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传热方程是一类常见的基本数学物理方程,热导率是土体重要的热物理参数。从基本传热方程出发,详细地推导了利用傅立叶级数求解一维传热方程的方法,以地面温度随时间变化的波动方程得到地下不同深度处土体温度分布的解析解。在此基础上,讨论了利用热导率进行土体含水率测量的基本原理,详细地推导了根据地下不同深度的温度计算土体热扩散系数的振幅法、相位法及其应用,介绍了利用传热方程进行数值模拟的计算原理。最后结合实例介绍了该方法的应用效果。
Heat transfer equation is a kind of common basic mathematical physics equation. Thermal conductivity is an important thermophysical parameter of soil. Starting from the basic heat transfer equation, the method of solving the one-dimensional heat transfer equation by using Fourier series is derived in detail. The analytic solution of soil temperature distribution at different depths is obtained from the wave equation of surface temperature with time. On this basis, the basic principle of measuring soil moisture content by thermal conductivity is discussed. The amplitude method and phase method for calculating soil thermal diffusivity based on the temperature at different depths are derived in detail. Heat transfer equation for numerical simulation of the calculation principle. Finally, an example is given to illustrate the application of this method.