STABILITY ANALYSIS AND BIFURCATIONS IN SORET CONVECTION WITHIN A SHALLOW POROUS ENCLOSURE

摘要

The present study concerns a stability analysis of a Soret convection within a porous layer subject to uniform fluxes of heat and solute on its horizontal boundaries.The solutal buoyancy forces are induced by the imposition of a solute gradient and by the thermal diffusion phenomenon.The Brinkman- extended Darcy model and the Boussinesq approximation are used to model the convective flow through the porous medium.Based on linear stability theory,the resulting linear perturbed equations are solved numerically using the finite element method. An analytical solution is derived on the basis of the parallel flow approximation,and validated against the numerical results obtained by solving the full governing equations using a finite difference method. The results corresponding to the cases of double- diffusive convection(without Soret effect)and Soret convection(with zero mass flux)are recovered by the present formulation as limiting cases.The two other limiting cases,namely the low porosity Darcy porous medium and the clear fluid medium emerge also from the present investigation.The critical Rayleigh numbers for the onset of subcritical and stationary convection are determined explicitly as functions of the governing parameters.The threshold of Hopf bifurcation is determined as function of the governing parameters by performing a linear stability analysis of the perturbed rest state.The existence of two co- dimension-2points(subcodimension-2 and Hopf- codimension-2)is proved and different flow regimes are delineated.The diagrams of stability show that there exists a range of Lewis number in which the subcritical convection disappears.It is shown that the thermal diffusion,has a strong effect on the instability thresholds and on heat and mass transfer characteristics.