Steady MHD free convection of Casson fluid over a vertical porous plate with cross-diffusion, thermal radiation, viscous dissipation, Joule heating and chemical reaction

Abstract A theoretical study examines steady magnetohydrodynamic (MHD) free convection of an incompressible, electrically conducting Casson fluid over a vertical porous plate, including coupled Soret and Dufour effects. Thermal radiation, viscous dissipation, Joule heating, internal heat generation, and a first-order chemical reaction are incorporated to capture relevant transport mechanisms. The governing nonlinear equations are transformed into ordinary differential equations via similarity transformations and solved analytically using the multiple regular perturbation method. The analysis highlights the combined influence of cross-diffusion, rheology, and the magnetic field on momentum, heat, and mass transfer characteristics. Results indicate that thermal and solutal buoyancy, higher permeability, thermal radiation, an internal heat source, and a rising Casson parameter significantly enhance fluid velocity within the boundary layer. Conversely, the magnetic field parameter, viscous dissipation, higher Prandtl and Schmidt numbers, and a destructive chemical reaction suppress the primary velocity profile. Furthermore, Soret and Dufour effects, radiation, and heat generation expand the thermal field, whereas higher Prandtl numbers sharply contract it. The concentration boundary layer thins with increasing Soret, Dufour, Schmidt, and chemical reaction parameters, thereby steepening the concentration gradient at the wall. Ultimately, increasing Prandtl and Schmidt numbers substantially improves the Nusselt and Sherwood numbers, respectively, while the non-Newtonian Casson fluid exhibits a notable heat-absorption transition at higher parameter values. These findings offer valuable insights for optimising thermal engineering systems and biomedical transport loops in porous media.