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ARTICLE

Soret driven thermosolutal convection in an inclined porous layer: search of optimum conditions of separation and validity of the boundary layer theory

A. Rtibi¹, M. Hasnaoui¹, A. Amahmid¹

1 Faculty of Sciences Semlalia, Department of Physics LMFE, Laboratory associated to CNRST (URAC 27) BP 2390, Marrakesh - Morocco

Fluid Dynamics & Materials Processing 2013, 9(2), 183-207. https://doi.org/10.3970/fdmp.2013.009.183

Abstract

In this paper we present an analytical and numerical study of Soret convection in an inclined rectangular porous layer saturated with a binary fluid and subject to uniform heat fluxes. In the problem formulation, the Darcy model is considered and the results are presented for wide ranges of R_T (50 ≤ R_T ≤ 1000), θ(0°≤θ≤180°) and φ(-1 ≤ φ ≤ 1) for Le = 10, where R_T, θ, φ, and Le are the thermal Darcy-Rayleigh number, the cavity inclination, the separation parameter, and the Lewis number, respectively. An analytical solution, derived on the basis of the parallel flow approximation, is validated numerically by solving the full governing equations with a finite difference method. It is found that the heat transfer is more sensitive to the variation of the cavity inclination than to the separation parameter while the mass transfer sensitivity is essentially related to positive values of φ in a short range of θ. The thresholds of R_T and φ from which the boundary layer approximations can be considered valid (with a maximum deviation of 5% for the numerical results) are determined; they are found to be dependent on θ. For positive values of the separation parameter, the boundary layer regime is reached at relatively lower values of R_T .

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