Heat transfer analysis of cheese cooling incorporating uncertainty in temperature measurement locations: Application to the industrial process

Abstract

A cylindrical cheese product with an irregular cross sectional geometry is cooled by partial immersion in brine. It is essential to calculate the temperature–time history of the product during this cooling phase to ensure its microbiological safety. The heat transfer analysis is complicated by both the non-standard product geometry and the non-uniform surface heat transfer coefficients that prevail. The flotation behaviour of the cheese at the air/brine interface is analysed to determine the heat transfer areas exposed to each cooling fluid. A finite element model is developed to predict temperature histories at various points in the product and to determine the slowest cooling region in the product. The cooling performance of the cheese is also studied experimentally. Comparison of the theoretical and experimental temperature histories is complicated by uncertainty in the location of the thermocouples in the product. By statistically quantifying the imprecision in thermocouple position, the expected temperatures in each region of interest can be found from the thermal model by Monte Carlo sampling. With the model, the top region of the cheese stick has been shown to determine cooling time because the existence of the non-uniform boundary condition is significant in determining the evolution of temperature.