Melting about a heated cylinder in an ice-filled square enclosure with an isothermals free surface

A numerical study of the flow about and heat transfer from a heated cylinde r centrally positioned in a square enclosure containing ice has been undert aken. The cylinder is heated to a uniform temperature that is higher than t he freezing temperature of water and melting, therefore, occurs in the vici nity of the cylinder. The two side-walls of the enclosure are kept at a uni form temperature that is below the freezing temperature. The conditions con sidered here are such that there can be significant natural convection in t he water near the cylinder. The lower surface of the enclosure is assumed t o be adiabatic. The liquid has a free surface which is assumed to be flat. In most previous numerical studies of such a situation it has been assumed that the free surface is adiabatic. In experimental studies of the is type of flow, however, the free surface is often effectively cooled. In order to evaluate the effect of this, it has here been assumed that the free surfac e is at the uniform temperature that is below the freezing temperature but that is, in general, higher than that of the cooled side-walls. The governi ng equations have been expressed in dimensionless form and solved using a f inite element procedure. The effect of the various governing parameters on the mean cylinder Nusselt number and on the thickness of the melted region about the cylinder have mainly been considered. The effect of the assumed f ree-surface temperature has, in particular, been studied.