This paper is devoted to introduce a numerical simulation using the implicit finite difference method (FDM) with the theoretical study for the effect of viscous dissipation on the steady flow with heat transfer of Newtonian fluid towards a permeable stretching surface embedded in a porous medium with a second-order slip. The governing non-linear partial differential equations are converted into non-linear ordinary differential equations (ODEs) by using similarity variables. Exact solutions corresponding to momentum and energy equations for the case of no slip conditions are obtained. The resulting ODEs are successfully solved numerically with the help of FDM. Graphically results are shown for non-dimensional velocities and temperature. The effects of the porous parameter, the suction (injection) parameter, Eckert number, first- and second-order velocity slip parameter and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.