Advances in Numerical Analysis
Volume 2011 (2011), Article ID 304124, 17 pages
doi:10.1155/2011/304124
Research Article

Unsteady Magnetohydrodynamic Heat Transfer in a Semi-Infinite Porous Medium with Thermal Radiation Flux: Analytical and Numerical Study

1Aerospace Engineering, Department of Engineering and Mathematics, Sheaf Building, Sheffield Hallam University, Sheffield S1 1WB, UK
2Thermal Engineering and Fluids Department, Technical University of Cartagena, Campus Muralla del Mar, 30202 Cartagena, Spain
3Magnetohydrodynamics, Applied Mathematics Program, Department of Mathematics, Narajole Raj College, P.O. Narajole, Midnapore 721 211, WB, India
4Institute for Advanced Studies, Tehran 14456-63543, Iran

Received 12 December 2010; Accepted 20 January 2011

Academic Editor: William J. Layton

Copyright © 2011 O. Anwar Bég et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The unsteady, buoyancy-induced, hydromagnetic, thermal convection flow in a semi-infinite porous regime adjacent to an infinite hot vertical plate moving with constant velocity, is studied in the presence of significant thermal radiation. The momentum and energy conservation equations are normalized and then solved using both the Laplace transform technique and Network Numerical Simulation. Excellent agreement is obtained between both analytical and numerical methods. An increase in Hartmann number ( 𝑀 2 ) strongly decelerates the flow and for very high strength magnetic fields ( 𝑀 2 = 2 0 ) , the flow is reversed after a short time interval. The classical velocity overshoot is also detected close to the plate surface for low to intermediate values of 𝑀 2 at both small and large times; however this overshoot vanishes for larger strengths of the transverse magnetic field ( 𝑀 2 = 1 0 ) . An increase in radiation-conduction parameter ( 𝐾 𝑟 ) significantly increases temperature throughout the porous regime at both small and larger times, adjacent to the plate, but decreases the shear stress magnitudes at the plate. Temperature gradient is reduced at the plate surface for all times, with a rise in radiation-conduction parameter ( 𝐾 𝑟 ). Shear stress is reduced considerably with an increase in Darcian drag parameter ( 𝐾 𝑝 ).