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

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 T-1 and T-2 with Delta T = T-2 - T-1. Species separation is governed by two control parameters, the temperature difference and the velocity of the upper plate U. The intensity of the thermodiffusion is controlled by the temperature gradient, while the velocity U (e(x)) over right arrow controls the convective flow. This problem depends on six dimensionless parameters, namely, the separation ratio psi 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 Peclet 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 Peclet number (Pe(m) = PeLe) and mass Rayleigh number (Ra-m = psi RaLe). The optimal separation m = root 42/15 approximate to 0.432 is obtained for Pe(m) = root 42 and Ra-m = 540. The numerical results, obtained using the full governing equations, are in good agreement with the analytical results based on a parallel flow approximation. (C) 2013 Elsevier Masson SAS. All rights reserved.