In the present paper, a numerical investigation of transport phenomena is considered in electrically-conducting nanofluid flow within a porous bed utilizing Buongiorno’s transport model and Runge-Kutta-Fehlberg fourth-fifth order method. Induced flow by non-isothermal stretching/shrinking sheet along with magnetic field impact, dissipation effect, and slip conditions at the surface are also included. The numerical results show the existence of two branches of the solution for a selected range of the governing parameters. The physical significance of both branches of solutions is ensured by performing a stability analysis in which a linearized eigenvalue problem is solved. The multiple regression analysis with the help of MATLAB LinearModel.fit package has also been conducted to estimate the dependence of the parameters on Nusselt number.