Onset of convective stability in a fluid-saturated porous layer subjected to time-dependent heating

A theoretical analysis of thermal instability driven by buoyancy forces in transient temperature fields is conducted in an initially quiescent, fluid-saturated, horizontal porous layer. Darcyʹs law is used to explain characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. Under the principle of exchange of stabilities, the stability analysis is performed on the basis of the linear amplification theory. The result predicts the critical condition of onset of buoyancy-driven convection, which is governed by the Darcy-Rayleigh number. The present stability criteria predict the experimental data quite well.