Computational analysis of radiation effects in Williamson fluid flow through a porous medium under an inclined magnetic field

Various technical and commercial processes, including polymer extrusion, biomedical transport, and improved oil recovery, depend on the simulation of non-Newtonian fluid behaviour. Of the non-Newtonian models, the Williamson fluid best reflects shear-thinning properties; nonetheless, its non-linear governing equations provide major difficulties for conventional numerical methods. This work tackles these issues by suggesting a unique two-stage explicit computational method to solve the time-dependent flow of Williamson fluid through a Darcy-Forchheimer porous media under the effect of thermal radiation and an angled magnetic field. The approach uses a compact finite difference method for space (sixth-order accuracy) and a modified exponential integrator for time discretization (second-order accuracy). Including internal heat generation and chemical reaction, the model is nondimensionalized and solved under unsteady boundary conditions. The suggested approach shows better accuracy and lower numerical error when compared to the classical second-order Runge-Kutta scheme. Key results show that although larger reaction rates result in lower concentration, more velocity is produced by raising the Darcy number and lowering the magnetic field intensity. Apart from presenting a quick numerical framework, the paper offers physical insights on regulating transport phenomena in complicated porous and electromagnetic settings, suggesting uses in thermal management, fluid processing, and MHD systems. • An explicit time integration method with sixth-order compact spatial accuracy is proposed. • The scheme outperforms Runge-Kutta methods in accuracy and efficiency for non-Newtonian fluid flows. • Applied to study radiation effects in Darcy-Forchheimer flow of Williamson fluids.Stability is analyzed for scalar parabolic equations to ensure robust performance. • Captures magnetic inclination and shear-thinning effects in porous media flow. • Useful for CFD applications like polymer processing, biomedical flows, and oil recovery.