Heat transfer analysis of cheese cooling incorporating uncertainty in temperature measurement locations: Model development and validation

Abstract

Successful modelling of the thermal behaviour of food products requires accurate knowledge of both the thermal properties of the product and the cooling media to which it is exposed to and a correct approach to validation of the model output against experimental temperature histories. This procedure is complicated where there is uncertainty in the location at which temperature is measured in the product. The cooling of a soft cylindrical cheese product that is partially immersed in brine and air is examined. As the cheese is very deformable, it is not possible to exactly identify the measurement location of the temperature-recording thermocouples. The Uniform and Exponential probability distributions were found to best represent the variability in thermocouple location at the centre and surface of the product, respectively. Expressions for the mean measured temperature at the centre and surface that result from the distributed nature of thermocouple location were obtained. These expressions were used to derive equivalent locations in the cheese which should be used when comparing model and experimental temperature predictions. The theoretical approach was also checked against Monte Carlo simulations and there was excellent agreement between them. It was shown that when validating model temperature histories against experimental readings that this phenomenon must be taken into account.