Numerical simulations of food freezing times using thermophysical food property models

Abstract

This work aims to evaluate the performance of a numerical modeling for prediction of food freezing times by comparing numerical with experimental results. A one-dimensional heat diffusion model including temperature dependent thermophysical properties, sudden variations of thermophysical properties during phase change and surface mass transfer was approximated using the finite differences method. The thermophysical properties of foods were modeled as functions of food composition, temperature and phase, using Choi and Okos correlations (Choi & Okos, 1986). Simple geometries such as thin slab, long cylinder and sphere were modeled, and the numerical results were compared with experimental data obtained in a pilot scale freezing tunnel. Numerical simulations were performed for some selected foods, namely sausages, potatoes, hamburger and cheese, in different geometries and sizes. The boundary conditions of the freezing surfaces were of heat and mass convection. The heat transfer coefficients were taken after usual correlations for these geometries. The mass transfer modeling was done using mass convection correlations, considering a known surface wetness. It was found that mass transfer due to moisture evaporation, thermodependency of properties and an accurate estimate for the heat transfer coefficient were crucial elements for the correct prediction of freezing curves. The numerical results were only able to predict the experimental freezing curve by adjusting the theoretical value of the heat transfer coefficient by a factor, varying from 0.7 to 1.3 in most cases, with some outliers up to 2.4. This means that although the heat conduction inside the food itself seemed to generate reasonable food freezing rates, the convection coefficients produced experimentally seemed to vary wildly from the ones predicted in the theoretical relationships. Therefore, one should be very keen of the magnitude of the convection coefficient while performing predictions for a given food freezing application problem.

Keywords: Food freezing, Transient heat conduction, Finite difference, Models for food thermal properties