Onset of buoyancy-driven convection in a liquid-saturated cylindrical porous layer supported by a gas layer

A theoretical analysis of convective instability driven by buoyancy forces under the transient concentration fields is conducted in an initially quiescent, liquid-saturated, cylindrical porous layer with gas diffusion from below. Darcy's law and Boussinesq approximation are used to explain the 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 equations are derived on the basis of the propagation theory and the dominant mode method, which have been developed in a self-similar boundary layer coordinate system. The present predictions suggest the critical Darcy-Rayleigh number RD, which is quite different from the previous ones. The onset time becomes smaller with increasing RD and follows the asymptotic relation derived in the infinite horizontal porous layer.