Effect of thermo-diffusion and parabolic motion on MHD second grade fluid flow with ramped wall temperature and ramped surface concentration

In this paper, effects of parabolic motion, heat generation/absorption and thermo-diffusion on unsteady free convective MHD flow of radiating and chemically reactive second grade fluid near an infinite vertical plate through porous medium have been considered. It is assumed that the bounding plate has a ramped temperature with ramped surface concentration and isothermal temperature with ramped surface concentration. For finding the exact solution, we applied Laplace transform technique on the governing nondimensionalized equations. Analytic expression of Skin friction, Nusselt number and Sherwood number is derived and represented through tabular form. The effects of Magnetic parameter M, second grade fluid α, Heat generation/absorption H, thermal radiation parameter R, chemical reaction Kr and thermo-diffusion Sr on velocity, temperature and concentration profiles are discussed through several figures. We found that velocity, temperature and concentration profiles in case of ramped temperature with ramped surface concentrations are less than those of isothermal temperature with ramped surface concentrations. It is also seen that Magnetic field M, second grade fluid α and chemical reaction Kr have retarding effects on velocity profile, whereas thermo-diffusion parameter Sr and thermal radiation parameter R have reverse effects on it.