Environmental Engineering Reference
In-Depth Information
Table 10.1 Thermal Conductivity versus Temperature
for Water
....
θ
p
,θ,θ
a
=
percentage of total volume that is solid par-
ticles, water, and air, respectively, and
λ
p
,λ
w
,λ
a
=
thermal conductivities of the solid particles,
water, and air phases, respectively.
Temperature,
◦
C
Thermal Conductivity,
λ
w
(W/m/K)
De Vries (1963) showed from experiments that the thermal
conductivity of quartz sand could vary from 0.25 to 1.9 W/m/K
when the temperature was 20
◦
C and increased to 2.5 when the
temperature increased to 60
◦
C. The volumetric water content
of water of the sand varied from zero to 10%. Riha et al.,
(1980) measured thermal conductivity values ranging from
0.1 to 1.0 W/m/K for silt loam where the volumetric water
content varied between zero and 55%, respectively.
A typical thermal conductivity value for water is 0.57
W/m/K while air has a thermal conductivity of 0.025 W/m/K
(de Vries, 1963; Jame, 1977). The amount of water in the
soil has a significant effect on the thermal conductivity of a
soil. The difference in thermal conductivity between air and
water (i.e., 0.025-0.57 W/m/K) gives rise to the change in
overall thermal conductivity. The latent heat of water vapor
also has an effect on thermal conductivity when there is a
temperature gradient.
The thermal conductivity of air,
λ
a
, consists of two com-
ponents (Jame, 1977):
0
0.5610
4
0.5694
5
0.5736
10
0.5862
15
0.5945
20
0.6029
25
0.6113
30
0.6196
35
0.6280
40
0.6322
45
0.6406
50
0.6448
60
0.6543
70
0.6631
80
0.6700
Source:
Data compiled from Lide (1992).
Table 10.2 Thermal Properties of Common Materials
and Soils
....
λ
a
=
λ
dry air
+
λ
water vapor
(10.5)
Table 10.3 Average Values of Thermal Conductivity
of Solid Particles
Substance
Thermal Conductivity,
λ
(W/m/K)
Air (20
◦
C)
0.025
ρ
s
(g/cm
3
)
Water (20
◦
C)
Material
λ
p
(W/m/K)
0.58
Ice (0
◦
C)
2.2
Quartz
8.8
Rocks
Anorthosite
Clay minerals
2.9
2.73
1.8
Soil organic matter
0.25
Basalt
2.90
1.7
Light soil with roots
0.11
Diabase
2.98
2.3
Wet sand (
θ
=
40%)
1.8
Dolostone
2.90
3.8
Gabbro
2.92
2.2
Gneiss
2.75
2.6
Source:
Data from de Vries (1963) and Rosenberg et al.
(1983).
Granite
2.75
2.5
Limestone
2.75
2.5
Marble
2.80
3.2
range of common materials. Average values for the ther-
mal conductivity of various rock and soil types are given in
Table 10.3.
The thermal conductivity
λ
of a soil consisting of soil
particles, water, and air can be expressed as follows (de
Vries, 1963):
Quartzite
2.65
5.0
Sandstone
2.80
3.0
Schist
2.65
1.5
Shale
2.65
2.0
Syenite
2.80
2.0
Trap rock
2.90
2.0
f
p
θ
p
λ
p
+
f
w
θλ
w
+
f
a
θ
a
λ
a
Coal
1.35
0.26
λ
=
(10.4)
Peat
1.50
0.25
f
p
θ
p
+
f
w
θ
+
f
a
θ
a
Silt and clay
2.75
2.90
where:
f
p
,f
w
,f
a
=
weighting factors for the solid particles,
water, and air phases, respectively,
Source:
Summarized by C ote and Konrad (2005) from var-
ious published sources.
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