Convection in a porous medium with solidification

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Abstract
The coupled effects of thermal convection and solidification of a Single-component liquid in a porous medium are investigated. A rigorous two-parameter perturbation analysis is used to determine the effects on both the stability of the basic state of heat conduction and the stability of finite-amplitude convection. The analysis shows that due to the kinematic conditions at the solid/liquid interface, hexagons having upflow in the center are stable near the onset of convection. For sufficiently supercritical Rayleigh numbers, however, rolls are the only stable mode. The transition from hexagons to rolls is characterized by a hysteresis loop. Moreover, the transition is shown to be controlled by one particular critical value of the convection amplitude. This generic property holds for non-Boussinesq convection in bulk liquid-layers too.