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 DT ¼ T 2 À T 1. Species separation is governed by two control parameters, the temperature difference and the velocity of the upper plate Ue x !. The intensity of the thermodiffusion is controlled by the temperature gradient, while the velocity Ue x ! controls the convective flow. This problem depends on six dimensionless parameters, namely, the separation ratio j, 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 (Pe m ¼ PeLe) and mass Rayleigh number ðRa m ¼ jRaLeÞ. The optimal separation m ¼ ffiffiffiffiffiffi 42 p =15z0:432 is obtained for Pe m ¼ ffiffiffiffiffiffi 42 p and Ra m ¼ 540. The numerical results, obtained using the full governing equations, are in good agreement with the analytical results based on a parallel flow approximation.
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