A Semi-Analytical Solution for the Dual-Probe Heat-Pulse Method That Accounts for the Presence of the Probes.

The dual-probe heat-pulse method is useful for measuring soil thermal properties and volumetric water content. The method involves measuring the temperature rise at a known distance from a cylindrical heater probe that contains resistance wire. A pulse of heat is introduced into the soil by passing electrical current through the wire. Temperature rise is measured as a function of time with a cylindrical probe oriented parallel to the heater probe. Thermal properties are usually estimated by fitting an analytical solution to the temperature rise data. To date, the solutions used for this purpose have not accounted for the finite diameter and finite thermal properties of the heater and temperature probes. In this paper we present a semi-analytical solution that takes into account the finite diameter and finite heat capacity of the probes. A closed-form expression for the Laplace transform of the solution was obtained by considering the probes to be cylindrical perfect conductors of infinite length. The Stehfest algorithm is used to invert the Laplace-domain solution numerically. Results obtained with the new solution are used to investigate the effects of the finite diameter and finite heat capacity of the probes.