Study of Rayleigh-Benard convection in a chemically reactive fluid using a generalized Lorenz model and the cubic-quintic Ginzburg-Landau equation

Analytical study of linear and weakly nonlinear stability analyses of Rayleigh-Benard convection in a chemically reactive two-component fluid system is reported by considering physically realistic and idealistic boundaries. Analytical expression for the eigenvalue as functions of the chemical potential and the relaxation parameter is reported in the cases of stationary, oscillatory, and subcritical instabilities. The preferred stationary mode at onset is attributed to the assumption of a chemical reaction. The possibility of subcritical motion in a specific range of values of the relaxation parameter is reported and the threshold value of this parameter at which the transition from the subcritical to the critical motion takes place is documented for different values of the chemical reaction rate. The higher-order generalized Lorenz model leads to the reduced-order cubic-quintic, Ginzburg-Landau equation (GLE), and using its solution, the heat transport is quantified in steady and unsteady convective regimes. The drawback of the cubic GLE and the need for the cubic-quintic GLE for studying the heat transfer in the case of subcritical regime is explained. The possibility of having pitchfork and inverted bifurcations at various values of the relaxation parameter is highlighted. The steady Nusselt number plots clearly show that in the case of a supercritical bifurcation, a smooth transition takes place from unity in the conduction state to a higher value as the Rayleigh number exceeds its critical value predicted by linear theory. In the case of subcritical bifurcation, however, a discontinuous transition is observed.