Linear and Nonlinear Stability Analyses of Double-Diffusive Convection in a Vertical Brinkman Porous Enclosure under Soret and Dufour Effects

Analytical and numerical investigations were performed to study the influence of Soret Dufour effects on double-diffusive convection in a vertical porous layer filled with binary mixture subject horizontal thermal solute gradients. In particular, was focused effect diffusion bifurcation types from rest state toward steady convective state, then oscillatory state. The Brinkman-extended Darcy model Boussinesq approximation employed flow within layer. Following past laboratory experiments, dealt particular situation where solutal buoyancy forces equal but acting opposite direction favor possible occurrence condition. For this situation, onset could be either supercritical or subcritical occurred at given thresholds following various routes. analytical investigation based parallel approximation, which valid only for tall A linear stability analysis diffusive states basis finite element method. supercritical, RTCsup, overstable, RTCover, computed. addition, established flow, predicted by studied numerically predict Hopf’s bifurcation, RTCHopf, marked transition point unsteady flows; route towards chaos. To support analyses flows methodology results, nonlinear solutions full governing equations obtained using second-order difference Overall, seen affect significantly stationary, overstable convection. Hopf secondary consisting superposed layers traveling waves. good agreement found between predictions solution results.