Modeling microwave heating of frozen mashed potato in a domestic oven incorporating electromagnetic frequency spectrum

• Electromagnetic frequency spectrum was incorporated in microwave modeling.
• A Gaussian frequency distribution (2.45, 0.052) gave the best prediction accuracy.
• The developed method can be used for modeling any frequency spectrum.

Domestic microwave oven magnetrons produce microwaves in a frequency range of 2.45 ± 0.05 GHz. Most microwave heat transfer simulations simplify that the magnetron produces a monochromatic electromagnetic wave of frequency of 2.45 GHz to reduce the computational complexity. This study assumes that the magnetron produces a frequency spectrum defined by a Gaussian distribution of frequencies with a central frequency of 2.45 GHz and investigates the effect of Gaussian distribution variance of (0.05 GHz)2, (0.025 GHz)2, (0.017 GHz)2 on prediction accuracy when compared to using monochromatic frequency of 2.45 GHz. A three-dimensional finite element model coupling electromagnetic and heat transfer physics was developed to simulate heating of 550 g of frozen mashed potato for 6 min. The model was validated in a 1250 W rated microwave oven with the mashed potato tray placed at the center of the stationary turntable. The electromagnetic power densities were determined separately at five different frequencies equidistant between 2.4 and 2.5 GHz. They were then weighted averaged, based on the selected Gaussian distribution. Simulated temperature profiles of the models using the monochromatic frequency of 2.45 GHz and Gaussian frequency spectrum with different variances were compared with experimental temperature profiles obtained using a thermal imaging camera at the end of cooking and five fiber-optic thermocouples during cooking. The model results showed that predicted spatial surface temperature pattern by the model using frequency spectrum with the largest variance (0.05 GHz)2 had better agreement with the experimental temperature pattern when compared to that using a monochromatic frequency of 2.45 GHz. In the transient temperature profile measurement, the average RMSE value of five locations was 7.5 and 13.1 °C for simulations using frequency spectrum and monochromatic frequency of 2.45 GHz, respectively. When compared to using the monochromatic frequency of 2.45 GHz, the frequency spectrum with an assumption of having a Gaussian distribution with mean of 2.45 GHz and variance of (0.05 GHz)2 improved the accuracy of temperature field pattern and transient temperature profile.