Page 166 - Biosystems Engineering

Models for Heat Transfer in Heated Substrates 145

Sun and Zhang (2004) evaluated the effect of the lower boundary
position selection for the Fourier equation on heat transfer and energy
balance in soil. Based on physical reasoning and the results of numer-
ical simulation, proper depth depended on the annual heat wave
damping depth, and for most soils it depended on the soil texture. In
order to calculate the temperature profiles in a more accurate way, dos
Santos and Mendes (2005) developed a computational code and con-
ceived to model the coupled heat and moisture transfer in soils. The
theory of Philip and de Vries was used to obtain variable thermophys-
ical properties for two types of soil. The governing equations were
discretized using the finite-volume method, and a three-dimensional
model was used to describe the physical phenomena of heat and mass
transfer in unsaturated moist porous soils. A finite-difference approxi-
mation of generalized solutions to the model was proposed by Thanh
et al. (2007) to introduce and validate another three-dimensional lin-
ear thermal model for detecting land mines, and its convergence prop-
erties were proved.
A mathematical model based on solving the heat-transfer equation
in the soil with FEM was developed by Antonopoulos (2006). The
heat-transfer model was incorporated as part of the integrated model
WANISIM (water and nitrogen simulation), which described soil
water movement and mass transport and nitrogen transformations in
the soil. Three different types of boundary conditions at soil surface
were considered: soil temperature varied cosinusoidally, heat balance,
and the erosion–productivity impact calculator model approach.
Saito et al. (2006) developed a numerical model in the HYDRUS-
1D code that solved the coupled equations governing liquid water,
water vapor, and heat transport, together with the surface water and
energy balance, and provided flexibility in accommodating various
types of meteorological information to solve the surface energy bal-
ance. This numerical model was used by Dahiya et al. (2007) to quan-
tify the effect of straw mulching and rotary hoeing on the soil water
and thermal regimes of a loess soil.
Karam (2000) developed a model based on electromagnetic analogy
that showed good agreement with analytical solutions, with a wider
application range, and with better results than the finite-difference
method. Guaraglia and Pousa (1999) based their model on the solu-
tion of Fourier equation using electrical analogy. The model produced
good results for radial heat conduction, which fitted the results
obtained using analytical methods. This method was applied and
experimentally validated for determining temperature and heat flows
in sandy soils (Guaraglia et al. 2001).
The neural network model has good prospects as a prediction
method but requires further development, as reported by Ferreira et al.
(2002) who developed a model for predicting greenhouse air tem-
perature. Use of this type of numerical method for the determination