In this research, the transient analysis of radiative combustible viscous chemical reactive two-step exothermic fluid flow past a permeable medium with various kinetics i.e Bimolecular, Arrhenius and Sensitized are investigated. The hydromagnetic liquid is influenced by a periodic vicissitudes in the axial pressure gradient and time along the channel axis in the occurrence of walls asymmetric convective cooling. The convectional heat transport at the wall surfaces with the neighboring space takes after the cooling law. The
non-dimensional principal flow equations are computationally solved by applying convergent and absolutely stable semi-implicit finite difference techniques. The influences of the fluid terms associated with the momentum and energy equations are graphically presented and discussed quantitatively. The results show that the reaction parameter (𝜆) is very sensitive and it is therefore needs to be carefully monitor to avoid systems blow up. Also, a rise in the values of the second step term enhances the combustion rate and thereby reduces the release of unburned hydrocarbon that polluted the environment.