Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium: non-Darcian model

The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Brinkman term (no-slip condition) to cover the flow. It is found that there are four dimensionless parameters controlling the local thermal equilibrium assumption: the volumetric Biot number (Biv), the modified Rayleigh number (Ram), the modified Darcy number (Da) and the ratio of effective to dynamic viscosity (λ). The effects of these parameters are investigated and a correlation equation is developed in order to determine the region where the local thermal equilibrium assumption is valid.