Marangoni convection in a liquid layer overlying a porous layer with evaporation at the free surface

Abstract

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 non-linear two-dimensional Navier–Stokes equation along with the energy equation is solved for the liquid layer. The Brinkman model with the energy equation describes the porous layer. The partial differential equations are solved numerically using the finite element technique. At the free surface, two conditions are treated simultaneously. The surface tension is assumed to vary linearly with temperature, therefore the existence of Marangoni convection. The second condition assumes that evaporation takes place at the free surface. With the cavity heated laterally, it is found that the switching of the flow from the liquid layer into the porous layer is due to the ratio of the liquid thickness to the porous thickness, designated as thickness ratio. Different aspect ratios, thickness ratios as well as saturation temperatures are also studied in detail for the pure thermocapillary case. Results reveal the importance evaporation at the free surface has on convection patterns in the cavity.