Natural Convection in a Shallow Porous Cavity Heated From the Side With a Uniform Heat Flux

Thermally driven flow in a thin rectangular cavity filled with a fluid saturated porous layer is studied analytically and numerically. A constant heat flux heating and cooling is applied on both vertical walls while the horizontal ones are assumed to be insulated. On the basis of the Darcy-Oberbeck-Boussinesq equations, the problem can be solved analytically, in the limit of a thin layer, using asymptotic expansions and an integral form of the energy equation. The flow field and temperature distributions are obtained explicitly in terms of the Rayleigh number in the conduction as well as intermediate regimes. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is also presented. A very good agreement is found between the numerical simulations and the analytical predictions. The various physical processes in this type of flow are discussed based on the findings of the analytical and numerical studies.