A NUMERICAL STUDY OF THE STEADY-STATE FREEZING OF WATER IN AN OPEN RECTANGULAR CAVITY

A numerical study of the flow in and heat transfer across a vertical c avity containing pure water when the aspect ratio of the cavity is low , i.e. 1 or less. has been undertaken. One vertical wail of the cavity is kept at a temperature that is below the freezing point of water wh ile the opposite wall is kept at a temperature that is above this free zing temperature Ice therefore forms in parr of the cavity, the condit ions being such that there can be significant natural convection in th e water. The upper surface of the cavity is open i.e. the water has a free surface, heat transfer from this surface being assumed negligible . The lower surface of the cavity is assumed to be adiabatic, Only the steady state has been considered here. It has been assumed that the f low is laminar and two-dimensional and that liquid and solid propertie s are constant except far the water density change with temperature wh ich gives rise to the buoyancy forces. The governing equations have be en written in dimensionless form and these equations have been solved using a finite element-based procedure in which the position of the so lid-liquid interface is obtained using an iterative approach. Solution s have been obtained for modified Rayleigh numbers of between 10(3) an d 10(8) for various degrees of under-cooling and for cavity aspect rat ios of between 0.25 and 1. The density inversion that occurs with wate r has been shown to have a large effect on the steady state freezing o f water in a cavity, The aspect ratio of the cavity has been shown to have a significant influence on the results when the aspect ratio is l ess than 0.5.