Linear stability analysis of a fluid-saturated porous layer subjected to time-dependent heating

A theoretical analysis of thermal instability driven by buoyancy forces under the transient temperature fields is conducted in an initially quiescent, fluid-saturated and horizontal porous layer. Darcy’s law is used to explain the characteristics of fluid motion and under the principle of exchange of stabilities, the linear stability theory is employed to derive stability equations. The stability equations are analyzed by the initial value approach with the proper initial conditions. Two stability limits, τs and τr are obtained under the strong and the relative stability concepts. The critical condition of onset of buoyancy-driven convection is governed by the Darcy–Rayleigh number, as expected. The growth period for disturbances to grow is seemed to be required until the instabilities are detected experimentally. The convective motion can be detected experimentally from a certain time τ0 ≅ 4τr.