Effect of Water Content on Thermo-Physical Properties and Freezing Times of Foods

Abstract

For the prediction of temperature change in different foodstuffs during freezing and thawing processes, accurate estimation of the thermo-physical properties of the product is necessary, such as specific heat, density, freezable water content, enthalpy, and initial freezing temperature. These data allow the adequate design and optimization of equipment and processes. Water is a main component in all foods and greatly influences the behavior of these properties, depending on its concentration. During the freezing process, which involves the phase change of water into ice, the specific heat, thermal conductivity, and density undergo abrupt changes due to the latent heat release. This complex process does not have an analytical solution and it can be described as a highly nonlinear mathematical problem. Many difficulties arise when trying to numerically simulate the freezing process, especially when using the finite element method (FEM), which is especially useful when dealing with irregular-shaped foodstuffs. Several techniques have been applied to consider the large latent heat release when using FEM. One traditional method is the use of the apparent specific heat, where the sensible heat is merged with the latent heat to produce a specific heat curve with a large peak around the freezing point, which can be considered a quasi-delta-Dirac function with temperature (depending on the amount of water in the food product) (Pham 2008). However, this method usually destabilizes the numerical solution. Implementation of the enthalpy method, which can be obtained through the integration of the specific heat with temperature (Fikiin 1996; Comini et al. 1990; Pham 2008; Santos et al. 2010), and the Kirchhoff function, which is the integral of the thermal conductivity, allows the reformulation of the heat transfer differential equation into a transformed partial differential system with two mutually related dependent variables H (enthalpy) and E (Kirchhoff function) (Scheerlinck et al. 2001). These functions, H and E versus temperature, are smoother mathematical functions compared to the specific heat, thermal conductivity, and density versus temperature, avoiding inaccuracies and/or divergence of the numerical method. Even though it brings great advantage to the resolution of the problem, with the simultaneous enhancement of the computational speed of the program, this transformation of variables is not widely used in the literature. Unleavened dough and cooked minced meat were selected due to their significant difference in water content in order to explore the performance of the computational code written using the enthalpy-Kirchhoff formulation. Another important reason is because cooked minced meat and dough are both present in several ready-to-eat meals, therefore contributing valuable information to food processors interested in optimizing cooling and freezing operating conditions of semi- or fully processed goods. The objectives of this work are (1) to experimentally determine by differential scanning calorimetry (DSC) the thermo-physical properties of dough and cooked minced meat in the freezing range: specific heat as a function of temperature, bound water, heat of melting, initial freezing temperature, etc.; (2) to develop and validate a finite element algorithm to simulate the freezing process in regular and irregularly shaped foodstuffs; and (3) to introduce appropriate equations of the thermo-physical properties in the numerical program to assess the effect of total water content, bound water, and surface heat transfer coefficient on freezing times in an irregular food system.