Analysis of thermal instability in a horizontal, porous layer heated from below

Abstract

The critical conditions for the onset of natural convection in an initially-quiescent, fluid-saturated, horizontal porous layer heated from below by ramp-heating at a constant rate are analyzed, using the theory of propagation. For deep-pool systems, the temperature profile at the base is modeled using the integral method. A new stability equation is derived from the theory of propagation, in which the variation in time in the disturbance is taken into account. For a porous layer with a relatively low permeability saturated with a high Prandtl-number fluid, the critical conditions for natural convection are τc = 6.55 γ4/3 Ra-2/3 and ac = 0.41 γ-2/3 Ra1/3. A comparison of the predictions of the present model with the experimental data of Kaviany indicates that the natural convection is detectable at time 4τc.