Asian Research Journal of Mathematics

This study presents a mathematical model to analyze the influence of thermophoresis on the unsteady flow of a non-Newtonian second-grade fluid, incorporating heat and mass transfer through a porous medium near a permeable, infinite vertical plate. The governing partial differential equations (PDEs) are derived and converted into a dimensionless form using similarity variables. The resulting nonlinear PDEs are solved numerically using the shooting method combined with a sixth-order Runge-Kutta scheme. The model integrates Hall current and magnetic effects into the continuity, momentum, energy, and concentration equations. Computational simulations are performed using Maple mathematical software. The formulated equations incorporate multiple physical phenomena, such as thermal radiation, heat generation, thermal diffusion (Soret effect), viscous dissipation, and chemical reactions. These dimensionless equations are solved numerically as functions of relevant physical parameters. The numerical solutions provide insights into the velocity components (u and w), temperature (θ), and concentration (C), as well as the Nusselt number (Nu) and Sherwood number (Sh). The findings are graphically illustrated and thoroughly discussed. The analysis highlights the impact of key physical parameters on the flow and transport characteristics. For instance, an increase in the heat source parameter (ϕ) boosts both primary and secondary velocities, while also elevating the temperature profile. Similarly, a rise in the chemical reaction parameter (γ) leads to higher velocities and significantly enhances the concentration distribution. These results are visually represented through graphs, offering a comprehensive understanding of the system's behavior under varying conditions.