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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).

In this paper, the study of the steady two-dimensional flow of an incompressible viscous fluid with heat and mass transfer and MHD heat generation past a moving vertical plate with suction in the presence of viscous dissipation and chemical reaction is investigated. Using similarity variables, the governing partial differential equations are transformed into non-linear ordinary differential equations. These equations are then solved numerically using fourth order Runge-Kutta method with shooting technique. The flow variables are presented graphically. The graphs showed that velocity rises for increasing Grashof number, mass Grashof numer, suction, heat generation and Eckert number while reducing with increasing magnetic parameter, Schmidt number, and chemical reaction parameter and Prandtl number. Comparisons with previously published work are performed and are found to be in an excellent agreement.