Double-diffusive and Soret-induced convection in a micropolar fluid layer

Abstract

This paper reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with a micropolar fluid. Neumann boundary conditions for temperature and concentration are applied to the horizontal walls of the enclosure, while the two vertical ones are assumed insulated. The governing parameters for the problem are the thermal Rayleigh number, Ra, Prandtl number, Pr, Lewis number Le, buoyancy ratio, φ, aspect ratio of the cavity, A, and various material parameters of the micropolar fluid, K, B, λ and n. For convection in an infinite layer (A≫1), analytical solutions for the stream function, temperature, concentration and microrotation 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. Also, results are obtained from the analytical model for finite amplitude convection for which the flow and heat transfer are presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are reported for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations. The influence of the material parameters on the flow and heat and solute transfers is demonstrated to be significant.