## 4 Results and Discussion
### Influence of Vacuum Level on Heat Transfer Characteristics  
It has been shown that the low-vacuum environment can significantly reduce the convection heat flux. Therefore, quantitative analysis of the vacuum level influence on convection heat transfer capacity is carried out. Figure 8 shows the averaged surface convection heat flux of the EMU during the heating process under different vacuum levels. The difference in convection heat flux magnitude gets bigger along the heating process. At the end of the heating process, the average surface convection heat flux of 1.0 atm and 0.1 atm are 644 W/m\({}^{2}\) and 104 W/m\({}^{2}\), respectively, which indicates that the low-vacuum condition can cause an 84% reduction in heat flux. Figure 7: Maximum temperature rise on EMU surface under different vacuum levels during heating process. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Vacuum Level (atm)** & **0.1** & **0.3** & **0.4** & **0.5** & **1.0** \\ \hline Temperature rise time (min) & 50.5 & 54.4 & 55.7 & 57.6 & 66.0 \\ Heating time difference (compared to heating under 1.0 atm, \%) & 23 & 18 & 16 & 13 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 5: 100 K temperature rise process at different vacuum levels. As the vacuum level increases, the dominant heat dissipation approach under vacuum condition will transfer from convection heat transfer to radiation heat transfer. Figure 9 gives the quantitative description of the weight of convection heat transfer flux over the total heat transfer flux (\(\varPhi\)) under different vacuum levels. Under 1.0 atm, the convection heat flux takes 49% of the overall heat flux at 60 min. While under 0.1 atm, the convection heat transfer flux takes only 17% of the overall heat transfer flux. At each vacuum level, the percentage of convection heat flux firstly increases and then decreases along the heating process. This is because during the initial stage of magnet heating, the surface temperature rise is insignificant. According to the Stefan-Boltzmann law, the radiation heat flux is proportional to the 4 th power of the temperature difference between the solid-fluid interface. In contrast, the convection heat flux is linearly proportional to this temperature difference. Therefore, during the heating process, when the temperature difference is small, the increase in radiation heat flux is insignificant. In contrast, the convection heat flux is more sensitive to the small temperature difference in the beginning stage. Thus, the curve in Figure 9 shows an increasing trend during the initial heating stage. As the temperature difference gradually builds up, the radiation heat flux increases significantly faster than the convection heat flux. This explains the decrease of \(\varPhi\) in Figure 9. It can be seen from Figure 9 that due to the higher temperature rise rate of the levitation electromagnets in a low-pressure condition, the inflection points on the curve are also advanced in the x axis, which indicates that the low-vacuum condition facilitates the transition of convection heat flux to radiation heat flux. The appearing time of inflection point is shown in Table 6. It can be concluded that the low-vacuum environment evidently lowered the convection heat flux of the levitation electromagnets. On the other hand, the temperature rise enhances the radiation heat flux of the levitation electromagnets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Vacuum Level (atm)** & **0.1** & **0.3** & **0.4** & **0.5** & **1** \\ \hline Time (min) & 10.9 & 11.3 & 17.2 & 18.3 & 21.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Appearance time of inflection point in Figure 9.  
Figure 8: Average convection heat flux on the levitation electromagnet surface. The total heat flux is significantly reduced along with the pressure drop. Among all investigated scenarios, the proportions of convection heat flux at each vacuum level are all less than 50%.