A numerical study of the steady state freezing of water in an open rectangular cavity

Abstract

A numerical study of the flow in and heat transfer across a vertical cavity containing pure water when the aspect ratio of the cavity is low, i.e. 1 or less, has been undertaken. One vertical wall of the cavity is kept at a temperature that is below the freezing point of water while the opposite wall is kept at a temperature that is above this freezing temperature. Ice therefore forms in part of the cavity, the conditions being such that there can be significant natural convection in the 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 flow is laminar and two‐dimensional and that liquid and solid properties are constant except for the water density change with temperature which gives rise to the buoyancy forces. The governing equations have been written in dimensionless form and these equations have been solved using a finite element‐based procedure in which the position of the solid‐liquid interface is obtained using an iterative approach. Solutions have been obtained for modified Rayleigh numbers of between 10³ and 10⁸ for various degrees of under‐cooling and for cavity aspect ratios of between 0.25 and 1. The density inversion that occurs with water has been shown to have a large effect on the steady state freezing of water in a cavity. The aspect ratio of the cavity has also been shown to have a significant influence on the results when the aspect ratio is less than 0.5.

Citation

Oosthuizen, P.H. and Paul, J.T. (1996), "A numerical study of the steady state freezing of water in an open rectangular cavity", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 6 No. 5, pp. 3-16. https://doi.org/10.1108/09615539610125926