A systematic procedure for testing the accuracy of freezing time prediction methods is discussed. It involves carrying out freezing time predictions by an accurate numerical method as well as the method under test, and careful cross-checking of prediction errors for correlation with a number of physical parameters. Criteria are given for selection of an appropriate numerical method. The need for systematic cross-checking is illustrated by comparisons between four recent prediction methods. The comparisons show the strengths and weaknesses of the four methods. They also indicate general shortcomings in available methods and data, and so highlight those areas in which future research might be most profitable.

Assessment of freezing time prediction methods.

A computer-aided method for the prediction of properties and freezing/thawing times of foods

A previous study of methods for predicting the freezing times of slabs, cylinders and spheres was extended to cover rectangular bricks of food materials. Experimental measurements of the freezing time were made over a wide range of conditions using a food analogue material, and these results compared to times calculated from various available prediction methods. The three-dimensional version of a three time-level finite difference scheme was found to be the most accurate numerical solution. Simple formulae are available for predicting the freezing time of rectangular bricks using the geometric factors derived by Plank. These factors are shown to be subject to error, and none of this group of methods gave accurate prediction of freezing time. A previously proposed group of formulae are extended to cover rectangular bricks. These formulae are simple to use and accurate. They are applicable to slabs (±5% with 95% confidence), and to cylinders and spheres (±7% with 95% confidence) as well as to bricks (±10% with 95% confidence). These extend the previously published formulae for slabs, cylinders and spheres without significant loss of accuracy.

Prediction of freezing times for foods in rectangular packages

An explicit numerical method, involving enthalpy formulation, to predict temperature distribution in foods during freezing and thawing was developed. The accuracy of the proposed method was validated using published experimental data obtained for freezing and thawing of Tylose. The enthalpy formulation avoids the problems of strong discontinuity experienced when the apparent specific heat formulation is used in predicting temperatures for situations involving phase change. The proposed method predicts temperatures in good agreement with experimental data. The computer code can be easily programmed on a desk-top computer for use in teaching and research on predicting freezing and thawing rates in foods.

Prediction of Freezing and Thawing Times of Foods Using a Numerical Method Based on Enthalpy Formulation

An assessment of the accuracy of numerical methods used in the prediction of freezing and thawing times was made using a comprehensive set of freezing and thawing data for both regular and irregular multidimensional shapes. For regular shapes, a finite difference method gave accurate predictions with reasonable computation costs. Predictions for two finite element method formulations were not always accurate. This was due to practical constraints on the computation costs which meant that time and spatial grids could not always be made sufficiently fine to ensure that the prediction method uncertainty was insignificant compared with the other sources of imprecision. Guidelines are suggested for the use of the finite element method as a freezing or thawing time predictor. These should ensure that the prediction method error is small while keeping the computation costs reasonable.

Prediction of freezing and thawing times for multi-dimensional shapes by numerical methods

The third kind of boundary condition in numerical freezing calculations

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The third kind of boundary condition in numerical freezing calculations