Onset of convection and finite amplitude flow due to Soret effect within a horizontal sparsely packed porous enclosure heated from below

The Soret effect on thermal natural convection within a horizontal porous enclosure heated uniformly from below by a constant heat flux is studied analytically and numerically using the Brinkman-extended Darcy model along with the Boussinesq approximation. The governing parameters of the problem are the Darcy-Rayleigh number, RT, the Lewis number, Le, the separation parameter, ϕ, the Darcy number, Da, and the aspect ratio of the enclosure, Ar. In the limit of a shallow enclosure, an analytical closed form solution is obtained on the basis of a parallel flow approximation. A numerical study is also conducted to validate the results of the analytical predictions. The thresholds for the onset of stationary and finite amplitude convection are determined explicitly as function of Le, ϕ and Da. The obtained results show that in the ϕ-Le plane there exists three regions that correspond to different parallel flow regimes, namely the subcritical and supercritical flows. The separation parameter has a strong effect on the threshold of instabilities and on the characteristics of heat and mass transfer. The threshold for Hopf bifurcation is obtained on the basis of the linear stability analysis. The wavenumber and the oscillation frequency at the onset of instabilities are null for an infinite extent layer.