Effects of flow inertia on vertical, natural convection in saturated, porous media

An analytical study is made for the effect of flow inertia on vertical, natural convection in saturated, porous media. Within the framework of boundary-layer approximations, Forchheimer's model was transformed into a set of non-similar equations. Effects of flow inertia are measured and examined in terms of the dimensionless inertia parameter ξ = Gr_xFo_x where Gr_x is the local Grashof number of determined by the bulk properties of saturated porous media, and Fo_x is a new dimensionless parameter governed by the microstructure of porous matrix. The non-similar solutions are presented and discussed for two types of flow: (1) the uniform heat flux surface; and (2) plane plume flows. Results show that thermal boundary layer in the non-Darcy regime is thicker than the corresponding pure-Darcy flow. In addition, the local wall heat fluxes for the first case and the maximum temperature gradient for the second case decrease with increasing ξ.