Double-diffusive natural convection study in a shallow horizontal porous layer filled with a binary fluid and submitted to destabilized conditions in the presence of Soret effect

Abstract

This paper reports an analytical and numerical study of thermosolutal convection in a Brinkman horizontal porous layer saturated with a binary mixture, destabilized by submitting it either to both heat and mass fluxes (a=0, with Soret effect) or only to a heat flux to recover the case of pure Soret effect (a=1). The analytical solution is derived based on the parallel flow approximation and validated numerically using a finite difference method. A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations. The governing parameters of this study are the Lewis number, Le, the Rayleigh thermal, RT, the Soret number, Sr, and the buoyancy ratio, φ. The thresholds for the onset of convection and the generated heat and mass transfer rates are examined both in the presence (a=0) and in the absence (a=1) of an external mass flux. The influence of the governing parameters on the onset of motion and the resulting fluid flow, temperature and concentration fields is discussed. It was found that the onset of convection for a=0 and positive values of Sr is delayed compared to the case a=1 (pure Soret effect) and, for the latter case, the onset of convection is delayed compared to a=0 and negative values of the Soret number.