## 4 Results and Discussion
### Evolution of EMU Surface Temperature Profile during Heating Process
In order to explain the temperature difference between EMUs, local temperature and velocity contours in the gap region of EMUs are shown in Figure 3. According to the velocity contour in Figure 3a,b, the heated air is driven by buoyancy force and flow towards the upper part of the fluid domain. This buoyancy flow therefore creates a low-pressure region on the lower part of the levitation electromagnet, and the low-pressure region is then filled by the unheated air on the bottom part of the fluid domain. This phenomenon explains the cause of spatial variance of temperature in the fluid domain. Additionally, it can be observed from Figure 3a that a local flow separation between H\({}_{2}\) and M\({}_{1}\) is formed. The flow velocity is decreased due to the increase in cross section near the flow separation region depicted in Figure 3a, the convection heat flow on the side of M\({}_{1}\) is then compromised and therefore leads to a higher temperature of the M\({}_{1}\) unit. The phenomenon shown in Figure 3a,c can also be observed between M\({}_{6}\) and H\({}_{3}\). As for the air-gap region between M\({}_{3}\) and M\({}_{4}\), the buoyancy-driven flow has a higher speed than the region between H\({}_{2}\) and M\({}_{1}\), which in turn leads to a lower fluid temperature and better cooling performance. This explains the variance of maximum temperature among EMUs as shown in Table 4. Based on the analysis above, the M\({}_{6}\) unit is selected for the proceeding quantitative analysis on thermal characteristics of EMUs. The heat dissipation of the levitation electromagnet is influenced by the convection heat flux and radiation heat flux on the solid-fluid interface. These factors contributed to three different temperature profiles on the surface of each EMU during the heating process. Figure 4 shows the surface temperature \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Heating Time (min)** & **10** & **20** & **30** & **40** & **50** & **60** \\ \hline Primary magnet units & 30.1 & 51.3 & 66.5 & 78.0 & 87.4 & 95.6 \\ Core-elevated magnet units & 30.4 & 50.9 & 65.3 & 76.3 & 85.7 & 94.0 \\ End magnet units & 29.9 & 50.0 & 64.5 & 76.1 & 86.0 & 95.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum surface temperature rise on different type of electromagnet units (EMUs) under 1.0 atm. distribution of M\({}_{6}\) during the heating process at some representative time frames and vacuum levels. The three reference time frames are selected as t\({}_{1}\), t\({}_{2}\) and t\({}_{3}\), where t\({}_{1}\)= 3 min, t\({}_{2}\)=10 min and t\({}_{3}\)= 60 min. Figure 4: Surface temperature contour of M\({}_{6}\) under different vacuum levels at different heating stage: (**a**) 3 min heating under 0.1 atm; (**b**) 3 min heating under 0.3 atm; (**c**) 3 min heating under 1.0 atm; (**d**) 10 min heating under 0.1 atm; (**e**) 10 min heating under 0.3 atm; (**f**) 10 min heating under 1.0 atm; (**g**) 60 min heating under 0.1 atm; (**h**) 60 min heating under 0.3 atm; and (**i**) 60 min heating under 1.0 atm. Figure 3: Local contour near the maximum temperature point of primary magnet units after 60 min of heating under 1.0 atm. This contour cross section is parallel to xz plane in Figure 1 and is 0.75 H away from the symmetric plane of the levitation electromagnet module in y direction. (**a**) Velocity contour near the maximum temperature point between H\({}_{2}\) and M\({}_{1}\), where the arrows represent velocity vector; (**b**) Velocity contour near the maximum temperature point between M\({}_{3}\) and M\({}_{4}\), where the arrows represent velocity vector; (**c**) Temperature contour near the maximum temperature point between H\({}_{2}\) and M\({}_{1}\); (**d**) Temperature contour near the maximum temperature point between M\({}_{3}\) and M\({}_{4}\). At the initial heating process t1, the heating of the EMU is relatively homogeneous. Only small a temperature rise can be observed on the unit surface except for the regions near the EMU's heating coil.