Unsteady MHD Flow in a Porous Channel with Thermal Radiation and Heat Source/Sink

TLDR: In this paper, the authors investigated the unsteady flow of a viscous, incompressible, electrically and thermally conducting fluid between two infinite parallel porous walls placed at y = 0 and y = 1.

Abstract: The current study investigates the unsteady flow of a viscous, incompressible, electrically and thermally conducting fluid between two infinite parallel porous walls placed at y = 0 and y = a. It is assumed that the electrically conducting fluid is driven by a mutual action of the imposed pressure gradient, thermal buoyancy and heat source or sink. The fluid injection occurs at the left boundary wall of the flow channel whereas the fluid suction occurs at the right boundary wall of the flow channel. The flow occurs only when the fluid starts to move with time. The flow is subjective to a convective heat exchange with the surrounding boundaries. The unsteady system of the non-dimensional form of PDEs with the corresponding boundary conditions are solved by employing the explicit Finite Difference Scheme. In the presence of pertinent parameters, a precise movement of the electrically conducting fluid within the flow channel is shown graphically in the form of profiles such as velocity, temperature, skin friction coefficient and Nusselt number. Distinct from the other studies, in which the boundary layer system of PDEs are usually transformed into a system of ordinary differential equations by means of the similarity transformations, the current study provides an efficient numerical procedure to solve the system of PDEs without using the similarity transformations which illustrate the precise movement of the electrically conducting fluid within the flow channel.