The present paper focus on simultaneous effects of thermal and concentration diffusions in unsteady magnetohydrodynamic free convection flow past a moving plate maintained at constant heat flux and embedded in a viscous fluid saturated porous medium is presented. The transported model employed includes the effects of thermal radiation, heat source and chemical reaction. Te fluid is considered as a gray absorbing – emitting but non-scattering medium and the Rosseland approximation in the energy equation is used to describe the radiative heat flux for optically thick fluid. The dimensionless coupled linear partial differential equations are solved by suing perturbation technique. The solution for the velocity, temperature and concentration as well as the skin friction coefficient and the rates of heat and mass transfer are shown graphically for different values of physical parameters involved.