The dual-probe heat-pulse (DPHP) method is useful for measuring soil thermal properties. Measurements are made with a sensor that has two parallel rods: one for introducing a pulse of heat and one for measuring change in temperature. Thermal properties are obtained by fitting a solution to the temperature data. The cylindrical perfect conductors solution of Knight et al. (https://doi.org/10.2136/vzj2011.0112) allows for accurate determination of those properties because it accounts for the finite radius and finite heat capacity of the rods. In this note, we show how their solution can be written in integral form. Specifically, we rearrange their Laplace-domain solution and perform contour integration in the complex plane to express their solution as the integral of a real function over the positive real axis. This form of their solution is easier to evaluate and thus improves its accessibility for routine use in determining thermal properties with the DPHP method.

中文翻译：

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双探针热脉冲法圆柱理想导体解的积分形式

双探头热脉冲 (DPHP) 方法可用于测量土壤热特性。使用具有两个平行杆的传感器进行测量：一个用于引入热脉冲，另一个用于测量温度变化。热特性是通过对温度数据进行拟合来获得的。Knight 等人的圆柱形完美导体解决方案。(https://doi.org/10.2136/vzj2011.0112) 允许准确确定这些属性，因为它考虑了杆的有限半径和有限热容量。在本笔记中，我们展示了如何以整数形式编写他们的解决方案。具体来说，我们重新排列他们的拉普拉斯域解并在复平面中执行轮廓积分，以将他们的解表示为实函数在正实轴上的积分。