature and concentration difference will add the velocity and then raise the skin-friction coefficient, Nusselt number and Sherwood number. Chemical reaction is just effect upon the mass transfer rate in mixed convection.

Agarwal, S. and Dhanapal, C.,“Flow and heat transfer in a micropolar fluid past a flat plate with suction and heat sources,” International Journal of Engineering Science, Vol. 2, pp. 1257-1266, 1988.

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

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

Anjalidevi, S. P. and Kandasamy, R., “Effects of chemical reaction, heat and mass transfer on laminar flow along semi infinite horizontal plate,” Journal of Heat and Mass Transfer, Vol. 35, pp. 465-467, 1999.

Arimana, T. and Turk, M. A. and Sylvester, N. D., ”Applications of microcontinuum fluid mechanics,” International Journal of Engineering Science, Vol. 12, No. 4, 1974, pp. 273-293.

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.

Arimanc, T and Turk, M. A. and Sylvester, N. D., ”Microcontinuum fluid mechanics- a review,” International Journal of Engineering Science, Vol. 11, pp. 905-930, 1973.

Bejan, A., ”Convection heat transfer-2nd ed.,” Wiley-Interscience, pp. 477-511, 1995.

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

Crank, J., “The mathematics of diffusion-2nd ed,” Oxford University Press, pp.350-351, 1975

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, N.C.K.U., Tainan, Taiwan, pp. 167-182, 1986.

Chen, C. K and Chen, W. L. “Study on the mixed convective heat transfer in 3-D channel,” N.C.K.U., Tainan, Taiwan, pp. 1-38 1989.

Chen, C. H., “Mixed convection cooling of a heated, continuously stretching surface,” Journal of Heat and Mass Transfer, Vol. 36, pp. 79-86, 2000.

Chakranarty, S. and Sannigrahi, A. Kr., “A nonlinear mathematical model of blood flow in a constricted artery experiencing body acceleration,” Mathematical and Computer Modeling, Vol. 29, pp. 9-25, 1999.

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.

Chiou, C. M., “Particle deposition from natural convection boundary layer flow onto an isothermal vertical cylinder,” Acta Mechanica, Vol. 129, pp. 163-176, 1998.

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

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.

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.

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.

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.

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.

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, C. C. ”Investigation of wavy surface effects in heat transfer of film condensation on horizontal plates and of non-Newtonian fluids through plates and channels,” Dissertation for Doctor of Philosophy, , N.C.K.U., Tainan, Taiwan, pp. 104-129, 2001.

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.

Wangb, P. and Kahawita, R., “Numerical integration of partial differential equations using cubic splines,” International Journal of Computer Mathematics, Vol. 13, No. 3-4, 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.