Analytical investigation of Bénard-Marangoni convection heat transfer in a shallow cavity filled with two immiscible fluids

The mechanism of natural and Marangoni convection in a system with two stratified fluid layers without mass transfer at the interface is investigated. The basis of the analytical solution is an assumption of parallel flow over a large portion of the system. The two cases of heat fluxes through horizontal or vertical opposite walls are considered. It is demonstrated that four different patterns of convection can be observed in the present system. The zone of occurrence of these flow patterns are specified in terms of non-dimensional parameters. Velocity and temperature distributions, stream function and Nusselt number are presented over a wide range of the governing parameters. The results obtained are explained in terms of the basic physical mechanisms that govern these flows showing many interesting aspects of the complex interaction between the buoyant and surface tension mechanisms.