Freezing times using time derivative of temperature on surface of foods

Abstract

A numerical model is developed to predict the freezing process of foods or analogues. The finite difference method (FDM) is employed to calculate the temperature distribution in a food T(x,t). The aim of this research study is to test the use of the time derivative of temperature on the surface, dT(i = n)/dt in x = L, and at the center of food, dT(i = 1)/dt in x = 0. This methodology is employed to predict the freezing time (tcalc), using the properties of tylose gel (k, ρ, and Cp), which is a food analog. Simulations were performed using the model, obtaining (tcalc), and compared with 227 experimental data points (texper). In summary, the main conclusions of this study are as follows. It is important to use the derivative dT(n)/dt at x = L in model (2) in relation to the use of dT(1)/dt at x = 0 in the same model. The evaluation of thermal conductivity using temperature T = Tn-2, k(Tn-2) at x = L with the proposed model and properties of tylose gel to calculate (tcalc) is adequate. Simulations using k(Tn-2) at x = L with the proposed model were performed, obtaining (tcalc), and compared with 227 experimental data points (texper), exhibiting good agreement. The following parameters were obtained for 227 experimental data points: minimum error Emin = -6.97 %, overall mean error Emean = 0.06 %, maximum error Emax = 8.08 %, and standard deviation σn-1 = 2.19 %.