Soret and Dufour effects on thresholds of stability in a horizontal Brinkman porous layer submitted to vertical temperature and species gradients using linear and non-linear analysis

Abstract

The present study deals with Soret and Dufour effects on the onset of double-diffusive natural convection in a horizontal Brinkman porous layer with a free-stress upper boundary. The thresholds of stationary, oscillatory, and subcritical bifurcations are derived on the basis of linear and non-linear analysis, as functions of the governing parameters. The effect of Dufour ( $Du$ ) and Soret $\left(Sr\right)$ parameters on the thresholds of instabilities is illustrated and discussed. There are critical combinations $(Sr,Du)$ for which the thresholds of supercritical bifurcations are independent of the buoyancy ratio. Particularly, for $Du=0$ and $Sr=Le/(1+Le)$ , the stationary convection starts at the threshold of the pure thermal convection whatever the value of the buoyancy ratio.