Page 164 - Biosystems Engineering

Models for Heat Transfer in Heated Substrates 143

in combination with a simple, but theoretically derived, equation for soil
thermal inertia without the requirement for in situ instrumentation.
Different numerical methods have been used in developing mod-
els for predicting soil temperature: finite difference (Sikora et al. 1990;
Hares and Novak 1992a, 1992b; Sharratt et al. 1992; de la Plaza et al.
1999; Buonanno and Carotenuto 2000; Ling and Zhang 2004; Ao et al.
2007; Keshari and Koo 2007), finite elements (Passerat de Silans et al.
1989; Renaud et al. 2001; Moroizumi and Horino 2002; dos Santos and
Mendes 2005), electromagnetic analogy (Guaraglia and Pousa 1999;
Karam 2000; Guaraglia et al. 2001), and neural networks (George
2001; Mihalakokou 2002).
Sikora et al. (1990) evaluated the sensitivity of soil temperature
predictions to the thermal diffusivity values of a model based on a
finite-different solution of the Fourier equation. The results of the
model were better than experimental results under severe compac-
tion. The authors concluded that the crop surface layer limited heat
flow in the soil due to its low thermal diffusivity, which had a stronger
influence than compaction values.
After having used analytical methods (Novak 1986, 1991), Hares
and Novak (1992a, 1992b) applied the finite-difference solution to the
heat-conduction equation to predict temperatures in soils under strip
tillage with residue mulch surfaces or bare soils. They adopted an
explicit solution that included a surface–energy–balance submodel.
This two-dimensional model was in agreement with analytical solu-
tions (Hares and Novak 1992a), and experimental validation of the
model (Hares and Novak 1992b) produced better results for mulched
soils than for bare soils.
Sharratt et al. (1992) compared finite-difference methods for the
implicit solution of a Fourier equation with harmonic analysis meth-
ods. After having applied both methods to the heat-flow prediction,
they performed an experimental validation of the models in fruit-tree
orchards and fields covered with barley stubble and obtained better
results with the numerical method. The finite-difference method has
been used by various authors for heated soils (Alvarez et al. 1996;
Kurpaska and Slipek 1996; de la Plaza et al. 1999). The aim of the models
focused on the analysis of the performance of the heating system.
Passerat de Silans et al. (1989) developed a one-dimensional
model of coupled flows solved by the finite-element method (FEM)
and applied it to stratified, partially saturated bare soils. They used
the Galerkin method to solve Fourier’s equation and considered
atmosphere boundary conditions. The model was first calibrated for
validation; the results obtained after the calibration phase fitted well
with values measured in the field.
The use of computer tools to solve the heat-conduction equation
for soils has shown to be useful in analytical modeling and essential in
numerical solutions. The continuous system modeling program (CSMP),