The present numerical attempt deals the sway to transfer of heat and mass characteristics on the time-dependent hydromagnetic boundary layer flow of a viscous fluid over an exponentially inclined preamble stretching. Furthermore, the role of viscous heating, thermal radiation, uneven energy gain or loss, velocity slip, thermal slip and solutal slips are depicted. The prevailing time-dependent PDE’s are rehabilitated into coupled non-linear ODE’s with the aid of apposite similarity transformations and then revealed numerically by using the 4th order R-K method incorporate with shooting scheme. Influence of various notable parameters like porosity, inertia coefficient, radiation, Eckert number, velocity, thermal and solutal slip are explored via graphs and tables for the cases of assisting and opposing flows. Comparison amid the previously published work and the present numerical outcomes for the limiting cases which are received to be in a righteous agreement. Temperature increments with large values of the non-uniform heat source.