Mathematical Analysis of the Effective Thermal Conductivity of Food Materials in the Frozen State

The effective thermal conductivity of binary aqueous solutions or gel systems of glucose, sucrose, potato starch, gelatin, and egg albumin in the frozen state were theoretically investigated. Structural models were used for evaluating heat conduction combined with the ice fraction measured for the same sample as that used in the measurement of effective thermal conductivity. The temperature-dependency of the ice fraction was determined by the phase diagram or DSC method. The structural models employed, with no fitting parameters involved, were the series, parallel, and Maxwell-Eucken models with ice as the dispersed phase (ME1 model) and as the continuous phase (ME2 model). The intrinsic thermal condictivity for each component was determined from measurements taken on unfrozen sample. Although all of the four models were applicable to the unfrozen sample with no substantial difference in prediction, the ME1 model, which was composed of the dispersed ice phase and continuous thick solution phase, was the only model applicable to the frozen sample for predicting the effective thermal conductivity within 10% accuracy. With all the samples tested, the ME1 model gave the best results of the four models, suggesting the wide applicability of this model for predicting the effective thermal conductivity of frozen food materials.