Onset of Buoyancy-driven Instability in Porous Medium Solidified from Above

Abstract

When a porous melt layer saturated by liquid is solidified from above, convection often sets in due to buoyancy forces. In this study, the onset of buoyancy-driven convection during time-dependent solidification is investigated by using the similarly transformed disturbance equations. The thermal disturbance distribution of the solid phase is approximated by the WKB method and effects of various parameters on the stability condition of the melt phase are analyzed theoretically. For the limiting case of λ → 0 and finite kr, the critical conditions approach asymptotically \({Ra_{\rm D,c}^\ast\,{=}\,25.89}\) and \({a_{\rm c}^\ast\,{=}\,1.80}\) . This study presenting a constant-temperature cooling model predicts greater instability and gives more unstable results than those obtained from the constant solidification rate model.