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Finite difference approach in porous media transport modeling for magnetohydrodynamic unsteady flow over a vertical plate : Darcian model

Sahin Ahmed (Department of Mathematics, Heat Transfer and Fluid Mechanics Research, Goalpara College, Assam, India)
Abdul Batin (Department of Mathematics, Indira Gandhi College, Boitamari, Bongaigaon, Assam, India)
Ali J. Chamkha (Manufacturing Engineering Department, The Public Authority for Applied Education and Training, Shuweikh, Kuwait)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 27 May 2014




The purpose of this paper is to examine the effects of Darcian drag force and radiation-conduction on unsteady two-dimensional magnetohydrodynamic flow of viscous, electrically conducting and Newtonian fluid over a vertical plate adjacent to a Darcian regime in presence of thermal radiation and transversal magnetic field. A well-tested, numerically stable Crank-Nicolson finite-difference procedure is employed for the conservation equations. Excellent agreement is obtained for numerical solutions with previously published work.


In this investigation, an efficient, accurate, extensively validated and unconditionally stable finite-difference scheme based on the Crank-Nicolson model is developed to solve the governing coupled, non-linear partial differential equations. The accuracy and effectiveness of the method are demonstrated.


Different numerical results are obtained and presented graphically to explain the effect of various physical parameters on the velocity and temperature profiles, local, as well as average, skin friction and Nusselt number. It is found that, with a rise in Darcian drag force, flow velocity and temperature are reduced, but increased for all times. Both average and local skin frictions are reduced considerably with an increase in Darcian drag force, but reversed behavior is observed for the local Nusselt number. Increasing the thermal radiation effects accelerated the flow velocity as well as the fluid temperature and wall local skin friction in a saturated porous medium, but effectively reduced the local Nusselt number and average Nusselt number at the wall. Comparison with previously published works in the limits shows excellent agreement.

Research limitations/implications

The analysis is valid for unsteady, two-dimensional laminar flow of an optically thick no-gray gas, electrically conducting, and Newtonian fluid past an isothermal vertical surface adjacent to the Darcian regime with variable surface temperature. An extension to three-dimensional flow case is left for future work.

Practical implications

Practical interest of such study includes applications in electromagnetic lubrication, boundary cooling, bio-physical systems and in many branches of engineering and science. It is well known that the effect of thermal radiation is important in space technology and high temperature processes. Thermal radiation also plays an important role in controlling heat transfer process in polymer processing industry.



Ahmed, S., Batin, A. and J. Chamkha, A. (2014), "Finite difference approach in porous media transport modeling for magnetohydrodynamic unsteady flow over a vertical plate : Darcian model", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 5, pp. 1204-1223.



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