MHD Darchy-Forchheimer Convective Flow above a Vertical Permeable Plate with Radiative Heat Transfer and Chemical Reaction

Abstract

This research investigates two-dimensional, steady-state magnetohydrodynamic (MHD) Darcy Forchheimer flow over a moving vertical permeable surface within a porous medium. The study considers a laminar convective heat-generating fluid subjected to thermal radiation and chemical reaction effects. By accounting for inertia effects, numerical simulations were performed to analyze how velocity, thermal, and concentration boundary layers respond to various physical parameters under a transverse magnetic field. The governing nonlinear PDEs—representing continuity, momentum, energy, and species concentration—were transformed into a system of ODEs using similarity transformations under the Boussinesq approximation. These equations were subsequently solved using the shooting method (ode45) and the MATLAB BVP4C solver. It is found that, the dimensionless velocity increased by approximately 10.80% as the local Darcy number (Dax) rose from 0.5 to 5. Conversely, velocity decreased by roughly 5.17% with an increase in the local Forchheimer number (Fcx) from 0.1 to 1.4, and by 69.38% as the Hartmann number (Hax) increased from 0.1 to 5. Thermal performance weakened by 5.72% when Dax increased and by 45.45% as the radiation parameter (R) rose from 0.1 to 5.0. Furthermore, solute concentration fell by nearly 54.75% due to an increase in the chemical reaction parameter (Krx) from 0.2 to 5. While the skin friction coefficient (Cf) declined with higher Darcy numbers, it rose significantly with intensified Lorentz forces (Hax) and inertial resistance (Fcx). Additionally, the local Nusselt number (Nux) showed a marked decrease as R intensified, whereas the local Sherwood number (Shx) was substantially enhanced by stronger chemical reactions (Krx).