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Natural convection in superimposed layers of fluids heated from below is commonly observed in many industrial and natural situations, such as crystal growth, coextrusion processes and atmospheric flow. The stability analysis of this system reveals a complex dynamic behavior, including potential multiplicity of stationary states and occurrence of periodic regimes. In the present study, a linear stability analysis (LSA) is performed to determine the convection onset as a function of imposed boundary conditions, geometrical configuration and specific perturbations with different wavenumbers. To investigate the effects of the non-linear terms neglected by the linear stability analysis, a direct numerical simulation of the full nonlinear problem is performed with the use of CFD techniques. The numerical simulations results show an excellent agreement with the LSA results near the convection onset and an increase in the deviation as the Rayleigh number increases beyond the critical value.

LINEAR STABILITY ANALYSIS AND DIRECT NUMERICAL SIMUALATION OF DOUBLE-LAYER RAYLEIGH-BÉNARD CONVECTION