Species separation of a binary mixture in the presence of mixed convection

Abstract

In this paper, an analytical and numerical study to determine the species separation process in a binary fluid mixture by decoupling the thermal gradient from the convective velocity was performed. The configuration considered is a horizontal rectangular cavity of large aspect ratio, filled with a binary fluid. A constant tangential velocity is applied to the upper horizontal wall. The two horizontal impermeable walls are maintained at different and uniform temperatures T1 and T2 with ΔT = T2 − T1. Species separation is governed by two control parameters, the temperature difference and the velocity of the upper plate Uex→. The intensity of the thermodiffusion is controlled by the temperature gradient, while the velocity Uex→ controls the convective flow. This problem depends on six dimensionless parameters, namely, the separation ratio ψ, the Lewis number Le, the Prandlt number Pr, the aspect ratio of the cell A and two control parameters: the thermal Rayleigh number, Ra and the Péclet number Pe. In this study, the separation (mass fraction difference between the two ends of the cell) is obtained analytically as a function of mass Péclet number (Pem = PeLe) and mass Rayleigh number (Ram=ψRaLe). The optimal separation m=42/15≈0.432 is obtained for Pem=42 and Ram = 540. The numerical results, obtained using the full governing equations, are in good agreement with the analytical results based on a parallel flow approximation.