Effect of the boundary conditions on convection in a horizontal fluid layer with the Soret contribution

Abstract

In this paper, the phenomenon of natural convection in a horizontal binary fluid layer is studied. The four walls of the cavity are subjected to uniform fluxes of heat. The Soret effect is taken into consideration. The different hydrodynamic boundary conditions applied on the horizontal walls are rigid-rigid, rigid-free and free-free. Based on the parallel flow approach, an analytical solution for the stream function, the temperature and the concentration is established. The numerical results obtained from a finite volume method show a good agreement with those predicted analytically. The system is governed by five control parameters; the aspect ratio of the cavity, A, the Rayleigh number, RT, the Lewis number, Le, the buoyancy ratio, ϕ, and the lateral heating intensity, α. For given sets of these parameters, the existence of natural and anti-natural flows is discussed.