Semianalytical solution for dual-probe heat-pulse applications that accounts for probe radius and heat capacity

Abstract

The dual-probe heat-pulse (DPHP) method is useful for measuring soil thermal properties. Measurements are made with a sensor that has two parallel cylindrical probes: one for introducing a pulse of heat into the soil (heater probe) and one for measuring change in temperature (temperature probe). We present a semianalytical solution that accounts for the finite radius and finite heat capacity of the heater and temperature probes. A closed-form expression for the Laplace transform of the solution is obtained by considering the probes to be cylindrical perfect conductors. The Laplace-domain solution is inverted numerically. For the case where both probes have the same radius and heat capacity, we show that their finite properties have equal influence on the heat-pulse signal received by the temperature probe. The finite radius of the probes causes the heat-pulse signal to arrive earlier in time. This time-shift increases in magnitude as probe radius increases. The effect of the finite heat capacity of the probes depends on the ratio of the heat capacity of the probes (C[subscript 0]) and the heat capacity of the soil (C). Compared to the case where C[subscript 0] / C = 1, the magnitude of the heat-pulse signal decreases (i.e., smaller change in temperature) and the maximum temperature rise occurs later when C[subscript 0] / C > 1. When C[subscript 0] / C > 1, the magnitude of the signal increases and the maximum temperature rise occurs earlier. The semianalytical solution is appropriate for use in DPHP applications where the ratio of probe radius (a[subscript 0]) and probe spacing (L) satisfies the condition that a[subscript 0] / L ≤ 0.11.