Modeling water quality assessment-based MHD flow with Forchheimer and chemical reaction effects over a stretching melting surface via RSM

Abstract

The study of magnetohydrodynamic (MHD) boundary layer flow over melting surfaces embedded in Darcy–Forchheimer porous media is essential for improving thermal management in industrial processes such as metal casting, polymer extrusion, and geothermal heat extraction. This research numerically investigates the combined effects of chemical reaction, thermal radiation, viscous dissipation, and Forchheimer inertial resistance on the velocity, temperature, and concentration distributions within an electrically conducting fluid flowing over a moving, melting surface. Assuming an incompressible Newtonian fluid and employing similarity transformations, the governing equations are formulated based on the conservation of mass, momentum, energy, and species concentration. The resulting system of nonlinear ordinary differential equations (ODEs) is solved using a shooting method in conjunction with the fourth-order Runge–Kutta scheme. Overall, the proposed numerical model effectively captures the interplay of magnetic, thermal, and chemical effects, offering valuable insights for the design of efficient thermal systems involving melting processes and porous structures.