MHD Three-Dimensional Porous Flow with Heat Source and Chemical Reaction: a Numerical Study

Abstract

In prior research on three-dimensional flow problems has predominantly focused on deriving analytical solutions. However, numerical studies addressing such three-dimensional flow problems are still relatively limited. So, In the present paper numerical attempt is made to study the impact of a heat source and chemical reaction on the free convection flow of a viscous, incompressible fluid within a porous medium, confined by an infinite vertical porous plate subject to constant suction and periodic permeability. A magnetic field is applied perpendicular to the flow. To solve this problem, the governing non-linear equations with boundary conditions are first transformed into ordinary and partial differential equations of zeroth and first order, respectively, using the perturbation method. Subsequently, the partial differential equations, which describe three-dimensional flow, are reduced to coupled non-linear differential equations using appropriate substitutions. These resulting coupled non-linear equations are then approximated into a system of equations via finite difference methods. The findings for the velocity and temperature profiles are presented and analyzed graphically. It is found that both velocity and temperature increase with the introduction of the heat source parameter.