Linear and nonlinear stability of Soret‐Dufour Lapwood convection near double codimension‐2 points

Abstract

AbstractIn this study, the Dufour and Soret effects on natural double‐diffusion convection in a horizontal porous layer was studied numerically using FORTRAN 90 programming and analytically near various convection onset thresholds. The porous layer was subject to a uniform heat and mass fluxes on the horizontal walls while the vertical walls were impermeable and adiabatic. The Darcy model along with the Boussinesq approximation was assumed in the problem formulation. The governing parameters of the problem are the thermal Rayleigh number, RT, the buoyancy ratio, N, the Lewis number, Le, the aspect ratio of the cavity, A, and the Dufour, Du, and Soret, Sr, numbers. For a shallow enclosure, the analytical solution was derived assuming zero convection wave number, which is valid near and above criticality. The onset of subcritical, supercritical and oscillatory convection was investigated. Two linear and nonlinear codimension‐2 points were found to exist. Whether the system was subject to constant fluxes and heat and solute, regardless of the aspect ratio of the layer, the subcritical convection behavior remained the same with similarity in the thresholds expressions for subcritical bifurcation.