Analytical Solution of the Heat Pulse Method in a Parallelepiped Sample Space

Abstract

The heat pulse method enables estimation of the thermal diffusivity (k), volumetric heat capacity (C), and thermal conductivity of soils (λ) and soil water content. In this study, analytical solutions were derived by the method of Green's function for a finite pulse cylinder source in a parallelepiped sample of size a by b by c with two kinds of boundary conditions. One is the zero surface temperature (ZST) boundary condition, and the other is the adiabatic boundary condition (ABC). The proposed solutions may be useful for evaluating the errors of a dual‐probe heat pulse (DPHP) system introduced by approximating the finite heater with an infinite line source (ILS) model. Applications of the solution are presented in the context of an air‐dried virtual soil sample to demonstrate how different factors (boundary conditions, soil sample size, heater needle length and radius, probe spacing, heating duration, and strength) can affect the error in k and C caused by using an ILS model. For a given parallelepiped (or soil column), the larger the ratio of lengths of the heater probe and the sample, the smaller the boundary influence on the temperature rise at the mid‐needle temperature sensing location, and the smaller the errors introduced by using the ILS approximation. For various heating strengths, it was found that the errors in both k and C were relatively constant when all other parameters were fixed. These errors increased monotonically and slowly, however, as heat duration increased.