## 1 Introduction  
Aerodynamic drag is a major source of resistance on operating high-speed trains. For trains operating at a speed of 350 km/h or higher, the aerodynamic drag takes more than 75% of the overall drag [1, 2, 3]. In order to reduce the aerodynamic drag, the vacuum tube transportation (VTT) system has been proposed. This system adopts a maglev train to eliminate the mechanical friction between rail and wheel. It also creates a low-vacuum environment such that the aerodynamic drag can be greatly reduced [4, 5]. Based on the demand for faster and more efficient high-speed railway transportation, various VTT system designs have been proposed [6, 7, 8]. Despite the huge reduction on aerodynamic resistance, the VTT systems are subjected to a new challenge: under low-vacuum conditions, the convection heat transfer between the heating source of the maglev and the environment will be compromised. This may lead to device overheating and in turn weaken device performances. For example, studies have shown that once the operating temperature of the levitation electromagnet exceeds the designed limit, permanent demagnetization will occur [9; 10], and the levitation capacity of the maglev may be sabotaged. The levitation electromagnet is a key component in a high-speed maglev system. Under operating mode, the input electric current serves for magnetic field generation, while energy loss from Joule heating will also inevitably occur. This Joule heating energy will accumulate within the electromagnet, causing a temperature rise and posing a potential threat on the lifespan of the device and the safety operation of the maglev [11; 12]. Compared to trains operating under 1.0 atm, when high-speed trains are operating at a low-vacuum environment, the heat dissipation rate is reduced [13; 14] and the maximum temperature of the device will be increased. In this way, the existing cooling design of the levitation electromagnets in the VTT system will be subjected to considerable challenge. Up to now, multiple studies have been conducted to investigate the thermal profile and temperature control solutions of on-board heating devices in maglev, which are based on either an enhanced passive cooling concept [15; 16] or an active cooling concept [17]. Low-vacuum heat transfer has been widely investigated in scientific and engineering research [18; 19; 20]. Typical research approaches include experimental studies and numerical studies. The experimental tests are usually essential in evaluating the thermal properties of novel materials, such as the measurement of thermal conductivity and heat transfer coefficient of nanofilms under vacuum conditions [21]. Numerical studies can conveniently harvest data at any desired location or field and separate the different type of heat flux according to the transport mechanism. For example, the convection heat transfer coefficient [22] as well as the weight of convection and radiation heat transfer over the total of heat flux [23] can be calculated from numerical simulation method. In heat transfer studies related to high-speed trains, [PERSON] et al. [24] and [PERSON] et al. [25] obtained the contribution of convection heat flux and radiation heat flux of on-board heating units through numerical methods and proposed optimization designs. Up to date, the studies regarding cooling performance of on-board heating units on the trains are usually conducted under standard atmosphere pressure. The low-vacuum heat transfer studies for VTT trains are much less reported. In the numerical methods related to the conjugate heat transfer problem, the key issue is the validity of the numerical model. Therefore, a large amount of conjugate heat transfer studies are based on numerical studies which have been verified by representative experimental tests [26; 27; 28]. This hybrid method can efficiently generate reliable results at relatively small cost. Hence, considering the model geometry and heat transfer mechanisms involved in this study, a combined numerical and experimental study method is used.