Approximation of heat and mass transport properties for one sided cake baking

Abstract

Abstract One-dimensional model for heat and mass transfer within a cake during a one-sided baking process is presented. Thermophysical properties from literature do not simulate temperature and mean moisture content trends close enough to experimental measurements. This makes reliable estimation of these properties extremely important. Hence, thermophysical properties are approximated as effective constant parameters using an inverse procedure. To ease parameter estimation, a coupled mathematical model is derived in nondimensional form showing up the key parameters driving the baking process. Complex step differentiation method is utilized to compute sensitivities in order to improve their precision. Optimal location and minimum number of temperature sensors are picked from D-optimality criterion. Effect of deformation is neglected in this study. Sensitivity analysis shows that the parameter derived from Darcy law representing a ratio of permeability to dynamic viscosity of gas seems to perturb the temperature and mean moisture content minutely. Weighted least square method with significant weight given to temperature measurements results in better approximation than ordinary and scaled least square objective functions. Inverse procedure is unable to estimate temperature profile with expected precision at boundary where heat flux enters above 100\xa0°C as the model fails to address dough transformation.