Effects of Nonlinear Thermal Density Variation and Radiation on MHD Mixed Convection Through a Porous Medium Over a Permeable Vertical Plate: A Numerical Approach

In the present paper, we study the effect of nonlinear thermal radiation on magnetohydrodynamic (MHD) flow through a porous medium subject to a convective boundary condition over a permeable vertical plate. The Boussinesq approximation is used to predict nonlinear density variation with temperature (NDT), which enhances thermal transport. Similarity transformations facilitate the conversion of the governing nonlinear partial differential equations into nonlinear ordinary differential equations, enabling further analysis. The solutions are obtained and presented graphically using the bvp4c method in MATLAB. The primary objective of our study is to analyze the effects of suction/injection, NDT, and nonlinear thermal radiation on MHD flow dynamics and temperature distribution. The conclusions reveal that the nonlinear Boussinesq approximation parameter and Grashof number enhance buoyancy forces, increasing velocity boundary layer thickness and improving heat dissipation. Higher nonlinear thermal radiation raises fluid temperature, reduces viscosity, and thickens both boundary layers. Suction enhances flow stability by thinning boundary layers and facilitating efficient heat transfer, whereas strong injection increases the boundary layer thickness, retains heat, and disrupts flow stability. A higher magnetic parameter slows velocity more in suction and thickens the thermal boundary layer in injection. A greater Prandtl number reduces boundary layer thickness and enhances the Nusselt number, while a higher convective heat transfer parameter increases both boundary layer thickness and skin friction in suction. We have compared our numerical results with those of previous studies and observed an excellent agreement. The novelty of this study lies in its unique approach to modeling nonlinear thermal radiation, suction/injection, and its impact on MHD flow and heat transfer in porous media. The findings have practical implications for various engineering fields, including energy systems, aerospace, biomedical engineering, chemical processing, and environmental engineering, contributing to the optimization of heat transfer in technological applications.