THE ONSET OF TRANSIENT CONVECTION IN FLUID-SATURATED POROUS LAYER HEATED UNIFORMLY FROM BELOW

摘要

A theoretical analysis of convective instability is conducted in an initially quiescent, fluid-saturated, horizontal porous layer heated from below with constant heat flux. Darcy's law is used to model the fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven convective motion. Under the principle of exchange of stabilities, the stability analysis is performed on the basis of the propagation theory which adopts the thermal penetration depth as a characteristic length scaling factor. The result predicts the critical condition of onset of buoyancy-driven convection which is governed by the Darcy-Rayleigh number. The present prediction compares favorably with CFD simulation result.