“…Situations in which the fully developed laminar flow in a vertical channel is described by nonlinear balance equations occur, for instance, when a magnetohydrodynamic force is present and the thermal generation due to Joule effect is non negligible. In recent years, much attention has been devoted to the study of magnetohydrodynamic effects on natural and mixed convection flows [6][7][8][9][10][11]. Indeed, convective flows in the presence of magnetic fields occur in many technical applications, such as, for instance, the optimization of industrial casting of metals [12].…”