A Perfect-Conductor Approach for Estimating Water Flux Density with the Heat-Pulse Method.

The heat-pulse method is one of the few methods available for measuring water flux density in-situ. The method involves measuring the temperature rise at known distances upstream and downstream from a pulsed heat source. The measurement is accompanied by a heat transfer model for analyzing the temperature data. The fitting of modeled to measured temperature data allows for estimation of the soil thermal properties (i.e. thermal conductivity, heat capacity, and thermal diffusivity) and heat-pulse velocity. Volumetric water content can be obtained from the estimated volumetric heat capacity, provided that specific heat of the solids and the soil bulk density are known. Furthermore, water flux density is obtained via the heat pulse velocity.
We present preliminary work that advances the method by using cylindrical probes that have relatively large diameter and high thermal conductivity, so they can be approximated as perfect conductors. This approximation is particularly appropriate for heat-pulse sensors with probes constructed from thick-walled stainless-steel tubing and whose diameter is large relative to the distance between the heater and temperature probes. A perfect conductor model accounts for the finite radius and heat capacity of the probe, but approximates its thermal conductivity as infinite, assuming that the thermal conductivity of the probe is significantly higher than that of the soil.
In this work we analyze the errors that arise from neglecting the thermal conductivity of the probes and the non-uniformity of the Darcy flux that is caused by these large-diameter probes. We demonstrate that these errors are relatively small. These small errors allow us to approximate the probes as perfect conductors and the flow as one dimensional, with minimal loss of accuracy, such that relatively simple semi-analytical expressions can be used for inverse modeling of the data.