An adiabatic boundary condition with cylindrical perfect conductors for improved approximations from heat-pulse measurement near the soil-atmosphere interface

Abstract

The cylindrical-perfect-conductors (CPC) theory, which assumes an infinite and homogeneous soil medium, can be used to analyze heat pulse (HP) measurements to estimate soil thermal property values. However, when a HP sensor is positioned near the soil surface, the CPC theory is not valid because of the change in media properties at the soil-atmosphere interface. In this study, a CPC solution considering an adiabatic boundary condition (CPC-ABC) is presented to account for the soil-atmosphere interface effect. Compared with the results from numerical simulations, the CPC-ABC solution gave more accurate soil temperature values at the sensing probe than did a CPC model. When a HP sensor was positioned horizontally at a depth of 1 mm below a sand soil surface, the relative errors (RE) of CPC estimated thermal property values were as large as 52%, while the RE values based on the CPC-ABC solution were about 8%. Results from numerical simulations and laboratory experiments both showed that the CPC model worked well for horizontally positioned HP sensors with probe lengths of 70-mm at burial depths greater than 15 mm. Soil-atmosphere interface effect was largely dependent on HP sensor dimensions and measurement volumes. Overall, the extended CPC-ABC theory provided accurate soil thermal property estimates by considering the effects of finite probe properties and the presence of the soil-atmosphere interface.