Linear stability bounds in a convection problem for variable gravity field

A problem governing the convection-conduction in a horizontal layer bounded by rigid walls of a fluid heated from below for a linearly decreasing across the layer gravity field is reformulated as a variational problem. Stability bounds from the case of classical convection [1] and the case of convection in a linearly decreasing across the layer gravity field are compared. The new criterion, which yields good stability bounds for the stability limit, is shown by the numerical evaluations obtained in [2–4].