## 3 Results and Analysis
### Time-Space Coupling Characteristics of Temperature Field  
Figure 7 displays the characteristic curve of the dimensionless temperature and dimensionless radius of the roadway-surrounding rock under specified conditions: air temperature of 25 \({}^{\circ}\)C, VRT of 50 \({}^{\circ}\)C, and thermal conductivity of 2 W/(m\(\cdot\)K). The point data are the numerical simulation calculation results, and the line data are the coupling function fitting results. Given the application range of the coupling function as \(R>0\), a position near the wall of the surrounding rock is selected for study, that is, \(R=0.1\). It is observed that the fitting effect of the space-time coupling characteristic curve of the dimensionless temperature field is improved, with the fitting degree R\({}^{2}\) ranging from 0.96 to 0.99. As ventilation time increases, the fitting degree of the characteristic curve gradually improves. This occurs because, as the surrounding rock extends radially to the deep, the temperature field is gradually affected by disturbances. Especially in the early stages of ventilation, the internal temperature field of the surrounding rock remains nearly unchanged, resulting in a less obvious correlation between the data and a poorer fitting effect. At a ventilation time of 1 day (\(Fo=0.024\)), the absolute error at \(R=0.1\) is \(-0.028\). Simultaneously, it is evident that the dimensionless temperature gradually increases with an increase in the dimensionless radius, but the temperature rise rate gradually decreases. Additionally, with an increase in dimensionless time, the characteristic curve shifts downward as a whole. This is attributed to the expanding disturbance range of the surrounding rock temperature field with increased ventilation time. However, the disturbance gradually weakens the temperature field of the surrounding rock due to the gradual decrease in the temperature difference between the airflow and the roadway wall. This demonstrates a gradual reduction in the downward rate of the characteristic curve. Figure 8 presents the characteristic curve of the dimensionless temperature and dimensionless time of the roadway-surrounding rock under specified conditions: air temperature of 25 \({}^{\circ}\)C, VRT of 50 \({}^{\circ}\)C, and thermal conductivity of 2 W/(m\(\cdot\)K). The point data are the numerical simulation calculation results, and the line data are the coupling function fitting results. The fitting effectiveness of the time-space coupling characteristic curve for the dimensionless temperature field is relatively satisfactory, with the fitting degree R\({}^{2}\) ranging between 0.95 and 0.99. With the increase in the dimensionless radius, the fitting degree of the characteristic curve decreases in the deep part. This is because the surrounding rock temperature in the deep part drops slightly, and the changing trend of the overall curve is not as obvious as that in the shallow part of the surrounding rock, resulting in a decrease in the fitting degree of the same function here. Simultaneously, the dimensionless temperature gradually decreases with an increase in dimensionless time, and the temperature drop rate also gradually decreases. For instance, the difference in dimensionless temperature  
Figure 6: The relationship between dimensionless temperature and dimensionless time under different thermal conductivity. between 1 day (\(Fo\) = 0.024) of ventilation at \(R\) = 0.1 and 361 days (\(Fo\) = 8.592) of ventilation is 0.70, whereas the difference in dimensionless temperature between 1 day (\(Fo\) = 0.024) of ventilation at \(R\) = 3.0 and 361 days (\(Fo\) = 8.592) of ventilation is 0.14. Additionally, with an increase in dimensionless radius, the characteristic curve rises as a whole. However, as it extends to the deep part of the surrounding rock, the temperature difference between the rocks gradually diminishes, and a gradual decrease in the upward movement speed of the characteristic curve is discernible.