Convection Currents in Porous Media. III. Extended Theory of the Critical Gradient

Abstract

The theory of the critical gradient for onset of thermal convection in a fluid entrapped in a porous medium is extended to allow for the exponential dependence of viscosity upon temperature and for non-linear vertical temperature-distributions which characterize transients in heat flow. Although there are approximations in the mathematical treatment, the extended theory agrees rather well with experimental data, as the simple theory does not in certain instances. New experimental data are reported for the critical gradient, obtained largely with silicone fluids in unconsolidated sands.