Numerical analysis of radiative MHD gravity-driven thin film third-grade fluid flow with exothermic reaction and modified Darcy's law on an inclined plane

This study presents a transient investigation of radiative magnetohydrodynamics (MHD) third-order (TO) chemical reactive single-step exothermic gravity-driven fluid flow through a porous medium with various kinetics, that is, zero-order, sensitised and bimolecular. The modified Darcy law to model the porous medium resistance to flow, temperature-dependent viscosity following the Nahme-type principle and convective heat exchange at the free surface boundary by Newton's cooling law are considered in the flow governing equations. Numerical solutions of the non-linear governing flow equations are obtained using a stable and convergent semi-implicit finite difference approach with Matlab. The physical insights reveal that the reaction and radiation parameters play an essential role in determining the thermo-dynamical behaviour of the system, particularly in averting thermal runaway. The study additionally shows that the velocity and temperature profiles are significantly influenced by the porous parameter, the Grashof number, the Reynolds number and the magnetic parameter. The graphical results demonstrate that a porous medium and magnetic field suppress the velocity and temperature, indicating a stabilising effect on the flow. The findings underscore the importance of meticulously controlling the radiation and reaction parameters to avoid potential blow-up scenarios in practical applications. The validity of our numerical investigations was compared with the published reported results and was found to be in excellent agreement.