Methods of estimating freezing and thawing times of foods are important in determining the design and operating regimes for processing plants to insure adequate product quality maintenance and achieve rated production throughput.

It is still useful, however, to use these idealized estimates since they show the effect on process times of changing various parameters and serve as a starting point for processing plant designs. Two of the easiest to use methods are Tao's charts and Plank's equation. These are described and examples given to illustrate their use.

A number of solutions have been proposed for various types of unsteady state conditions. They are idealized in that they do not take into account the the homogeneous nature of foods or variations in thermal properties with temperature. The solutions also place various constraints on the geometric shape of the material and the freezing or thawing regime used.

Most analytical solutions to problems of heat conduction with phase change are highly mathematical, involving cumbersome and lengthy calculations (1). The net result is that designers find difficulty working with the solutions and even if they eventually get some sort of answer they lack confidence in the result and hesitate to use it in actual plant design.

Two methods for estimating either freezing or thawing times, that are simple to use are Tao'scharts and Plank's equation. These two methods were chosen because they seem to be the bestfrom the standpoint of general reliability and simplicity of application. If freezing times areto be estimated, the thermophysical properties of the frozen material are used in the equations;for thawing calculations the properties of the thawed material are used. Tao's charts wereobtained from the numerical solutions of a heat conduction equation without the use of any assumptionregarding temperature distribution in a sample object. On the other hand, Plank's formulawas derived by assuming linear temperature distribution in the frozen portion of the object.Therefore, freezing or thawing times estimated using Tao's charts are probably more reliablethan those calculated by Plank's equation. Comparative determinations over a range of conditionsindicated that freezing or thawing times estimated using Tao's charts were always 5 to 15% longerthan the corresponding times determined using Plank's equation.

Over the years a great deal of work has been done to compare the theoretical results of thesetwo methods with experimental measurements (2, 3, .4, 5, 6, 7). While there have been discrepancies depending on the test conditions, accuracies are usually within 15 to 20% and often muchcloser. For more accurate estimates, semi-empirical methods incorporating arbitrary constantsto suit a particular application wili probably be needed. Another approach recently being usedinvolves iterative solutions using computer programs which take into account varying thermalproperties as temperature and phase changes occur. Both of these techniques are, however,the scope of the present paper.