## 3 Results and Analysis
### Time-Space Coupling Characteristics of Temperature Field
For instance, after 31 days of ventilation (\(Fo\) = 0.738), the dimensionless temperature difference between the characteristic curves at \(R\) = 0.1 and \(R\) = 1 is 0.63, whereas the dimensionless temperature difference between the characteristic curves at \(R\) = 2 and \(R\) = 3 is 0.02. This occurs because, with the deep extension of the surrounding rock, the disturbance of the wind flow to the temperature of the surrounding rock gradually weakens, resulting in less noticeable temperature changes in the deep rock mass. Figure 8: The characteristic curves of dimensionless temperature and dimensionless time at different depths. Figure 7: The characteristic curves of dimensionless temperature and dimensionless radius at different depths. Discussion: The Influence of Thermal Conductivity on the Space-Time Coupling Characteristics of Dimensionless Temperature Field of Roadway-Surrounding Rock  
Figure 9 illustrates the impact of thermal conductivity on the time-space coupling characteristics of the dimensionless temperature field of the roadway-surrounding rock at various time points. It is observed that the fitting degree of the characteristic curve varies between 0.90 and 0.99, and the change pattern of the characteristic curve is mainly consistent with the observations above. The fitting effect of the characteristic curve is gradually improved with increasing thermal conductivity, particularly in the early stages of ventilation. For instance, at a ventilation time of 1 day, the curve fitting performs worst with a thermal conductivity of 1 W/(m\(\cdot\)K), and the R\({}^{2}\) is 0.90. In contrast, the curve fitting is more effective with thermal conductivities of 2 W/(m\(\cdot\)K) and 3 W/(m\(\cdot\)K), resulting in an R\({}^{2}\) of 0.96 and 0.98. Simultaneously, in the early stages of ventilation, fitting errors are primarily concentrated in the shallow parts. For example, at a ventilation time of 1 day, under different thermal conductivity conditions, the maximum absolute errors occur at \(R\) = 0.1: \(-\)0.043, \(-\)0.029, \(-\)0.018, and at \(R\) = 0.5: 0.009, 0.017, 0.019. Additionally, with an increase in ventilation time, the fitting effect of the characteristic curve is gradually improved. However, the fitting error curve gradually shifts towards the depths of the surrounding rock. For instance, at a ventilation time of 181 days, under different thermal conductivity conditions, the maximum absolute error occurs at \(R\) = 4: 0.008, 0.013, 0.011. Finally, when the ventilation days were increased to 361 days, the fitting errors were evenly distributed across locations and not concentrated in one location. Figure 9: The characteristic curves of dimensionless temperature and dimensionless radius at different thermal conductivities. (**a**) 1 day; (**b**) 31 days; (**c**) 181 days; (**d**) 361 days. Figure 10 illustrates the impact of thermal conductivity at different positions on the spatial-temporal coupling characteristics of the dimensionless temperature field of the roadway-surrounding rock. Owing to varying thermal conductivity, the corresponding \(Fo\) also differs at the same time. It is evident that the fitting degree of the characteristic curve gradually increases with the augmentation of thermal conductivity. For instance, at \(R=3\), with the augmentation of thermal conductivity, the fitting degree of the characteristic curve is 0.89, 0.95, and 0.97, respectively. But there are exceptions; for example, at \(R=0.1\), with the augmentation of thermal conductivity, the fitting degree of the characteristic curve is 0.99, 0.99, and 0.98, respectively. Additionally, the absolute error of the characteristic curve is observed to vary by \(\pm 0.1\). Moreover, as the dimensionless radius increases, the absolute error of the characteristic curve gradually diminishes.