Unsteady natural convection in a porous layer

Abstract

The focus of this paper is on the fundamentals of the transient mechanism responsible for the establishment of natural convection in a two-dimensional porous layer confined between isothermal vertical walls and insulated horizontal walls. In the first part of the paper, pure scaling arguments are used to identify the characteristic time scales of the phenomenon and, based on these scales, the evolution of the porous system to steady state. The type of steady state is shown to depend on the relative order of magnitude of the characteristic time scales. Distinct vertical boundary layers are shown to be possible if (L/H)Ra1/2>1, and distinct horizontal layers if (H/L)1/2 Ra1/4>1. In the second part of the paper, these and other scaling laws of the transient evolution to steady state are successfully tested against a series of transient numerical experiments conducted in the range H/L=0.2–5 and Ra=10–50.