Validity of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in a porous medium

The validity of the local thermal equilibrium assumption in natural convection over a vertical flat plate embedded in a porous medium is investigated analytically. The study is based on the two-phase (Schumann) model, using the Darcy model (slip condition) to govern the flow. It is found that there are three dimensionless parameters controlling the local thermal equilibrium assumption: the Biot number (Bi), the modified Rayleigh number (Ra_m), and the Darcy number (Da). 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.