Mathematical and computational study of magnetohydrodynamic flow and mass transfer past a semi-infinite vertical plate

Abstract

This study presents a resolution numerical investigation of transient magnetohydrodynamic (MHD) flow of an electrically conducting, incompressible, and viscous fluid past a semi-infinite vertical plate in the presence of mass transfer and a transverse magnetic field. Unlike previous studies, the present work simultaneously accounts for unsteady effects, buoyancy-driven convection, and species diffusion within a unified computational framework. The analysis assumes that viscous dissipation and induced magnetic field effects are negligible, which is appropriate for flows characterized by low magnetic Reynolds numbers. The governing conservation equations for momentum, energy, and species concentration are formulated in dimensionless form, resulting in a system of coupled, nonlinear, and time-dependent partial differential equations. To accurately capture the transient behavior and strong coupling between physical variables, an implicit finite difference method is employed. This numerical scheme provides unconditional stability, high computational efficiency, and rapid convergence, making it well suited for simulating complex MHD convection problems. The computational approach allows precise resolution of velocity, temperature, and concentration fields within the boundary layer region. Special attention is given to the influence of buoyancy forces associated with external cooling conditions, corresponding to positive values of the thermal Grashof number $(Gr>0)$, which characterize free convection regimes where density gradients drive the flow. The effects of key governing parameters, including the magnetic field strength and buoyancy intensity, on the fluid dynamics and thermal transport characteristics are systematically examined. The results demonstrate that the presence of a magnetic field significantly alters the velocity distribution due to the Lorentz force, which acts to suppress fluid motion and modify the boundary layer thickness. Additionally, variations in buoyancy forces strongly influence the development of thermal and momentum boundary layers. Important engineering quantities, such as skin friction, are evaluated to quantify surface shear stress behavior under different physical conditions. The findings provide valuable insights into the coupled interaction between magnetic fields, heat transfer, and mass transport, with potential applications in thermal management systems, metallurgical processes, cooling technologies, and electromagnetic flow control.