ANALYTICAL SOLUTION OF ONE-DIMENSIONAL TRANSIENT HEAT CONDUCTION EQUATION AND ITS APPLICATION
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摘要: 探究路基及浅层土体的温度随深度的分布规律，对冻土区域路基的合理设计有重要意义。该文根据实际浅层土体温度边界情况，建立了一维传热瞬态模型并给出其解析解，通过与数值模拟及现场测试结果的对比验证了解析解的正确性。仔细考察介质分层情况下的热传导过程发现，传热问题在一定程度上存在与波动问题类似的现象，即在分层界面处有热传导的反射与透射，结合对解析解的分析及数值模拟，对此种“温度波”现象进行了论证分析，发现此种波总是伴有明显的衰减。此外，还探讨了解析解在冻深估计、有关模型试验中几何相似关系的确定、“覆盖效应”数值模拟等方面的应用。Abstract: Exploring the temperature distribution characteristics of embankment and soil in shallow depth is of great significance to the rational design of embankment in permafrost areas. A one-dimensional transient heat conduction model is first established based on the actual temperature boundary conditions of shallow soil, and then the analytical solution is derived, which is verified through comparisons between numerical simulations and field test results. Careful inspection of the heat conduction process in multi-layered media found that the heat conduction problem resembled, to a certain extent, the wave problem in the reflection and transmission of heat conduction at the interface. This “temperature wave” phenomenon is explored through examining the formula as well as the calculated results of the analytical solution. It is found that this wave is always accompanied by obvious attenuation. In addition, further discussions are given with regard to the application of this analytical solution in the estimation of frost heave depth, determination of geometric similarities in related model tests and numerical simulation of "canopy effects".
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Key words:
- heat transfer equation /
- analytical solution /
- numerical simulation /
- field test /
- interface /
- covering effect
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图 2 解析解和模拟结果对比
Figure 2. Comparison between analytical solution and simulation results
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