Abstract A mathematical model is conducted for the unsteady magnetohydrodynamic viscous, incompressible free convective flow of an electrically conducting Newtonian fluid over an impulsively-started semi-infinite vertical plate adjacent to saturated porous medium in the presence of appreciable thermal radiation heat transfer and chemical reaction of first order taking transverse magnetic field into account. The fluid is assumed optically thin gray gas, absorbing-emitting radiation, but a non-scattering medium. The governing non-linear partial differential equations are non-dimensionalized and are solved by an implicit finite difference scheme of Crank–Nicholson type. It is found that, increasing magnetic parameter serves to decelerate the flow, but increased temperatures and concentration values. An increase in the porosity parameter (K) is found to escalate the local skin friction (τx), Nusselt number (Nux) and the Sherwood number (Shx). Applications of the model include fundamental magneto-fluid dynamics, MHD energy systems and magneto-metallurgical processing for aircraft materials.