Page 156 - Biosystems Engineering

Models for Heat Transfer in Heated Substrates 135

as soil water fluxes. For this reason, a number of authors have analyzed
design factors that influence the accuracy of the probe (Ham and
Benson 2004; Saito et al. 2007). Combining this technique for estimating
soil heat properties, water flux, and water content with a Wenner array
measurement of bulk soil electrical conductivity allows for simultane-
ous measurement of coupled water, heat, and solute transport in unsat-
urated porous media and provides a better understanding of flow and
transport processes (Mortensen et al. 2006).

Determining Thermal Properties from Other Soil Properties
Obtaining exact measurements of the soil thermal properties and
analyzing the variation of such properties is very complex. As a result,
modeling soil thermal properties from soil data that can be readily
measured becomes difficult. Kersten (1949) proposed a purely empir-
ical expression for estimating effective thermal conductivity based on
measurements from five soils. This expression determined the value
of thermal conductivity from the physical properties of other soils
(volume fraction and bulk density) and from three dimensionless
empirical factors that needed to be determined for each specific soil.
De Vries (1963) proposed a method for determining the heat capac-
ity and effective thermal conductivity of the soil. The method by de
Vries (1963), with successive modifications, has been used in many
models of heat transfer in soils because it allows for determining ther-
mal properties from the physical, textural, and structural characteristics
of the soil and from values of the physical properties of the soil phases.
To estimate soil thermal properties, it has been assumed that the soil
consists of three phases—solid, liquid, and gas—all of them contribut-
ing to the overall value of the thermal properties of the soil.
Specific heat has been computed as the weighted sum of the ther-
mal capacities of each separate constituent, using the volume fraction
of each element as a weighting factor. The specific heat of the solid
phase is constant with moisture and is computed from the heat capac-
ity per volume of the minerals that compose the solid phase and of
soil organic matter. An increase in moisture reduces the volume frac-
tion of air and subsequently increases specific heat. Considering that
the specific heat of air is small as compared to the specific heat of
water and solids, this term can be neglected, such that soil specific
heat is a function of the volume fractions of water and solid constituents.
Consequently, soil specific heat can be determined from the porosity and
water content of a soil whose texture is known. The values of specific
heat thus calculated corresponded well with the values measured
directly by de Vries (1963) with the help of a calorimetry.
To determine soil effective thermal conductivity, de Vries (1963)
modeled the soil as a continuous medium in which soil particles are
dispersed and considered as regular-shaped granules. In dry soils, air
is considered to be a continuous medium, and the solid and liquid
phases represent the regular-shaped granules randomly arranged in