## 2 Temperature Field Fitting and Simulation of CRTS III Slab Track  
### Temperature Field Fitting  
In general, there are three methods of heat transfer: convective heat transfer, heat radiation, and heat conduction. For slab ballastless track, the temperature field inside the slab is affected by solar radiation and ambient temperature, that is, the convective heat transfer of air above the slab, solar radiation, and the self-balance and transfer of temperature inside the slab. Figure 2 is a schematic diagram of the heat exchange process of the ballastless track. The adjacent CRTS III slab tracks are not directly connected. There is a gap between the two slab tracks, and the mutual heat transfer can be ignored; therefore, only one of them was the focus of this study. The Newtonian cooling equation is used to describe convective heat transfer:  
\[q^{\prime\prime}=h(T_{\rm s}-T_{B}) \tag{1}\]  
where \(h\) is the convective heat transfer coefficient, which is related to the surface shape, air temperature, and other factors. \(T_{S}\) is the surface temperature of the slab track and \(T_{B}\) is the ambient air temperature. According to the literature [5], the atmospheric radiation on a sunny day can be calculated by the following formula:  
\[G_{a}=\varepsilon_{a}C_{0}(273+T_{a})^{4} \tag{2}\]  
where \(\varepsilon_{a}\) is the atmospheric radiation coefficient, \(C_{0}\) is the Stefan-Boltzmann constant, and \(T_{a}\) is the effective temperature, \({}^{\circ}\)C.  
Combined with the internal temperature field distribution of slab ballastless track, the basic law of heat conduction is  
\[\frac{Q}{t}=\frac{KA(T_{hot}-T_{cold})}{d} \tag{3}\]  
where \(Q\) is the total heat transfer in time period \(t\), \(K\) is the heat conductivity, \(T\) is the temperature, \(A\) is the area of the plane, and \(d\) is the area between the two planes. The model was established according to the dimensional parameters shown in Table 1. The density of the slab track is 2500 kg/m\({}^{3}\), the heat transfer coefficient is 4.74 W/(m\({}^{2}\)-K), the specific heat capacity is 960 J/(kg-K), and the thermal conductivity is 1.75 W/(m\(\cdot\)K). The density of self-compacting concrete is 2450 kg/m\({}^{3}\), and the density of the base plate is 2500 kg/m\({}^{3}\). The model ignores the influence of rails and fasteners on the temperature of the slab track and the influence of solar radiation on the surroundings of the slab track. Figure 2: Schematic diagram of the heat exchange process of the ballastless track. The solar direction vector, direct normal solar radiation from the earth's surface, diffuse solar radiation from the vertical and horizontal surface, and ground reflection solar radiation are calculated by the calculation module in the CFD software. This study used the slab track of a section of a high-speed railway in operation in China as an example. According to meteorological data, the temperature in this area reaches its highest around 15 August every year. To explore the temperature gradient and deformation of the slab track under extreme conditions, the model was developed to simulate and calculate the temperature field distribution of the slab track in this section on 15 August. The slab ballastless track is mainly exposed to solar radiation on the surface of the slab. Due to the rotation of the sun, the four sides of the slab will receive direct sunlight at different times, and the area around the slab is small and will not receive solar radiation all the time. To simplify the model, the influence of solar radiation around the model was not considered in the calculation. The boundary conditions around the model mainly consider heat conduction and convective heat transfer. The lower part of the base plate and the surface of the bridge conduct heat. Therefore, the boundary conditions mainly consider heat conduction.