Page 154 - Biosystems Engineering

Models for Heat Transfer in Heated Substrates 133

near the heat source. He proposed to simultaneously perform the test
for two materials: soil and reference material (1.0 percent agar). The
representation of the temperatures obtained for both materials
allowed Kasubuchi (1977) to determine effective thermal conductiv-
ity without solving the heat-conduction equation.
Campbell et al. (1991) proposed the single-probe heat-pulse method,
a method that was later used by other authors. Specific heat was deter-
mined by placing a line heat source and measuring temperature varia-
tions at a short distance from the source. Kaminsky (1994) proposed a
very similar method to determine specific heat, effective thermal con-
ductivity, and thermal diffusivity, which was applicable to heat conduc-
tion in materials with nonhomogeneous structure. Both methods used
analytical solutions of the heat equation for cylindrical geometries with
an axial heat source in a homogeneous and isotropic medium at a uni-
form initial temperature (Abu-Hamdeh and Reeder 2000).
Based on the method proposed by Campbell et al. (1991), Bristow
et al. (1994a) developed the dual-probe heat-pulse technique. By mea-
suring the temperature response at a short distance from the line
source, and applying short-duration heat-pulse theory, Bristow et al.
(1994a) could extract all the soil thermal properties, thermal diffusiv-
ity, heat capacity, and thermal conductivity, from a single heat-pulse
measurement. In addition, Bristow et al. (1995) presented a computer
implementation of the dual-probe heat-pulse technique for labora-
tory experiments. The results obtained for specific heat, effective
thermal conductivity, and thermal diffusivity were identical to the
results obtained using the Marquardt algorithm, and the computer
implementation approach allowed for rapid and automated monitor-
ing of these parameters.
Indirect heat-pulse methods for determining soil thermal properties,
both single-probe and dual-probe methods, are affected by time- and
temperature-measurement errors. The influence of noise on the temper-
ature curves required to determine thermal properties using heat-pulse
methods has been analyzed by Bristow et al. (1994a, 1994b). Noise prob-
lems that affect temperature measurement are particularly relevant in
situations in which temperature rises faster (Kluitenberg et al. 1995).
Moreover, the dual-probe heat-pulse technique has shown to be a good
tool for determining the thermal properties of porous materials insofar
as the use of nonlinear least squares curve fitting for temperature data
offers highly accurate estimates of such properties (Bilskie et al. 1998).
Heat flux plates are commonly used to measure soil heat flux, a
component of the surface energy balance. This method is based on
the establishment of a vertical heat flow between a warm and a cold
plate where the temperature gradients and the response of a soil heat
flux plate are measured. The plate method is simple, but several studies
have demonstrated the potential for relatively large errors. The standard-
plate method has underestimated the magnitude of the heat flux by
18 to 66 percent depending on the site and type of plate due to a