Mathematical model for determining thermal properties of whole bananas with peel during the cooling process

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

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.

Dynamic Thermal Properties Estimation Using Sensitivity Coefficients for Rapid Heating Process

Thermal conductivity determination of food at temperatures > 100 °C still remains a challenge. The objective of this study was to determine the temperature-dependent thermal conductivity of food using rapid heating (TPCell). The experiments were designed based on scaled sensitivity coefficient (SSC), and the estimated thermal conductivity of potato puree was compared between the constant temperature heating at 121.10 °C (R12B10T1) and the rapid heating (R22B10T1). Temperature-dependent thermal conductivity models along with a constant conductivity were used for estimation. R22B10T1 experiment using the k model provided reliable measurements as compared to R12B10T1 with thermal conductivity values from 0.463 ± 0.011 W m⁻¹ K⁻¹ to 0.450 ± 0.016 W m⁻¹ K⁻¹ for 25–140 °C and root mean squares error (RMSE) of 1.441. In the R12B10T1 experiment, the analysis showed the correlation of residuals, which made the estimation less reliable. The thermal conductivity values were in the range of 0.444 ± 0.012 W m⁻¹ K⁻¹ to 0.510 ± 0.034 W m⁻¹ K⁻¹ for 20–120 °C estimated using the k model. Temperature-dependent models (linear and k models) provided a better estimate than the single parameter thermal conductivity determination with low RMSE for both types of experiments. SSC can provide insight in designing dynamic experiments for the determination of thermal conductivity coefficient.