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A mathematical model analysis has been developed to investigate the effect of thermophoresis on unsteady flow of non- Newtonian fluid with heat and mass transfer through a porous medium over a permeable infinite vertical plate. The considered non- Newtonian fluid follows a second grade model and is stressed by a uniform strong magnetic field; so the Hall currents are taken into consideration. The problem is modulated mathematically by a system of coupled non-linear partial differential equations which pertaining to describe the continuity, momentum, energy and concentration. These equations involve the effects of thermal radiation, heat generation, thermal diffusion(Soret), viscous dissipation and chemical reaction. The numerical solutions of the dimensionless equations are found as a functions of the physical parameters of this problem. The numerical formulas of the velocity components (u) and (w), temperature (q ) and concentration (C) as well as Nusselt number(Nu) and Sherwood number(Sh) are computed. The physical parameters effects of the problem on these formulas are described and illustrated graphically through some figures and tables.

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