The reason of this study is to find a numerical solutions of Jeffrey's compact, non-stressed, smooth, conductive, magnetic hall currents in the vertical optical direction in the occurrence of heat_flux, “heat”(h) & group transmit. The limited dissimilarity is solved to explain the “equations”(Eq). The effect of different constraints on “velocity”(V), “temperature”(temp) & concentration distributions was investigated at the boundary layer. Also, there is a computational discussion about the effect of relevant or important factors on the coefficients of skin_friction and the rate of h and “mass”(m) relocate according to the values of Nusselt and Sherwood information correspondingly. Great interconnection is achieved by using Perturbation and Finite difference techniques. Applications of magnetic materials, MHD generators and crude oil refinements have been found in this model.