## 4 Results and Discussion  
### Evolution of EMU Surface Temperature Profile during Heating Process  
The levitation electromagnet module is heated under five different vacuum levels, where the 1.0 atm heating process can be treated as a reference for evaluating the reduction in heat dissipation and increase of maximum temperature caused by vacuum environment. During the heating process, the maximum temperature rise on each type of EMU is shown in Table 3. For each vacuum level, \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \
\begin{tabular}{c} **Medium** \\ **(Segregated** \\ **Solver**) \\ \end{tabular} &
\begin{tabular}{c} **Medium** \\ **(Coupled** \\ **Solver**) \\ \end{tabular} & **Fine** & **Experiment** \\ \hline Total number of grids (million) & 2.94 & 10.03 & 10.03 & 47.82 & / \\ \hline Temperature rise & 10 min & 30.66 & 30.26 & 30.25 & 30.16 & 24.6 \\ during heating & 20 min & 52.99 & 52.65 & 52.62 & 52.55 & 47.63 \\ process (K) & 30 min & 69.37 & 69.02 & 68.98 & 68.93 & 65.91 \\ process (K) & 40 min & 82.28 & 82.04 & 82.02 & 81.99 & 80.14 \\  & 50 min & 93.25 & 93.11 & 93.1 & 93.09 & 93 \\  & 60 min & 101.72 & 102.21 & 102.25 & 102.41 & / \\ \hline
100 K temperature rise time (min) & 58.6 & 58.2 & 58.1 & 57.9 & 57.0 \\ \hline Heating time difference (\%) & 2.8 & 2.1 & 1.9 & 1.6 & / \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters and results in mesh sensitivity study. the EMUs are heated for 60 min. The maximum temperature rise profiles of EMUs exhibit a symmetrical pattern due to the symmetrical distribution of the levitation electromagnet module. In the first 10 min of the heating process, the temperature differences among the 3 types of EMUs are small. After 10 min heating, the temperature rise of the end magnet units appear to be slower than that of the primary magnet units and core-elevated magnet units. This is because the end magnet units are located on both sides of the levitation electromagnet module as illustrated in Figure 1a. The heated air around the end magnet units has more sufficient space for convection heat flow, which in turn lowers the temperature of air near the fluid-solid interface on the end magnet unit and results in a better cooling. Meanwhile, the end magnet units have a lower heat-generation rate than that of the primary magnet units and core-elevated magnet units. This is another reason for the low temperature in the end magnet units. After 20 min of heating, the maximum temperature of the core-elevated magnet units gradually appears to have a slower increase speed than the primary magnet units. This is because the core-elevated magnet unit has an extruded top structure (as shown in Figure 2), which provides more surface area for heat dissipation. Therefore, the primary magnet unit in the levitation electromagnet module is the most likely to have overheating problems among all the EMUs. In order to further analyze the temperature distribution of the primary magnet units, the maximum temperatures of all the 6 primary magnet units after 60 min of heating are shown in Table 4. According to the results in Table 4, M\({}_{1}\) and M\({}_{6}\) have the maximum temperature rise, followed by M\({}_{2}\) and M\({}_{5}\), while M\({}_{3}\) and M\({}_{4}\) have the lowest temperature rises among all the heating magnet units. It should be noted that in the experimental section, it is mentioned that the maximum-temperature point appears at point P\({}_{\text{m}}\) on M\({}_{3}\). However in the simulation analysis it is found that the maximum temperature among EMUs appears at M\({}_{1}\) and M\({}_{6}\). This is because the thermocouple in the experiment was not placed at an exact position with the maximum temperature in M\({}_{1}\) and M\({}_{6}\). However, the vertical height of point P\({}_{\text{m}}\) does agree with the height of the maximum-temperature points in M\({}_{1}\) and M\({}_{6}\).