Abstract
A numerical investigation is performed to study the MHD free convection flow past a semi-infinite inclined plate subjected to a variable surface temperature. The Joule heating and viscous dissipation effects are taken into account in the energy equation. The governing equations of the flow are transformed into a nondimensional form using suitable dimensionless quantities. A fully developed implicit finite-difference scheme of Crank-Nicolson type is engaged to solve the dimensionless governing equations, which is more accurate, fast convergent, and unconditionally stable. The effects of the MHD, inclination angle, power law, Grashof number, Prandtl number, Joule heating, and viscous dissipation effects are studied on the velocity, temperature, shear stress, and heat transfer coefficients during transient periods. It is observed that the MHD has retarding effects on velocity.
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Hellums, J.D. and Churchill, S.W., Transient and Steady State, Free and Natural Convection, Numerical Solutions: Part 1. The Isothermal Vertical Plate, AIChEJl, 1962, vol. 8, pp. 90–692.
Soundalgekar, V.M. and Ganesan, P., Finite-Difference Analysis of Transient Free Convection on an Isothermal Vertical Flat Plate, Reg. J. Energy Heat Mass Transfer, 1981, vol. 13, pp. 219–224.
Kierkus, W.T., An Analysis of Laminar Free Convection Flow and Heat Transfer about an Inclined Isothermal Plate, Int. J. Heat Mass Transfer, 1968, vol. 11, pp. 241–253.
Chen, T.S., Tien, H.C., and Armaly, B.F., Natural Convection on Horizontal, Inclined and Vertical Plates with Variable Surface Temperature or Heat Flux, Int. J. Heat Mass Transfer, 1986, vol. 29, pp. 1465–1478.
Ekambavannan, K. and Ganesan, P., Finite Difference Solution of Unsteady Natural Convection Boundary-Layer Flow over an Inclined Plate with Variable Surface Temperature, Wärme Stoffübertragung, 1994, vol. 30, pp. 63–69.
Gebhart, B., Effects of Viscous Dissipation in Natural Convection, J. Fluid Mech., 1962, vol. 14, pp. 225–232.
Soundalgekar, V.M., Lahurikar, R.M., and Pohanerkar, S.G., Transient Free Convection Flow of an Incompressible Viscous Dissipative Fluid, Heat Mass Transfer, 1997, vol. 32(4), pp. 301–305.
Soundalgekar, V.M., Jaiswal, B.S., Uplekar, A.G., and Takhar, H.S., Transient Free Convection Flow of Viscous Dissipative Fluid past a Semi-Infinite Vertical Plate, J. Appl. Mech. Eng., 1999, vol. 4, no. 2, pp. 203–218.
Ganesan, P. and Palani, G., Transient Free Convection Flow of Viscous Dissipative Fluid Past a Semi-Infinite Inclined Plate, J. Appl. Mech. Eng., 2003, vol. 8, no. 3, pp. 395–402.
Pantokratoras, A., Effect of Viscous Dissipation and Pressure Stress Work in Natural Convection along a Vertical Isothermal Plate, New Results, IJHMT, 2003, vol. 46, pp. 4979–4983.
Pantokratoras, A., Effect of Viscous Dissipation in Natural Convection along a Heated Vertical Plate, Appl. Math. Modell., 2005, vol. 29, pp. 553–564.
Magyari, E. and Rees, D.A., Effect of Viscous Dissipation on the Darcy Free Convection Boundary-Layer Flow over a Vertical Plate with Exponential Temperature Distribution in a Porous Medium, Fluid Dyn. Res., 2006, vol. 38, pp. 405–429.
Sparrow, E.M. and Cess, R.D., The Effect of a Magnetic Field on Free Convection Heat Transfer, Int. J. Heat Mass Transfer, 1961, vol. 3, no. 4, pp. 267–274.
Kumari, M. and Nath, G., Development of Two-Dimensional Boundary Layer with an Applied Magnetic Field Due to an Impulsive Motion, Ind. J. Pure Appl. Math., 1999, vol. 30, pp. 695–708.
Takhar, H.S., Chamkha, A.J., and Nath, G., Unsteady Mixed Convection Flow from a Rotating Vertical Cone with Magnetic Field, Heat Mass Transfer, 2003, pp. 297–304.
Chamkha, A.J. and Al-Mudaf, A., Unsteady Heat and Mass Transfer from a Rotating Vertical Cone with a Magnetic Field and Heat Generation or Absorption Effects, Int. J. Thermal Sci., 2005, no. 44, pp. 267–276.
Mehmet, C.E., Free Convection Flow about a Vertical Spinning Cone under a Magnetic Field, Appl. Math. Comp., 2006, no. 179, pp. 231–242.
Takhar, H.S. and Soundalgekar, V.M., Dissipation Effects on MHD Free Convection Flow past a Semi-Infinite Vertical Plate, Appl. Sci. Res., 1980, vol. 36, pp. 163–172.
El-Amin, M.F., Combined Effect of Viscous Dissipation and Joule Heating on MHD Forced Convection over a Non-Isothermal Horizontal Cylinder Embedded in a Fluid Saturated Porous Medium, J. Magnetism Magnetic Materials, 2003, vol. 263, pp. 337–343.
Pop, I. and Watanabe, T., Hall Effects on Magnetohydrodynamic Free Convection about a Semi-Infinite Vertical Flat Plate, Int. J. Eng. Sci., 1994, vol. 32, pp. 1903–1911.
Megahed, A.A., Komy, S.R., and Afify, A.A., Similarity Analysis in Magnetohydrodynamics: Hall Effects on Free Convection Flow and Mass Transfer past a Semi-Infinite Vertical Flat Plate, 2003, vol. 38, pp. 513–520.
Roming, M.F., The Influence of Electric and Magnetic Fields on Heat Transfer to Electrically Conducting Fluid, Advances in Heat Transfer, New York: Academic Press, 1964, pp. 286–354.
Abd El-Naby, M.A., Elsayed, M.E., and Nayed, Y.A., Finite Difference Solution of Radiation on MHD Unsteady Free-Convection Flow over Vertical Porous Plate, Appl. Math. Comp., 2004, vol. 151, pp. 327–246.
Carnahan, B., Luther, H.A., and Wilkes, J.O., Applied Numerical Methods, New York: Wiley, 1969.
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Palani, G., Kim, K.Y. Joule heating and viscous dissipation effects on MHD flow past a semi-infinite inclined plate with variable surface temperature. J. Engin. Thermophys. 20, 501–517 (2011). https://doi.org/10.1134/S1810232811040138
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DOI: https://doi.org/10.1134/S1810232811040138