  We study the conductive and convective states of phase-change of pure water
in a rectangular container where two opposite walls are kept respectively at
temperatures below and above the freezing point and all the other boundaries
are thermally insulating. The global ice content at the equilibrium and the
corresponding shape of the ice-water interface are examined, extending the
available experimental measurements and numerical simulations. We first address
the effect of the initial condition, either fully liquid or fully frozen, on
the system evolution. Secondly, we explore the influence of the aspect ratio of
the cell, both in the configurations where the background thermal-gradient is
antiparallel to the gravity, namely the Rayleigh-B\'enard (RB) setting, and
when they are perpendicular, i.e., vertical convection (VC). We find that for a
set of well-identified conditions the system in the RB configuration displays
multiple equilibrium states, either conductive rather than convective, or
convective but with different ice front patterns. The shape of the ice front
appears 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 the
VC case the ice front morphology is more robust, due to the presence of two
vertically stacked counter-rotating convective rolls for all the studied cell
aspect-ratios.
