Freezing of Water in a Slab with Boundary Conditions of the Third Kind

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Freezing of water in a slab with boundary conditions of the third kind

Predictions for freezing heat transfer in a slab with convective boundary conditions at the cold surface are obtained from heat balance integral approximations, which consider conduction as the only mode of heat transfer in both the solid and liquid and consider durations of precooling and freezing in the heat transfer process. The thermal penetration dimensionless parameter α is presented to distinguish two cases of freezing, and analytical results for α ≥1 are given in this paper. An experimental investigation on freezing of water is reported for comparison with the one-dimensional conduction model to show that experimental modeling for freezing heat transfer with convective boundary conditions using Peltier devices is feasible. The comparison also demonstrated that the freezing rate in this case was decreased by natural convection in the liquid just as freezing with boundary conditions of the first kind and phase change approximately proceeds linearly with time rather than with square root of time at the initiation of freezing.