## 4 Results and Discussion
### Influence of Vacuum Level on Temperature Distribution of EMU Surface and Fluid Field  
Based on the results in the reference case (1.0 atm), under standard atmosphere pressure, the convection heat transfer flux takes 49% of the total heat flux at 60 min. At a low-vacuum environment, the convection heat transfer will be compromised with the decrease of air density. Therefore, it is important to investigate the influence of vacuum level on the EMU temperature rise. The influence of vacuum level on temperature distribution of M6 can be compared in each row of Figure 4, in that each row in Figure 4 represents the surface temperature profile of M6 under different vacuum levels at the same reference time frame of the heating process. According to the comparison results, it is found that the maximum temperature in the EMU becomes higher along with the decrease of environmental pressure as a result of weakened convection heat transfer. After 3 min of heating, the magnet surface under 0.1 atm and 0.3 atm has a higher maximum temperature gradient than that under 1.0 atm. This difference in temperature gradient under different vacuum levels becomes more obvious over time. After 10 min of heating, a high-temperature region can be observed on the side of the magnet unit for 0.1 atm and 0.3 atm heating cases. However, this high-temperature region is not very obvious for the magnet unit heating under 1.0 atm. The temperature of air around the EMU surface is also increased in low-pressure cases due to the elevated temperature of the EMU surface. The influence of vacuum level on the convection heat transfer is also reflected on the flow field around the levitation electromagnet. Figure 5 shows the flow velocity distribution on the symmetric plane of the fluid domain that is perpendicular to the y direction according to Figure 1b. The EMUs in Figure 5 are heated for 60 min at two different vacuum levels. It can be observed that during the heating process, the buoyancy force drives the heat flow upwards, and the low-pressure region created by the heat flow is filled by the unheated air. In this way, some mid-scale circulation flow can be observed in the fluid domain. Compared with the flow field under 0.1 atm, the fluid convection under 1.0 atm has a larger impact area. Meanwhile, the velocity vector above the levitation electromagnet has a relatively uniform upward alignment direction. This is because the buoyancy flow becomes the dominant flow type and its intensity is proportional to the air density. With the increment of environmental pressure, the flow velocity on both sides of the levitation electromagnet also increases. Except for the surfaces that are located on both side of the air gaps between different EMUs, the rest of the side surfaces on the EMU gets a higher convection-induced cooling heat flux under a 1.0 atm case due to the more-adequate convection in the fluid domain. For the flow field above the top levitation electromagnet module, the flow velocity near the gap region is greater than the flow velocity above the EMUs' top surface. This is because the core of each EMU is not a power source and therefore has a relatively low temperature,which in turn results in a much weaker buoyancy force than the air-gap region. This phenomenon gets more significant as the environmental pressure increases. The effect of natural convection on temperature distribution of the flow field around the levitation electromagnet is then analyzed. Figure 6 shows the temperature and temperature gradient along the surface's outer-normal direction of measuring point \(\mathrm{P_{d}}\). The horizontal axis represents the location at different distances away from the measurement points along the surface's outer-normal direction (referred in Figure 6 as Y distance). It is shown that under low-pressure conditions, the space variance of the temperature gradient magnitude becomes smaller. In low-pressure cases, the temperature gradient along the surface normal direction tends to decrease in a linear trend.