Convection in a vertically heated cavity filled with two stratified fluids.

Abstract

Natural convection in a composite system of two immiscible Bousinessq fluids in a vertically heated cavity is numerically simulated. The effects of interfacial stresses and bouyancy forces are incorporated in the discretization of the unsteady incompressible Navier-Stokes equations. The present numerical formulation makes no a priori assumptions on the shape and dynamical role of the interface, and its behavior can be obtained as part of the solution of the problem. A proper stress and heat balance is enforced depending on the interface conditions (flat or deformable). In order to resolve the details near the walls and fluid interface, a skewed mesh is used such that the node density is higher in these places. Extensive computations are carried out to check the performance of the present formulation. Special attention is paid to the effects of a deformable interface and surface stresses on the flow and thermal fields within the enclosure. For the conditions under considerations, it is found that at low capillary number, a periodic behavior is established independently of the strenght of the Marangoni number.