Selection of better mathematical model describing cake baking for inverse analysis

Abstract

This paper presents selection criteria based on inverse solutions for mathematical models that predict heat and mass transfer involved in contact baking of cake. For the models in focus, the evaporation-condensation effect occurring during baking is incorporated by non-equilibrium (model-I) and equilibrium approach (model-II). Effect of product parameters on baking process is studied. To select an accurate model, weighted least square objective function and complex step differentiation method are employed. A numerical study with simulated measurements is performed to check the feasibility of parameter estimation from a single experiment. This numerical study showed that model-II (i.e. with equilibrium approach) is more suitable for further inverse analysis. Significant weight given to temperature measurements resulted in better inverse solutions for both the models. Comparing final estimates from the models to the actual measurements, thermal properties approximated are close enough but mass transfer properties show deviations up to an order of magnitude. On extending the study for other baking conditions, it is found that inverse solution from model-II can adapt better than model-I for any change in the baking condition. Conclusively, a mechanistic model with equilibrium approach should be preferred than a model with explicit evaporation (model-I) for an inverse analysis. Eventually, this work aims to present an effective approach intended to resolve the challenges in accurate modeling of the baking process that arise due to limited knowledge of physical properties.