Page 150 - Biosystems Engineering

Models for Heat Transfer in Heated Substrates 129

conductivity is dependent on the evolution of the volumetric pro-
portions of each component, on the size and arrangement of the solid
particles, and on the contact between the solid and liquid phases
(Jury et al. 1991).
There are large differences among the conductivities of the solid,
liquid, and gaseous phases. Thus, the ratio of the thermal conductivi-
ties for quartz, water, and air is 333:23:1 (Jury et al. 1991; Porta et al.
1999). Because of such a large difference, the thermal conductivity of
granular soils depends largely on the degree of contact of solid par-
ticles, which in turn depends on the extent to which air is displaced
by water in the pore spaces between the particles (Jury et al. 1991).
Thermal conductivity depends upon many factors, which can
be classified into two groups: those that are inherent to the soil and
those that can be managed or controlled by humans (Abu-Hamdeh
and Reeder 2000). Factors that are inherent to the soil include the
texture and mineralogical composition of the soil (Wierenga and
de Wit 1970), whereas factors that can be managed externally
include water content and soil management (Yadav and Saxena
1973). Some of the factors that affect the thermal conductivity are
listed as follows:
1. Size of the solid particles: The thermal conductivity of the min-
eral components is lowered with the decrease in particle size
(Patten 1909).
2. Degree of packing and porosity of the soil: An increase in the soil
bulk density (i.e., a decrease in porosity), improves contact
between the particles, and reduces the volume of soil filled
with air (van Rooyen and Winterkorn 1959), thus increasing
thermal conductivity.
3. Moisture content: The presence of water films on the solid
particles increases the contacting surface between the parti-
cles and displaces the air from the soil pores, which has the
lowest conductivity (Jury et al. 1991). At very low moisture
content, thermal conductivity first varies negligibly and then
begins to increase from a critical moisture content whose
value tends to depend on clay mass fraction (Tarnawski and
Leong 2000).
4. Temperature: Thermal conductivity increases with tempera-
ture in wet soils, reaching values that are 3 to 5 times higher at
90°C than at room temperature (Campbell et al. 1994). This
assumption is not valid for soils subject to freezing water
temperatures, where an increase in thermal conductivity is
observed for frozen peat (Kujala et al. 2008).
5. Salt concentration: The increase in salt concentration causes a
decrease in the thermal conductivity of water (Abu-Hamdeh
et al. 2001) and, consequently, of soil.