Environmental Engineering Reference
In-Depth Information
Table 3.1 Thermal conductivities and diffusivities for selected fluid, solid and mixed phases
(Sources: H
afner et al
.
1992
; Lide
1995
)
€
Phase
Density
[kg/dm
3
]
Thermal
conductivity
[W/m
C]
Specific heat
capacity
[kJ/kg
C]
Thermal diffusivity
[10
6
m
2
/s]
Water at 5
C
1.0
0.5724
4.202
0.13622
Water at 10
C
0.9998
0.5820
4.192
0.13886
Water at 20
C
0.9982
0.5984
4.182
0.14335
Water at 30
C
0.9957
0.6154
4.178
0.14793
Water at 40
C
0.9922
0.6305
4.179
0.15206
Water at 50
C
0.988
0.6405
4.181
0.15505
Water at 90
C
0.962
0.6753
4.210
0.16674
Seawater at 10
C
1.0269
0.5781
3.911
0.1439
Calcite
2.6-2.8
2.2
0.91
0.92984
Sand (dry)
1.2-1.6
0.6 (0.33)
0.8
0.62500
Fine sand (dry)
1.635
0.627
0.76
0.50459
Fine sand (saturated)
2.02
2.75
1.419
0.95940
Gravel (dry)
1.745
0.557
0.766
0.41671
Gravel (saturated)
2.08
3.07
1.319
1.11900
When the coefficient on the left side of the equality is regarded as the heat
capacity of the solid/fluid sediment system:
rðÞ¼yrð
f
þ
ð
1
y
Þ rð
s
(3.24)
one can stay with the formulation of the energy conservation as noted above in
(
3.21
). In a multi-phase environment (
rC
) is a property of the system including
all phases.
The heat transport will be derived from this equation by specifying the flux j
e
with respect to the relevant processes. In order to reach an equation like that for
mass transport, one has to express the heat flux vector in terms of temperature. For
advective heat flux this can be achieved in analogy to (2.9):
j
e
¼ yrð
f
v
T
(3.25)
For diffusive heat flux there is an analogue to Fick's Law, which is Fourier's
Law.
6
In 1822 J.B. Fourier stated a linear relation between heat flux on one side
and the temperature gradient on the other:
j
e
¼l
T
rT
(3.26)
The proportionality factor is the thermal conductivity
l
T
that depends on the
medium through which heat transfer is taking place.
l
T
is thus a material property
6
Jean Baptiste Fourier (1786-1830), French mathematician.
