Analytical and Numerical Solutions for Natural Convection in a Shallow Cavity Filled with Two Immiscible Fluids: Shear Stress Action

Abstract

A shallow horizontal cavity filled with two layers of nonmiscible fluids, is studied both analytically and numerically. The upper free surface of the layer is subject to a shear stress. The analytical solution, based on the parallel flow approximation, is found to be in good agreement with a numerical solution. The existence of both natural and antinatural flows is demonstrated. Indeed, the critical Rayleigh number for the onset of motion is dependent on the side heating intensity. Multiple steady state solutions are possible in a range of the rate of fluids dynamics viscosity that depends strongly on the upper fluid one.