Convection in Superposed Liquid and Porous Layers with Heat and Mass Transfer at the Free Surface

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer in the presence of a free surface with evaporation is investigated. The Navier-Stokes equations are solved for the liquid layer, while the Brinkman model describes the porous layer.  Two and three-dimensional geometrical models are considered, with bottom heating and lateral heating. Buoyancy convection, thermocapillary convection and combined convection are studied in detail for different aspect ratios. For the evaporation analysis, two conditions are treated simultaneously at the free surface. In the first, surface tension is assumed to vary linearly with temperature. In the second, a linear saturation temperature is imposed at the free surface to allow evaporation. Different aspect ratios, thickness ratios as well as Marangoni numbers are studied in detail. Results reveal the significant effect evaporation in the liquid layer has on convective flow patterns.