Modelling of heat transfer to foods incorporating uncertainty in the location of experimental temperature measurement

A cheese product in the shape of a rectangular slab is cooled by immersion in brine. The temperature of the cheese during cooling was measured by inserting thermocouples into the product. As the cheese is very soft and deformable, it is not possible to exactly identify the measurement location. The Uniform and Exponential probability distributions were found to best represent the variability in thermocouple location at the centre and surface respectively. Cooling of the product was modelled with the one dimensional Fourier field equation. 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. Experiments were conducted to quantify the variability in thermocouple location and the associated dispersion in temperature readings. It was shown that when validating model temperature versus time histories against experimental readings that this phenomenon must be taken into account.