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Technical Briefs

Unsteady Magnetohydrodynamic Free Convection Flow Past a Semi-Infinite Permeable Moving Plate Through Porous Medium With Chemical Reaction and Radiation Absorption

[+] Author and Article Information
Mohamed A. Hassan

e-mail: M_a_Hassan_gk@hotmail.com

Wessam A. Godh

e-mail: al_ostaz_y2k@yahoo.com
Department of Mathematics,
Faculty of Education,
Ain Shams University,
Heliopolis, Cairo, 11566, Egypt

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received September 16, 2011; final manuscript received August 17, 2012; published online December 26, 2012. Assoc. Editor: Ali Ebadian.

J. Heat Transfer 135(2), 024501 (Dec 26, 2012) (5 pages) Paper No: HT-11-1446; doi: 10.1115/1.4007474 History: Received September 16, 2011; Revised August 17, 2012

The effect of the chemical reaction and radiation absorption on the unsteady free convective flow of an incompressible viscous fluid through porous medium past a semi-infinite vertical permeable moving plate is studied. The system is stressed by a uniform transverse magnetic field. The system equations are derived for the flow over a vertical plate and the resulting nonlinear coupled differential equations are solved numerically by finite difference technique. Also, the case of the flow over a horizontal plate was studied analytically by using the perturbation technique. A comparison between the case of vertical and horizontal flow was illustrated graphically to access the accuracy of our numerical calculations, and the results show an excellent agreement. The effects of various parameters on the velocity, temperature and concentration profiles are presented graphically and the physical aspects of the problem are highlighted and discussed.

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References

Hassanien, I. A., Bakier, A. Y., Gorla, R. S. R., 1998, “Effect of Thermal Dispersion and Stratification on Non-Darcy Mixed Convection From a Vertical Plate in a Porous Medium,” Heat Mass Transfer, 34, pp. 209–212. [CrossRef]
Chamkha, A. J., Khaled, A. A., 2000, “Similarity Solutions for Hydromagnetic Mixed Convection Heat and Mass Transfer for Hiemenz Flow Through Porous Media,” Int. J. Num. Methods Heat Fluid Flow, 10(1), pp. 94–115. [CrossRef]
Patil, P. M., and Kulkarni, P. S., 2008, “Effects of Chemical Reaction on Free Convective Flow of a Polar Fluid Through a Porous Medium in the Presence of Internal Heat Generation,” Int. J. Therm. Sci., 47(8), pp. 1043–1054. [CrossRef]
Makinde, O. D., and Sibanda, P., 2008, “Magnetohydrodynamic Mixed-Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium With Constant Wall Suction,” ASME J. Heat Transfer, 130, p. 112602. [CrossRef]
Shercliff, J. A., 1965, A Text Book of Magnetohydrodynamics, Pergamon Press, Inc., New York.
Davidson, P. A., 2001, An Introduction to Magnetohydrodynamics, Cambridge University Press, New York.
Kandasamy, R., Periasamy, K., and Sivagnana Prabhu, K. K., 2005, “Chemical Reaction, Heat and Mass Transfer on MHD Flow Over a Vertical Stretching Surface With Heat Source and Thermal Stratification Effects,” Int. J. Heat Mass Trans., 48(21), pp. 4557–4561. [CrossRef]
Chen, C. H., 2004, “Combined Heat and Mass Transfer in MHD Free Convection From a Vertical Surface With Ohmic Heating and Viscous Dissipation,” Int. J. Eng. Sci., 42, pp. 699–713. [CrossRef]
Kinyanjui, M., Kwanza, J. K., and Uppal, S. M., 2001, “Magnetohydrodynamic Free Convection Heat and Mass Transfer of a Heat Generating Fluid Past an Impulsively Started Infinite Plate With Hall Currents and Radiation Absorption,” Energy Convers. Manage, 42, pp. 917–931. [CrossRef]
Ibrahim, F. S., Elaiw, A. M., and Bakr, A. A., 2008, “Effect of the Chemical Reaction and Radiation Absorption on the Unsteady MHD Free Convection Flow Past a Semi Infinite Vertical Permeable Moving Plate With Heat Source and Suction,” Commun. Nonlinear Sci. Numer. Simul.13, pp. 1056–1066. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Flow configuration and coordinate system

Grahic Jump Location
Fig. 2

Velocity plotted versus y with analytical and numerical results at Pr = 0.7, Gr = 0, M = 5, φ = 1, n = 0.05 π, K = 0.6, Gm = 0, Q1 = 1, Ec = 0.5, Sc = 0.3, up = 0.5, γ = 0.5, ε = 5

Grahic Jump Location
Fig. 3

Plots of Cf versus t for the effects of Ec and K at Pr = 0.7, φ = 1, M = 5, ε = 0.001, n = 5 π, Gm = 2, γ = 0.5, Sc = 1.5, up = 0.5, Gr = 1, Q1 = 1

Grahic Jump Location
Fig. 4

Plots of Nux/Rex versus t for the effects of Ec and K at Pr = 0.7, φ = 1, M = 5, ε = 0.001, n = 5 π, Gm = 2, γ = 0.5, Sc = 1.5, up = 0.5, Gr = 1, Q1 = 1

Grahic Jump Location
Fig. 5

Plots of Nmx/Rex versus t for the effects of Sc and γ at Pr = 0.7, φ = 1, M = 5, ε = 0.001, n = 5 π, Gm = 2, K = 0.6, Ec = 0.5, up = 0.5, Gr = 1, Q1 = 1

Grahic Jump Location
Fig. 6

Velocity plotted versus y with analytical and numerical results at Pr = 0.7, Gr = 0, M = 5, φ = 1, n = 0.01 π, K = 0.6, Gm = 0, Q1 = 1, Ec = 0.5, Sc = 0.3, up = 0.5, γ = 0.5, ε = 0.01

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