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In the present paper the numerical study of effects of thermal Grashof parameter and concentration Grashof parameter on steady MHD Casson fluid flow through non-Darcy porous media, over a nonlinear boundary surface under slip-conditions is explored. By suitable similarity transformations, the governing boundary layer equations are transformed to ordinary differential equations. The method of the numerical computation with bvp4c, a MATLAB program is applied to solve these equations. The effects of thermal Grashof, concentration Grashof and stretching index, velocity slip, thermal slip, and concentration slip parameters on velocity, heat transfer, and concentration profiles, Skin-friction, local Nusselt number and local Sherwood number are computed and discussed numerically and presented through tables and graphs.