Freezing Time Modeling for Small Finite Cylindrical Shaped Foodstuff

Abstract

A model was developed consisting of a modified Plank's equation to estimate phase change time and two unsteady state cross-product heat transfer equations for estimating precooling and tempering times. It accurately predicted total time to proceed from an initial temperature above the freezing point to a final temperature of -18°C. A correction factor was developed and incorporated in the P term in Plank's equation to correct for the effect of initial and freezer medium temperatures and heat transfer coefficients. The model, tested over a broad range of freezing conditions, had a mean absolute error of 5.9% in predicted values relative to experimental values.

One-dimensional finite-difference modeling on temperature history and freezing time of individual food

“…In order to verify the model's prediction accuracy for cylindrical foodstuffs, the experimental data in the literature published by Chung and Merritt (1991) was used as basic parameters in the numerical model. In the literature, KTS was used as the freezing material in all experiments pertaining to cylinders (Cleland & Earle, 1977), and the center temperature of KTS is À10°C at the end of freezing.…”

“…Plank (1941) derived an analytic formula for the freezing time from a hypothesis and analysis, which is an approximate solution in common use. However, its accuracy is not satisfactory for complex conditions so that many researchers presented their revised Plank equations (Chung & Merritt, 1991;Hossain, Cleland, & Cleland, 1992;Le Blanc, Kok, & Timbers, 1990;Ló pez-Leiva & Hallstr om, 2003;Pham, 1996;Sanz, Ramos, & Mascheroni, 1996. By comparison, numerical solution method is more effective to analyze the actual situation.…”

COLLECTION of ACCURATE EXPERIMENTAL DATA FOR TESTING the PERFORMANCE of SIMPLE METHODS FOR FOOD FREEZING TIME PREDICTION

“…Overall, the data are of high quality as confirmed by the excellent agreement of experimental results and finite difference predictions (mean percentage difference = 0.5 %, standard deviation 3.5%). Chung and Merritt (1991) made 49 measurements of freezing time of finite cylinders of scallop meats. About 70% of the runs were done in air, the remainder in liquid immersion.…”

Metastable States of Water and Ice during Pressure-Supported Freezing of Potato Tissue

“…Related to the processing time, several numeric prediction methods were reported in the literature, but mainly for atmospheric conditions (Agnelli and Mascheroni, 2001;Mannapperuma and Singh, 1988;Pham, 1985Pham, , 1987Pham, , 1989Pham, and 1996Chung and Merritt, 1991;Sanz et al, 1999;Cleland and Earle, 1984;Miyawaki et al, 1989;Franke, 2000;Martens et al, 2001;Bon et al, 2001). Few reports have been published for numerical modeling of high-pressure-supported freezing processes.…”

“…The peak value of the apparent specific heat function (Weibull) was markedly reduced at high pressure, but the general shape of the applied distribution of the specific heat could be retained. Sanz and Otero (2000) applied a mathematical model in three steps (precooling, phase change, and tempering) based on Chung and Merritt (1991) transient state heat transfer equations for finite agar gel (99% water) cylinders and based on the Newmann's rule for finite geometry at 92, 130, 180, and 210 MPa. In this case, as the model was divided in three steps, the predictability of the jump to the plateau temperature after supercooling is lost, and only pressure-shift freezing was studied to compare the overall process times with higher or lower degree of supercooling.…”