Non-Darcian flow and heat transfer along a permeable vertical surface with nonlinear density temperature variation

The non-Darcy free convection flow on a vertical flat plate embedded in a fluid-saturated porous medium in the presence of the lateral mass flux with prescribed constant surface temperature is considered. The coupled nonlinearities generated by the density variation with temperature, inertia, and viscous dissipation are included in the present study. In particular, we analyze a system of nonlinear ODEs describing self-similar solutions to the flow and heat transfer problem. These transformed equations are integrated numerically by a second-order finite difference scheme known as the Keller box method. Furthermore, some analytical results are provided to establish relationships between the physical invariants in the problem, and also to validate the numerical method. One of the important findings of our study is that an increase in the Rayleigh number increases the velocity boundary layer thickness, while the opposite is true for the thermal boundary layer thickness.