Lie similarity analysis of MHD Casson fluid flow with heat source and variable viscosity over a porous stretching sheet

The current study presents a novel examination of heat transfer properties in a magnetohydrodynamic (MHD) flow of Casson fluid across a porous stretching sheet, uniquely incorporating the effects of heat source and variable viscosity. Unlike previous studies, this research employs the Lie similarity transformation to convert the governing equations into a dimensionless form. These transformed equations are then solved using advanced numerical techniques, specifically the fourth-order Runge-Kutta (RK) along with shooting method. The findings reveal that the velocity decreases with the adjustment of significant parameters such as the Casson fluid properties, variable viscosity, heat source, magnetic field, and porosity, leading to an inverse increase in temperature within the convection system. As the Prandtl number increases, the temperature gradient and thermal boundary layer thickness decrease, resulting in reduced heat transfer rates within the convection system. Likewise, an increase in the Schmidt number decreases the concentration gradient and mass transfer rate within the fluid. This novel approach provides new insights into the behavior of Casson fluids, with significant applications in industrial processes, energy systems, environmental engineering, material science, and aerospace and automotive industries, where understanding heat transfer mechanisms in complex systems can enhance efficiency, performance, and safety.