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

Abstract

A one-dimensional unsteady state mathematical model with variable physical property parameters is developed to simulate the freezing time of individual food in freezing process. The phase-change problem in the freezing process is solved with apparent heat capacity approach, and the physical property change is described with a quadratic curve. The model’s numerical algorithm is finite-difference method with Crank–Nicolson scheme, which is programmed with Visual Basic 6.0. The predicted temperature history of cucumber slice in freezing process is validated with a set of actual experimental data. The predicted freezing times of spherical, cylindrical and tabulate foodstuffs are also validated with several sets of experimental data, and the accuracies of freezing times predicted by the model are all better than that of several other models in the literatures based on the same experimental data. In all the cases, the linear regression correlation coefficients ( R 2) between predicted and experimental values are over 0.989, which means that the model could be used to predict the freezing time and the temperature history of spherical, cylindrical and tabulate food with various physical properties at different cooling medium temperatures. So it could be used to give a guideline for freezing experiments, freezing equipment design and frozen-food production.