Page 163 - Biosystems Engineering

142 Cha pte r F o u r

4.3.2 Methods Used to Build Models for
Predicting Soil Temperature

Physical Methods
Because most models for predicting soil temperature are based on solv-
ing the transient heat-conduction equation, we need to use analytical
or numerical calculation methods with implicit or explicit solutions.
Transient analytical methods have been widely implemented
using the Fourier series. Horton and Wierenga (1983) estimated heat
flows in homogeneous soils by using the Fourier series, and although
the results were similar to the results obtained from integration
methods, they obtained results that were not strictly applicable to
nonuniform soils. Differences between the thermal behavior of uni-
form soils and nonuniform soils were also spotted by Wiltshire
(1983), who calculated periodic heat flow by harmonic analysis. The
harmonic analysis method was used by Cenis (1989), Alvarez et al.
(1996), and Shao et al. (1998) and was combined with dynamic filter-
ing and spectral analysis by Persaud and Chang (1983) and Matthias
and Warrick (1987), who developed soil temperature models that
were successfully validated. With appropriate simplifications, ana-
lytical treatment allowed for predicting temperature fields of the
fluid in the pipe and the soil in the proximity of the buried pipe of
earth-to-air heat exchangers installed at different depths, and used
for building cooling/heating (Cucumo et al. 2008).
Despite the good results of analytical methods, many research-
ers have used numerical methods to analyze heat flow in soils
(Hanks et al. 1971). The reason for this is that using analytical meth-
ods in the integration of the heat-transfer equation requires assum-
ing some simplifications, whereas using numerical methods allows
for introducing thermal properties that are dependent on particular
soil and water conditions, and of more complex boundary condi-
tions (Porta et al. 1999).
Horton (1989) developed a two-dimensional numerical model to
predict heat and water flow in soils with row crops. Papadakis et al.
(1989) estimated soil surface temperature in greenhouses using
numerical methods, whereas Novak (1991) suggested the use of
numerical models to improve the accuracy of temperature prediction
on the soil surface after having used analytical methods to model soil
surface temperature. Later, Novak (1993) proposed an analytical
model with two-dimensional solutions for temperature and heat flows
in soils with bare strips alternating with strips covered with plastic or
other materials and used radiation surface boundary conditions.
Physically based equations solved by analytical methods combined
with remote-sensing techniques permitted a more theoretically rigor-
ous estimation of area–average soil heat flux. Muffay and Verhoef
(2007) used a standard physical equation to estimate the soil heat flux