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The objective of the present study is to investigate thermal diffusion and radiation effects on unsteady MHD flow past a linearly accelerated vertical porous plate with variable temperature and also with variable mass diffusion in presence of heat source or sink under the influence of applied transverse magnetic field. The fluid considered here is a gray, absorbing/ emitting radiation but a non-scattering medium. At time t > 0, the plate is linearly accelerated with a velocity u = u0t in its own plane. And at the same time, plate temperature and concentration levels near the plate raised linearly with time t. The dimensionless governing equations involved in the present analysis are solved using the closed analytical method. The velocity, temperature, concentration, skin-friction, the rate or heat transfer and the rate of mass transfer are studied through graphs in terms of different physical parameters like magnetic field parameter (M), radiation parameter (R), Schmidt parameter (Sc), Soret number (So), Heat source parameter (S), Prandtl number (Pr), thermal Grashof number (Gr), mass Grashof number (Gm) and time (t).

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The flow has been made by considering variable temperature and radiation effects for the magnetohydrodynamic viscoelastic fluid past a moving vertical plate in a porous medium. Chemical reaction and concentration have been taken into account. The governed mathematical statement is handled analytically by perturbation technique. The main view of this research is to investigate the effects of parameters and numbers in the problem on fluid flow, thermal boundary and concentration profiles. The velocity profile has been reduced by increasing the magnetic parameter due to the Lorentz force in the opposite direction of flow. Temperature profile is increased by rising thermal radiation and concentration distribution is decreased by enhancing the chemical reaction and Schmidt number. The Schmidt number represents the relative ease of the molecular momentum and mass transfer and it is very important in multiphase flows. The effect of increasing values of the Schmidt number is to reduce the momentum boundary layer and this leads to the thinning of the diffusion layer. Furthermore, at the end of this paper the effects of different parameters on skin friction coefficient and local Nusselt number are investigated.

An analysis of two dimensional free convective hydro-magnetic flow of an electrically conducting visco-elastic fluid past a vertical porous surface has been studied in the presence of magnetic field and chemical reaction of first order with heat source. Simultaneously effects of heat and mass transfer are also studied in combination of the physics of diffusion thermo (Dufour effect) and suction at the plate is assumed to be constant. The equations governing are solved by perturbation technique. Analytical expressions for velocity, temperature and concentration fields, non-dimensional skin friction coefficient and Nusselt number are obtained. The results are analyzed graphically for various values of visco-elastic parameter along with a combination of other flow parameters involved in the solution.