Combined effect of suction/injection on MHD free-convection flow in a vertical channel with thermal radiation

Abstract

Transient hydromagnetic free-convection and thermal radiation flow of viscous, incompressible electrically conducting fluid in the presence of magnetic field in a vertical channel formed by two infinite porous plates is analyzed. The Rosseland diffusion approximation describes the radioactive heat flux in the energy equation. The non-linear time dependent energy and momentum equations under relevant initial and boundary conditions are solved numerically using implicit finite difference. To verify the accuracy of the numerical scheme, steady state version of the problem is solved by perturbation method. A series of numerical experiments show that time required to reach steady state velocity and temperature is directly proportional to the Prandtl number of the working fluid. In the course of numerical computation, an excellent agreement was found between transient and steady state solution at large value of time. The effect of various dimensionless parameters controlling the physical situation is extensively discussed with the aid of graphs. Keywords: Thermal radiation, MHD, Transient, Rosseland approximation