The present study aims to numerically investigate the coupled momentum, heat, and mass transfer characteristics of magnetohydrodynamic (MHD) Casson fluid flow over a nonlinear stretching sheet embedded in a porous medium under variable thermal conditions. A review of existing literature indicates that the combined influence of variable viscosity, variable thermal conductivity, Soret Dufour effects, thermal radiation, viscous dissipation, melting heat transfer, chemical reaction, and regression-based prediction has not been addressed comprehensively in a single framework. To bridge this research gap, a mathematical model incorporating these multiphysics effects is developed. The governing nonlinear partial differential equations are transformed into a system of coupled ordinary differential equations using suitable similarity transformations and are solved numerically with MATLAB’s bvp4c boundary-value solver. An extensive parametric study is performed to analyze the effects of key dimensionless parameters on velocity, temperature, and concentration distributions, supported by streamline and isotherm visualizations for enhanced physical interpretation. The results indicate that increasing magnetic and porosity parameters significantly suppress the velocity field, while a higher Prandtl number reduces thermal boundary layer thickness. The melting parameter is found to decrease temperature and concentration profiles due to enhanced latent heat absorption, whereas Soret and Dufour effects strongly influence mass and heat transfer coupling. Skin friction coefficient, Nusselt number, and Sherwood number are evaluated, and regression-based correlations are developed, showing excellent agreement between predicted and numerical results. The findings of this study provide valuable insights for the design and optimization of engineering systems such as polymer extrusion processes, metallurgical cooling operations, electronic thermal management, geothermal energy systems, and chemical processing in porous environments.
B.C. et al. (Tue,) studied this question.