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MATHEMATICAL MODELLING ON FREEZING AND THAWING (EQUATION, FOODS)
Freezing and thawing are important food processing operations, often carried out by placing objects in an air stream which exchanges heat with the objects. These objects, even when rectangular, have more than two surfaces and the heat transfer coefficient (h) for each surface is almost always different. Based on equations for predicting effective heat capacities, enthalpies and thermal conductivities, freezing and thawing equations for time-temperature estimation for an isolated infinite slab and low Biot number (Bi) have been developed. These were extended using correction factors based on Bi, as to provide equations which can be used for rectangular objects in a row with two, or four exposed faces. Because thermal conductivity (k) changes during freezing and thawing, Bi also changes. An equation for the variation in Bi as k varies is obtained. Average Bi values defined by 2ha/(k(,o)+k(,f)), 0.5 ha/k(,o)+0.5 ha/k(,f), and ha/k(,o) for thawing and ha/k(,f) for freezing were also used. When h is different on opposite surfaces, the maximum temperature does not occur at the center plane of the object. Approximated solutions are obtained using correction factors based on Bi values determined with the position of the plane where the maximum temperature occurs or based on the different Bi values obtained with the different h. Average temperature vs time results are compared using these Bi and the numerical PDE solutions. h, was experimentally evaluated and an alternative correlation was developed. With this correlation the individual surface h's could be predicted as a function of the approach air velocity and the geometric characteristics of the row and object, and the freezing and thawing temperature vs. time behavior of the object placed in the row could then be predicted using this h. Typical cases were tested and the differences between the experimental results, the values predicted by the approximation equations for low Bi and the numerical solutions of the PDE were determined.
RUBIOLO DE REINICK, AMELIA CATALINA, "MATHEMATICAL MODELLING ON FREEZING AND THAWING (EQUATION, FOODS)" (1985). Doctoral Dissertations Available from Proquest. AAI8602686.