Use of Inverse Method to Determine Thermophysical Properties of Minimally Processed Carrots during Chilling under Natural Convection

Abstract

The aim of this study was to determine the thermophysical properties and process parameters of cylindrical carrot pieces during their chilling. For this, the temperature of the central point of the product, initially at 19.9 °C, was recorded during chilling under natural convection, with the refrigerator air temperature maintained at 3.5 °C. A solver was created for the two-dimensional analytical solution of the heat conduction equation in cylindrical coordinates. This solver and the experimental data set were coupled to the LS Optimizer (V. 7.2) optimization software to simultaneously determine not only the values of thermal diffusivity (α) and heat transfer coefficient (hH), but also the uncertainties of these values. These values were consistent with those reported in the literature for carrots; in this study, the precision of these values and the confidence level of the results (95.4%) were also presented. Furthermore, the Biot numbers were greater than 0.1 and less than 40, indicating that the mathematical model presented in this study can be used to simultaneously estimate α and hH. A simulation of the chilling kinetics using the values obtained for α and hH showed good agreement with the experimental results, with a root mean square error RMSE = 9.651 × 10−3 and a chi-square χ2 = 4.378 × 10−3.

Keywords

• minimal processing
• analytical solution
• thermal diffusivity
• heat transfer coefficient
• optimization