SINOPSIS

The influence of natural convection during the melting of a long ice block in a rectangular cavity with isothermal vertical walls is analyzed numerically. The ice block is fixed in the middle of the cavity and the initial volume of ice is 1/8 of the cavity volume.
The unsteady two-dimensional melting of ice is governed by the continuity, momentum and energy equations and by the following assumptions: the liquid phase is incompressible and the Boussinesq approximation is met, the flow is laminar, and viscous dissipation is neglected.
The finite volume method is adopted and computations are carried out on a non-uniform fixed grid. The governing equations are discretised using the exponential differencing scheme for the spatial derivatives and the fully implicit scheme for the time integration. The SIMPLER algorithm is used for the pressure-velocity coupling.
In the cases of the wall temperature higher than 8°C, the melting process can be divided into three typical successive regimes: an initial pure conduction regime, a transition regime and a convection dominated regime. The latter regime can be divided into three sub-regimes characterized by: (i) the expansion of the clockwise vortex; (ii) the fact that it occupies the space above the ice block, and (iii) complete prevailing of the clockwise vortex over the counterclockwise one. In the case of hot wall temperature equal to 8°C, two vortices are separated by nearly vertical 4°C isotherm and the average Nusselt number remains constant during the time interval corresponding to the first sub-regime of the convection dominated regime.
In the case of hot wall temperature higher than 8°C, the ice melts faster from above, and for the one lower than 8°C from below.