Nonlinear Magnetohydrodynamic Radiating Flow Over an Infinite Vertical Plate in a Saturated Porous Medium: Laplace and Numerical Approaches

Abstract

A buoyancy-induced unsteady hydromagnetic thermal convection flow in a semi-infinite porous medium adjacent to an infinite vertical plate moving uniformly in the presence of a strong thermal radiation was investigated. The temperature of this flow was assumed to be very high to ensure that the radiative heat transfer was significant, which makes the problem highly nonlinear even in the case of differential approximation for the radiative heat flux. A system of nonlinear partial differential equations describing an unsteady flow of an MHD Newtonian fluid was normalized and solved using the Laplace transform technique and an implicit finite-difference scheme of the Crank–Nicolson type. The solutions obtained by the analytical and numerical methods are in excellent agreement. It was established that an increase in the porosity of the medium or in the magnetic field significantly decreases the shear stress in the case of air flow. As the radiation increases, the rate of heat transfer increases progressively in both the cases of air and water flows.