There is an increasing incidence of overheating in subway tunnels in recent years especially in old subways without air-conditioning e.g., London Underground. There is still lack of a clear understanding how tunnel-air temperature is determined by complex thermal processes in subway tunnels. In this study, a mathematical model that describes the thermal processes in deeply buried subway tunnels was developed. Analytical solution was derived by separating the solution into time-averaged component and periodic component. The results show that the time-averaged component of tunnel-air temperature will approach steady state as the time tends to infinity, which has a positive linear relation with internal heat-source and average ambient temperature. Active cooling or heat-recovery systems could soon become a necessity in subway tunnels due to both global warming and increasing internal heat generation. Compared with outdoor air, the amplitude of the tunnel-air temperature shows a significant reduction in the day period but not in the year period. The surrounding soil temperature will keep changing for thousands of years. This study offers a new physical insight to analyse and mitigate overheating in subway tunnels.

地铁过热的发生率越来越高近年来的隧道，尤其是在没有空调的旧地铁中，例如伦敦地铁。仍然缺乏清楚的了解，如何通过地铁隧道中复杂的热过程确定隧道的空气温度。在这项研究中，建立了描述深埋地铁隧道中热过程的数学模型。通过将解分为时间平均分量和周期分量，可以得出解析解。结果表明，随着时间趋于无穷大，隧道空气温度的时均分量将趋于稳态，与内部热源和平均环境温度呈正线性关系。由于全球变暖和内部热量增加，主动冷却或热量回收系统可能很快成为地铁隧道中的必需品。与室外空气相比，隧道空气温度的幅度在白天显着降低，但在一年中没有降低。周围的土壤温度将持续几千年的变化。这项研究为分析和减轻地铁隧道的过热提供了新的物理见解。