Modeling the Influence of Temperature-dependent Thermal Properties on the Freezing Front

Abstract

Although numerical methods enable comprehensive analyses of food freezing, a thorough quantification is lacking the effects on the process introduced by uncertainties in variable thermal properties. Analytical models are, however, more suitable tools to perform such calculations. We aim to quantify these effects by developing a solution to the freezing front (FF) problem subject to temperature-dependent thermal properties and one-dimensional convective cooling. The heat integral balance method, Kirchhoff's transformation, and Plank's cooled-surface temperature equation (as a seed function) enabled us to obtain an approximate solution to the FF penetration time. To optimize model accuracy, two adjustable parameters were correlated with the inputs via nonlinear regression referenced to numerical simulation FF data. The mapped sensitivities, generated by perturbations in the temperature-dependent thermal conductivity and effective heat capacity, undergo rapid nonlinear changes for Biot numbers below 6. Above this level, these sensitivities stabilize depending on the cooling medium temperature and a thermal conductivity parameter. The median thermal conductivity-driven sensitivity is 0.348 and its interquartile range (IQR) is 0.220 to 0.425, whereas the median latent heat-driven sensitivity is 0.967 (IQR: 0.877 to 0.985). Statistical error measures and a ten-split K-fold validation support the model accuracy and reliability of the parameter estimates. Together, the model allows for gaining insights into the nonlinear behavior and magnitude of the influence of variable properties on the FF for a wide range of conditions. Nonlinear methods and prior information enable practical modeling of transport phenomena in foods.