Double-diffusive and Soret-induced convection in a shallow horizontal porous layer

Abstract

This paper reports an analytical and numerical study of the natural convection in a horizontal porous layer filled with a binary fluid. A uniform heat flux is applied to the horizontal walls while the vertical walls are impermeable and adiabatic. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the horizontal walls (double-diffusive convection, $a\,{=}\,0$) or by temperature gradients (Soret effects, $a\,{=}\,1$). The governing parameters for the problem are the thermal Rayleigh number, $R_T$, the Lewis number, $Le$, the solutal Rayleigh number, $R_S$, the aspect ratio of the cavity, $A$, the normalized porosity of the porous medium, $\varepsilon$, and the constant $a$. The onset of convection in the layer is studied using a linear stability analysis. The thresholds for finite-amplitude, oscillatory and monotonic convection instabilities are determined in terms of the governing parameters. For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained by assuming parallel flow in the core of the cavity. The critical Rayleigh numbers for the onset of supercritical, $R_{\hbox{\scriptsize\it TC}}^{\hbox{\scriptsize\it sup}}$, or subcritical, $R_{\hbox{\scriptsize\it TC}}^{\hbox{\scriptsize\it sub}}$, convection are predicted by the present theory. A linear stability analysis of the parallel flow pattern is conducted in order to predict the thresholds for Hopf bifurcation. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical prediction and the numerical simulations.

Soret Convection in a Shallow Porous Cavity under a Magnetic Field and Submitted to Uniform Fluxes of Heat and Mass

“…(8)- (10) and Eqs. (14)- (15) Also, the results obtained by Bahloul et al (2003), while studying double-diffusive and Soret-induced convection in a shallow horizontal porous layer in the absence of magnetic field are deduced successfully from the present study, by using the limits → 0 , → − , → 0 and → 0. Particularly, the expression of the threshold of oscillatory convection is deduced from the present solution as:…”

Unsteady Double Diffusive Natural Convection with Dufour and Soret Effects

“…Joly et al [12] studied the Soret effect on natural convection in a vertical enclosure; they analyzed the particular situation where the buoyancy forces induced equal intensities opposing thermal and solutal effects. Double diffusive and Soret effects, inducing convection in a shallow horizontal enclosure, was analytically and numerically studied by Bahloul et al [13]. The same configuration was also investigated numerically by Mansour et al [14].…”

Stability analysis of soret effect on thermohaline convection in dusty ferrofluid saturating a Darcy porous medium

“…Lakshmi Narayana et al [7] investigated the linear stability analysis of a steady convective double diffusive flow of Hadley type considering the Soret effect which is set up by the horizontal components of temperature and concentration gradient in a shallow horizontal layer of a fluid saturating a porous medium. Bahloul et al [8] studied numerically and analytically, natural convection in a horizontal Darcy porous layer filled by a binary fluid. In both cases double-diffusive and Soret induced convections were used.…”