Onset of Buoyancy-Driven Convection in a Fluid-Saturated Porous Medium Bounded by a Long Cylinder

Abstract

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 column. 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 in self-similar boundary-layer coordinate. The present predictions suggest the critical $$R_D$$ , and the onset time and corresponding wavenumber for a given $$R_D$$ . The onset time becomes smaller with increasing $$R_D$$ and follows the asymptotic relation derived in the infinite horizontal porous layer.