## 2 Operating Principles of the TPCT  
In the energy exchange systems, TPCT is an efficient heat transfer device without any external energy [15]. Usually, a TPCT consists of three parts, including the evaporator section, the adiabatic section, and the condenser section [16]. When it was applied in the highways in the permafrost region, the condenser section is exposed to the air and the evaporator section is inserted into the embankments. The evaporator section is placed under the condenser section. It can effectively transport a large amount of heat energy along the tube wall with a small temperature difference between the condenser section and the evaporator section [17; 18].  
The detailed working principle is shown in Figure 3[19]. It mainly relies on the gas-liquid phase change of the internal work material and gravity reflux to transmit heat, the work material is accumulated at the bottom of the heat pipe, which can be liquid ammonia with low boiling point and environmental protection, etc. The evaporation section is in the lower half of the heat pipe, the condensation section is in the upper half of the heat pipe, and the adiabatic section is in the middle part. In the cold season, when the temperature of the evaporation section of the heat pipe is higher than the temperature of the condensing section, the heat pipe evaporation section of the workpiece is heated and evaporated into steam, under the action of differential pressure, the steam flows upward and rises to the condensing section, the exothermic condensation in the condensing section into a liquid, and then returns to the evaporation section under the action of gravity to complete the cycle of work. Through the constant vaporization of the mass of heat absorption--condensation and exothermic, a steady stream of heat pipe evaporation section occurs near the heat transfer to the condensing section. As long as there is a temperature difference between the condensing section and the evaporating section, the heat pipe will continue this cycle of heat transfer [11; 20; 21].  
Figure 3: The detailed working principle of the TPCT [22].  
In addition, the concept of equivalent thermal resistance [23] is mentioned in order to facilitate the calculation and simulation of heat pipes. When the heat pipe works in the roadbed in the permafrost zone, its thermal resistance includes the thermal resistance between the air and the wall of the condensing section \(R_{\rm{f}}\), the thermal resistance of the wall of the condensing section \(R_{\rm{cw}}\), the thermal resistance of the liquid film of the condensing section \(R_{\rm{cl}}\), the thermal resistance of the adiabatic section \(R_{\rm{a}}\), the thermal resistance of the liquid film and the pool of liquid in the evaporating section \(R_{\rm{el}}\), the thermal resistance of the wall of the evaporating section \(R_{\rm{ew}}\), the thermal resistance between the soil and the wall of the pipe \(R_{\rm{s}}\), respectively. As illustrated in Figure 4, \(T_{\rm{a}}\), \(T_{\rm{co}}\), \(T_{\rm{cl}}\), \(T_{\rm{cl}}\), \(T_{\rm{el}}\), \(T_{\rm{ei}}\), \(T_{\rm{eo}}\), and \(T_{\rm{s}}\) are the air temperature, the wall temperature outside the condensing section, the wall temperature inside the condensing section, the liquid film temperature in the condensing section, the liquid film temperature in the evaporating section, the wall temperature outside the evaporating section, and the soil temperature, respectively.