The effect of Hall current on an unsteady MHD free convective Couette flow between two permeable plates in the presence of thermal radiation

Abstract

An investigation on the non – linear problem of the effect of Hall current on the unsteady magneto hydrodynamic free convective Couette flow of incompressible, electrically conducting fluid between two permeable plates is carried out, when a uniform magnetic field is applied transverse to the plate, while the thermal radiation, viscous and Joule’s dissipations are taken into account. The fluid is considered to be a gray, absorbing – emitting but non – scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The dimensionless governing coupled, non – linear boundary layer partial differential equations are solved by an efficient, accurate, and extensively validated and unconditionally stable finite difference scheme of the Crank – Nicolson method. The effects of thermal radiation and Hall current on primary and secondary velocity, skin friction and rate of heat transfer are analyzed in detail for heating and cooling of the plate by convection currents. Physical interpretations and justifications are rendered for various results obtained.