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In this paper we investigate numerically the influence of variable viscosity and thermal conductivity on MHD convective flow of heat and mass transfer problem over a moving non-isothermal vertical plate. The viscosity of the fluid and thermal conductivity are presumed to be the inverse linear functions of temperature. With the help of similarity substitution, the flow governing equations and boundary conditions are transformed into non-dimensional ordinary differential equations. The boundary value problem so obtained is then solved using MATLAB bvp4c solver. The effects of various parameters viz. magnetic parameter, viscosity parameter, thermal conductivity parameter, stratification parameter and Schmidt number on velocity, temperature and concentration are obtained numerically and presented trough graphs.  Also the coefficient of skin-friction, Nusselt number and Sherwood number are computed and displayed in tabular form. The effects of the viscosity parameter and thermal conductivity parameter in particular are prominent. This study has applications in a number of technological processes such as metal and polymer extrusion.