Ice-water convection in an inclined rectangular cavity filled with a porous medium

This paper reports on the results of a numerical study on the equilibrium state of the convection of water in the presence of ice in an inclined rectangular cavity filled with a porous medium. One side of the cavity is maintained at a temperature higher than the fusion temperature while the opposite side is cooled to a temperature lower than the fusion temperature. The two remaining sides are insulated. Results are analysed in terms of the density inversion parameter, the tilt angle, and the cooling temperature. It appears that the phenomenon of density inversion plays an important role in the equilibrium of an ice-water system when the heating temperature is below 20°. In a vertical cavity, the density inversion causes the formation of two counterrotating vortices leading to a water volume which is wider at the bottom than at the top. When the cavity is inclined, there exist two branches of solutions which exhibit the bottom heating and the side heating characteristics, respectively (the Bénard and side heating branches). Due to the inversion of density, the solution on the Bénard branch may fail to converge to a steady state at small tilt angles and exhibits an oscillating behavior. On the side heating branch, a maximum heat transfer rate is obtained at a tilt angle of about 70° but the water volume was found to depend very weakly on the inclination of the cavity. Under the effect of subcooling, the interplay between conduction in the solid phase and convection in the liquid leads to an equilibrium ice-water interface which is most distorted at some intermediate cooling temperature.