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

• The linear stability of natural convection between infinite vertical walls is investigated.
• The wall thickness and conductivities are taken into account.
• The hydrodynamic modes of instability are weakly influenced.
• However the thermal modes can become critical for Prandtl number below 12.45, encompassing the case of warm water.

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.