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This paper presents a detailed account of unsteady, incompressible, viscous, electrically conducting, unidirectional, free convective second grade fluid through an exponentially accelerated vertically infinite plate with both applied electric field and magnetic field being present. The equation of motion and energy manifested as nonlinear partial differential equation are represented as algebraic equations using implicit finite difference scheme and solved numerically by implementing the damped-Newton method. With the help of the momentum and energy equation, we defined the expressions for skin friction and Nusselt number. The cases  n  = 1(constant acceleration) and  n  = 0.5(variable acceleration) are also taken into consideration. The solution obtained is eventually simulated using MATLAB and the resulting graphs representing the influence of non-dimensional parameters on flow field and temperature field are discussed thoroughly. We have also validated the results obtained from the present methodology with the results obtained from already existing methodologies under some limited cases. It is interesting to note that when the plate is being cooled by free convection current, with increase in viscoelastic parameter the viscous forces are dominated by the elastic effects which results in accelerating the velocity flow profile. For comparatively smaller values of  Ec  the temperature distribution decreases with increasing  Re  as the suction propagation facilitates decrease in boundary layer thickness which consequently enhances heat transfer rate. The effect of  Ec  is to raise the temperature profile due to enhancement in viscous dissipation effects. Practically, the combined effects of the physical parameters are remarkably important in various engineering, medical and industrial applications.

Unsteady EMHD free convective second grade fluid flow past an exponentially accelerated vertical porous plate