MHD THREE-DIMENSIONAL COUETTE FLOW THROUGH A POROUS MEDIUM IN THE PRESENCE OF THERMAL RADIATION
KOTAGIRI SRIHARI *
Department of Mathematics, Mahatma Gandhi Institute of Technology, Gandipet, Hyderabad, Telangana State, 500075, India
*Author to whom correspondence should be addressed.
Abstract
Usually obtaining exact solution for three-dimensional flow problems is very difficult due to its non-linearity and also numerical investigations pertaining to it are very limited. However, in the present work a numerical attempt is made to study the effect of thermal radiation on Couette flow of a viscous incompressible electrically conducting fluid between two horizontal parallel porous flat plates. A magnetic field is introduced perpendicular to the flow. Roseland approximation is used to describe the radiative heat flux in the energy equation. The plate in uniform motion and stationary plate are subjected to constant suction and the transverse sinusoidal injection of the fluid respectively. The flow becomes three-dimensional due to this type of sinusoidal injection velocity. The governing equations with corresponding conditions are solved using implicit-finite difference scheme and perturbation methods, for which simulation is carried out by coding in C-Program. Graphical results for velocity, temperature and Nusselt number are presented and discussed at various parametric conditions. It is observed that temperature and Nusselt number decrease in the presence of thermal radiation. The graphical results, which are obtained for Nusselt number in the absence of radiation and magnetic parameters, show a good agreement with previously published data.
Keywords: Three-dimensional, couette flow, magnetic field, thermal radiation, implicit-finite difference scheme