Wall effects on the stability of convection in an infinite vertical layer

Abstract

The stability of buoyancy-driven convection in a vertical infinite fluid layer between two rigid walls with different thermal conductivities and thicknesses is presented. Analytical solutions are derived for parallel base flow, for which linear stability analysis predicts the growth of two-dimensional disturbance. The resulting eigenvalue problem was solved using finite-elements method. Neutral stability curves and associated critical Grashof numbers and wavenumbers are supplied for different characteristic parameters of the flow. It is shown that thermal conductivity and thickness of the walls has a weak influence on hydrodynamic modes but a strong influence on thermal modes which become critical for lower values of Prandtl number than in the case of perfect conducting walls.