# A Fast and Accurate Method for Computing the Microwave Heating of Moving Objects
## 3 Results and Discussion
### The Influence of Rotational Speed on the Microwave Heating  
The speed of the rotating turntable always acts as an important factor in optimizing the domestic microwave oven, which was infrequently investigated by previous moving-mesh methods because this was too time-consuming [16]. Here, we use the same model verified above to study the influence of the rotational speed on the microwave heating. To mimic a real microwave oven, the input power of the waveguide is added to 1 KW and three rotational speeds, i.e., 10 rpm, 5 rpm, and 2.5 rpm, are calculated and compared. To ensure more accurate simulation results, a finer mesh with 163,965 quadratic tetrahedral elements and a smaller rotation angle of 15\({}^{\circ}\) are selected for the computation, i.e., the rotation parts will stay at each location for 0.25 s, 0.5 s, and 1 s, respectively. The microwave heating lasts 24 s. Additionally, for comparing the heating uniformity we also compute for the potato remaining stationary during the whole microwave heating. Firstly, the time-dependent scattering parameter S\({}_{11}\) of the rectangular waveguide, which reflects the effective output microwave power of the microwave oven, is quantitatively given in Figure 10. It is clear that all scattering parameters of the microwave ovens with rotating potatoes fluctuate with the time and the time interval of the ups and downs are almost a half period of the rotation of the turntable, suggesting that the effective output power is sensitive to the location of the heated potato. Moreover, with the increment of heating time, the fluctuant S\({}_{11}\) gradually increases and the amplitude of fluctuation decreases. This can be explained based on the temperature-dependent dielectric properties of the potato. As shown in Table 1, both real and imaginary parts of the dielectric constant of the potato decrease with the increment of temperature from 20 to 100 \({}^{\circ}\)C, indicating that its microwave absorption also decreases. Therefore, when the heating time adds, the temperature of the potato increases and the absorbed microwave power decreases. \begin{table}
\begin{tabular}{l l l} \hline \hline \multicolumn{1}{c}{**Property**} & \multicolumn{1}{c}{**ALE Method**} & \multicolumn{1}{c}{**Proposed Method**} \\ \hline \(SD\) in P1 & 9.28 & 9.37 \\ \(SD\) in P2 & 4.89 & 5.29 \\ \(SD\) in P3 & 6.26 & 6.49 \\ \(SD\) in P4 & 1.58 & 1.80 \\ \(SD\) in P5 & 6.22 & 6.60 \\ Average \(SD\) for all points & 6.19 & 6.45 \\ Total computation time, s & 50,117 & 5555 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Total computation time and standard deviation (\(SD\)) in different calculations at five locations. Secondly, we compare the temperature field distribution on the top surface of the potato after heating 24 s at different rotational speeds as shown in Figure 11. It can be seen that all temperature distributions have similar patterns, whereas the dark areas are more obvious for the rotational speeds of 2.5 rpm. This means that a slow rotational speed is not good for improving the heating uniformity. To further qualitatively compare the effects of speed on the temperature inside the potato, the maximum and minimum temperatures are also plotted. As shown in Figure 12a, for low rotational speeds, the turntable rotates faster, the minimum temperature of the potato is higher. When the turntable rotates faster than 5 rpm, the minimum temperature of the potato is almost no longer affected by the speed. On the other hand, the rotational speed is an effective way to lower the maximum temperature of the potato as presented in Figure 12b. It is clear that the maximum temperature roughly decreases with the increment of rotational speed. However, for the speed of 5 rpm and 2.5 rpm, the influence of the speed on the maximum temperature is not obvious. Combining Figure 12a,b, it can be concluded that increasing the rotational speed is an effective way to decrease the difference between the maximum and minimum temperatures of the potato and improve the heating uniformity.