An Approach to implement viscous dissipative Couette flow between vertical permeable plates with Thermal radiation effect on Magneto Hydro Dynamic

Abstract

The objective of this paper to find the numerical solution of unsteady magneto hydro dynamic free convective Couette flow of viscous incompressible fluid confined between two vertical permeable parallel plates in the presence of thermal radiation is performed. A uniform magnetic field which acts in a direction orthogonal to the permeable plates, and uniform suction and injection through the plates are applied. The magnetic field lines are assumed to be fixed relative to the moving plate. The momentum equation considers buoyancy forces while the energy equation incorporates the effects of thermal radiation. The fluid is considered to be a gray absorbing – emitting but non – scattering medium in the optically thick limit. The Roseland and approximation is used to describe the radioactive heat flux in the energy equation. The two plates are kept at two constant but different temperatures and the viscous and Joule dissipations are considered in the energy equation. The non – linear coupled pair of partial differential equations are solved by an efficient Crank Nicholson method. With the help of graphs, the effects of the various important flow parameters entering into the problem on the velocity, temperature and concentration fields within the boundary layer are discussed. Also the effects of these flow parameters on skin friction coefficient and rates of heat and mass transfer in terms of the Nussle and Sherwood numbers are presented numerically in tabular form.