A Simple Rational Approximation for Heat Capacity Determination with the Dual-Probe Heat-Pulse Method

Abstract

A number of mathematical expressions are available for calculating soil volumetric heat capacity from data obtained with the dual-probe heat-pulse (DPHP) method. One of the more attractive options is a polynomial approximation that is simple to evaluate and yields estimates of heat capacity with error no greater than about 2% for typical DPHP measurement configurations (i.e., configurations with a probe spacing of approximately 6 mm and a heating duration in the range of 8–15 s). Unfortunately, the polynomial approximation is less accurate for measurement configurations with relatively small probe spacing or a relatively long heating duration. In this note we present a rational approximation that is more accurate, has a wider range of applicability, and is even simpler in mathematical form than the polynomial approximation. The rational approximation has error no greater than 0.015% for typical DPHP measurement configurations, but its primary advantage is that it yields heat capacity estimates with error no greater than 0.03% for a wide range of measurement configurations.