Onset of Buoyancy-Driven Convection in Porous Media Saturated with Cold Water Cooled from Above

摘要

When porous media saturated with initially stagnant cold water around the density maximum temperature are cooled from above, convection may be induced in an unstable lower layer. In this study, the onset of buoyancy-driven convection during time-dependent cooling is investigated using the propagation theory, which transforms disturbance equations similarly, and also considering the density inversion effect. The critical Darcy-Rayleigh number Ra_(D,c) is found as a function of the dimensionless density maximum temperature θ_(max). For Ra_D > Ra_(D,c) the dimensionless critical time τ_c to mark the onset of instability is presented as a function of Ra_D and θ_(max). These critical conditions are compared with previous theoretical results.