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We study the conductive and convective states of phase-change of pure waterin a rectangular container where two opposite walls are kept respectively attemperatures below and above the freezing point and all the other boundariesare thermally insulating. The global ice content at the equilibrium and thecorresponding shape of the ice-water interface are examined, extending theavailable experimental measurements and numerical simulations. We first addressthe effect of the initial condition, either fully liquid or fully frozen, onthe system evolution. Secondly, we explore the influence of the aspect ratio ofthe cell, both in the configurations where the background thermal-gradient isantiparallel to the gravity, namely the Rayleigh-B\'enard (RB) setting, andwhen they are perpendicular, i.e., vertical convection (VC). We find that for aset of well-identified conditions the system in the RB configuration displaysmultiple equilibrium states, either conductive rather than convective, orconvective but with different ice front patterns. The shape of the ice frontappears to be always determined by the large scale circulation in the system.In RB, the precise shape depends on the degree of lateral confinement. In theVC case the ice front morphology is more robust, due to the presence of twovertically stacked counter-rotating convective rolls for all the studied cellaspect-ratios.

Equilibrium states of the ice-water front in a differentially heated rectangular cell