Estimation of heat flux in bread baking by inverse problem

Optimal Design of Complementary Experiments for Parameter Estimation at Elevated Temperature of Food Processing

Simultaneous estimation of thermal properties can be challenging, especially when the parameters are temperature-dependent. Previous research has shown that by using a complementary experiment, temperature-dependent thermal conductivity can be estimated using a single experiment. The objective of this study was to optimize the complementary experiments that can facilitate the simultaneous estimation of temperature-dependent thermal conductivity and volumetric heat capacity. A theoretical study was conducted with two experiments in a single trial with the sample being kept in a cylindrical sample holder, which had a thin film heater in the center. The first part of the experiment was conducted by keeping the external surface temperature at 50 °C for 300 s and allowing the center temperature to equilibrate with the boundary temperature. Then, the second part of the experiment followed, where the thin film heater was supplied with electrical power to increase the center temperate to 140 °C. Several heating profiles were studied to maximize the information obtained from the complementary experiments, and the best one was the power profile with a sinusoidal function. All four parameters of sweet potato puree temperature-dependent thermal conductivity (0.509 to 0.629 W/mK at 25 °C and 140 °C, respectively) and volumetric heat capacity (3.617 × 106 to 4.180 × 106 J/m3K at 25 °C and 140 °C, respectively) were estimated with low standard errors.

Dynamic Thermal Properties Estimation Using Sensitivity Coefficients for Rapid Heating Process

Thermal conductivity determination of food at temperatures > 100 °C still remains a challenge. The objective of this study was to determine the temperature-dependent thermal conductivity of food using rapid heating (TPCell). The experiments were designed based on scaled sensitivity coefficient (SSC), and the estimated thermal conductivity of potato puree was compared between the constant temperature heating at 121.10 °C (R12B10T1) and the rapid heating (R22B10T1). Temperature-dependent thermal conductivity models along with a constant conductivity were used for estimation. R22B10T1 experiment using the k model provided reliable measurements as compared to R12B10T1 with thermal conductivity values from 0.463 ± 0.011 W m⁻¹ K⁻¹ to 0.450 ± 0.016 W m⁻¹ K⁻¹ for 25–140 °C and root mean squares error (RMSE) of 1.441. In the R12B10T1 experiment, the analysis showed the correlation of residuals, which made the estimation less reliable. The thermal conductivity values were in the range of 0.444 ± 0.012 W m⁻¹ K⁻¹ to 0.510 ± 0.034 W m⁻¹ K⁻¹ for 20–120 °C estimated using the k model. Temperature-dependent models (linear and k models) provided a better estimate than the single parameter thermal conductivity determination with low RMSE for both types of experiments. SSC can provide insight in designing dynamic experiments for the determination of thermal conductivity coefficient.