Simple modelling of time-temperature profiles in food during baking

Abstract

Time-temperature profiles (TTP) in food during baking and other heat treatments are essential to understand and characterise a series of changes related to product quality, and for design, control and optimisation of the process. Experimental determination of TTP is not always practical, so mathematical modelling has been applied to characterise and predict TTP. Although physics-based models may be available, their implementation can result quite complex at industrial level or for use in applications outside the field of process modelling and simulation, e.g., kinetic modelling of quality changes. Therefore, the objective of this work is to develop and test simple and effective equations to characterise TTP at core and surface of the product during baking, since these positions determine the most important quality changes. For the core position, a modified Gompertz equation type is proposed, while an adapted Page model is used for the surface position; both models have only two fitting parameters and are easily implementable tools. Models were tested with data generated by a baking numerical model and also experimental TTP. In addition, capability of simple equations was evaluated with frying and oven roasting data, since all three processes can be considered as moving boundary problems with a water vaporisation front. Overall, a good fitting performance was obtained: mean absolute percentage error is less than 5% in most of cases.

Keywords

• Heat transfer
• Heating rate
• Modeling
• Moving boundary problem