Modelling supercooling in frozen strawberries: Experimental analysis, cellular automation and inverse problem methodology

Abstract

The quality of frozen strawberries ( Fragaria ananassa) is influenced by the supercooling capacity during freezing. This present research aims at (i) evaluating the supercooling capacity of strawberries as function of the operational variables: initial temperature, air temperature, air velocity and strawberry maximum diameter; (ii) use the data records to develop a cellular automata model of supercooling inside a finite element space domain; and (iii) use the inverse problem methodology to validate the developed model and estimate the strawberry thermal capacity and thermal conductivity, of both pulp and vascular tissues during phase transition. Experimental data emphasises that the nucleation temperature is dependent on the thermocouple position. Higher supercooling capacities are obtained at the surface and middle positions than at the centre. Nucleation at the surface shows to be dependent upon the initial temperature, where maximum supercooling capacities are obtained with temperatures near +2.9 °C. Furthermore, a pattern of increasing nucleation temperatures towards the centre was detected during principal components analysis. This observation is used to derive thermodynamic restriction rules to nucleation inside the cellular automata model. Thermal capacity and conductivity were successfully obtained by the inverse problem methodology. The optimised model proved to be statistically similar to the experimental freezing curve ( p < 0.001); although minimal systematic errors were still found. Supercooling and nucleation was modelled in macroscopic terms and considered inherently stochastic. Cellular automation proved to be a powerful tool to reproduce and explain the temperature patterns across the strawberry’s physical domain during the freezing of strawberries inside an air blast freezer.