Extension of Homann’s axisymmetric rear stagnation-point flow: Unsteady MHD and heat transfer over a porous surface

This study extends Homann’s axisymmetric rear stagnation-point model by incorporating unsteady magnetohydrodynamic (MHD) effects and porous boundary influence, motivated by applications in electromagnetic cooling, porous material processing, and advanced thermal management. A new similarity transformation reduces the governing equations to nonlinear boundary value problems, which are solved using a hybrid symbolic–numerical method with MATLAB’s bvp4c. Results reveal dual solutions for $\lambda <0$; increasing the magnetic parameter $M$ enhances surface shear but reduces heat transfer, while negative unsteadiness increases skin friction and suppresses the Nusselt number. Boundary layer separation accelerates with rising $M$ and $\kappa$, and only the primary solution is stable. The proposed framework combines analytical reduction, numerical integration, and a new similarity formulation, offering improved predictive capability for controlling heat transfer and flow behavior in electromagnetic cooling systems and porous media devices.