土体一维传热方程解析解及热扩散系数测定

Analytical solution for one-dimensional heat transfer equation of soil and evaluation for thermal diffusivity

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 basic mathematical-physical equation. The thermal diffusivity is an important thermal physical parameter for soil. The derivation was presented for the one-dimensional heat tranfer equation by means of Fourier series. With the assumption of wave equation for ground temperature, the analytical solution for the distribution of ground temperature at different depths was presented. Based on the analytical solution of heat transfer equation, the principle of measured soil moisture by means of thermal diffusivity was discussed, and two kinds of methods were forward put to evaluate the soil thermal diffusivity, i.e., the amplitude method and the phase method. The principle of numerical methods to simulate heat transfer in soil was also discussed. Finally, these methods were verified by examples.