Natural convection in a horizontal layer of a binary mixture

Abstract

This paper reports an analytical and numerical study of the natural convection in a horizontal shallow cavity filled with a binary fluid. Neumann boundary conditions for temperature and solute concentration are applied to the two vertical walls of the enclosure. The governing parameters of the problem are the thermal Rayleigh number Ra T , the aspect ratio A, the buoyancy ratio φ, the Lewis number Le and parameter a. Both double diffusive convection ( a = 0 ) and Soret induced convection ( a = 1 ) are considered. An analytical model, based on the parallel flow approximation, is proposed for the case of a shallow layer ( A ≫ 1 ). The particular case where the buoyancy forces induced by the thermal and solutal effects are opposing each other and of equal intensity ( φ = − 1 ) is considered. For this situation the critical Rayleigh number for the onset of supercritical and subcritical convection is predicted. The study is completed by a numerical solution of the full governing equations.