Analytical and numerical solutions of a non-linear MHD flow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting and Boussinesq’s fluid over a vertical oscillating plate embedded in a Darcian porous medium in the presence of thermal radiation effect have been presented. The fluid considered here is gray, absorbing/emitting radiating, but non-scattering medium. At time t > 0, the plate temperature and concentration near the plate raised linearly with time t. The dimensionless governing coupled, non-linear boundary layer partial differential equations are solved by an efficient, accurate, extensively validated and unconditionally stable finite difference scheme of the Crank–Nicolson type as well as by the Laplace Transform technique. An increase in porosity parameter (K) is found to depress fluid velocities and shear stress in the regime. Also it has been found that, when the conduction-radiation (R) increased, the fluid velocity and the temperature profiles decreased. Applications of the study arise in materials processing and solar energy collector systems. Keywords: Crank–Nicolson, Absorbing/emitting radiation, Darcian porosity, Shear stress, Materials processing, Boussinesq’s approximation
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