Newtonian steady state flow of fluids with electrical conduction properties was examined adjacent to a moving heated vertical plate subjected to a magnetic field and a heat source/sink. The impact of magnetic parameter, Prandtl number, permeability coefficient, heat source/sink volumetric rate and temperature difference between heated plate and ambient temperature. A reduced system of ODEs was created via group similarity method. The solution led to some important results. Increasing permeability coefficient of the plate material resulted in a significant increase in flow velocity and a slight increase in heat flux but the magnitude of shear stress and temperature distribution decreased. Moreover, increasing the magnetic parameter, M, led to a significant decrease in velocity and a decrease in heat flux, whereas shear stress and temperature distribution increased. Furthermore, increasing Prandtl number, Pr, reduced the velocity significantly and the heat flux slightly. On the other hand, the magnitude of shear stress and temperature distribution increased. In case of using heat source, the increase in its energy rate decreased the heat flux with no significant effect on shear stress. Finally, the increment of temperature difference led to noticeable increase in velocity and a slight increase in heat flux, whereas the shear stress decreased.