Darcy–Forchheimer flow of hydromagnetic nanofluid over a stretching/shrinking sheet in a thermally stratified porous medium with second order slip, viscous and Ohmic dissipations effects

A boundary layer analysis is carried out to study the influences of second order slip, viscous and Ohmic dissipations on steady two dimensional, incompressible flow of water based nanofluid over a stretching/stretching sheet embedded in a thermally stratified porous medium with inertia effect in the presence of magnetic field. The governing boundary layer nonlinear PDEs are transformed into nonlinear ODE’s using scaling transformation. The transformed equations are solved numerically by the fourth order Runge–Kutta method with shooting technique. Moreover, analytical solutions are presented for a special case. A unique solution is obtained for stretching sheet and dual solutions are found for shrinking sheet which depend on the suction parameter and local inertia coefficient. The effects of physical parameters on the dual solutions, temperature profile, local skin friction coefficient and the reduced Nusselt number are discussed. Comparisons are found to be good with benchmark solution. Keywords: Darcy–Forchheimer flow, Nanofluid, Ohmic dissipation, Second order slip, Thermally stratified medium