Soret and thermosolutal effects on natural convection in a shallow cavity filled with a binary mixture

This paper reports an analytical and numerical study of the combined Soret and thermosolutal effects on natural convection in a shallow rectangular cavity filled with a binary mixture. Neumann boundary conditions for temperature and concentration are applied to the horizontal walls of the enclosure, while the two vertical ones are assumed impermeable and insulated. The governing parameters for the problem are the thermal Rayleigh number, RaT, the Lewis number Le, the buoyancy ratio φ, the solute flux imposed on the horizontal boundaries j, the Prandtl number Pr, the aspect ratio of the cavity A, and the real number a (a = 0 for double diffusive convection and a = 1 for the coexistence of double diffusion convection and Soret effect). For convection in an infinite layer (A ≫ 1), analytical solutions for the stream function, temperature and concentration fields are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy and constituent equations. The critical Rayleigh numbers for the onset of supercritical and subcritical convection are predicted explicitly by the present model. A linear stability analysis of the parallel flow model is conducted and the critical Rayleigh number for the onset of Hopf’s bifurcation is predicted numerically. Also, results are obtained for finite amplitude convection for which the flow and heat and solute transfers are presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations.