Environmental Engineering Reference
In-Depth Information
The material was assumed to be silica flour with material
properties equal to those defined by Jame (1977). The thermal
conductivity was calculated based on the Johansen method
(Johansen, 1975) and a value of 2.873 W/m/K was obtained.
The volumetric heat capacity was calculated based on the spe-
cific heat of the solid component, water, ice, soil dry density,
and respective volumetric fractions (Jame, 1977; Newman,
1995). The thermal conductivity, volumetric heat capacity,
and dry density of the soil are required as input when solving
this problem. The volumetric heat capacity of the solid com-
ponent was 837 J/kg/K. The latent heat of fusion was taken as
3 . 34
Temperature applied
to upper boundary condition
Location to monitor
temperature
5 m
10 8 J/m 3 . The volumetric water content was 47% and
the dry density was 1330 kg/m 3 .
The SFCC was estimated using the Fredlund and Xing
(1994) SWCC equation. It was assumed that the phase
change from water to ice commenced at -0.1 C and that the
phase change was complete when the temperature reached
×
Unit heat flux applied to
lower boundary condition
0.607 C. The Fredlund and Xing (1994) equation was fitted
to laboratory data of unfrozen water content as a function of
soil suction.
The computer results are presented in terms of temper-
ature contours and are presented in Fig. 10.39. The frost
depth (i.e., zero degree isotherm) is shown in Fig. 10.40.
The closed-form analytical solution could only be applied
for the freezing period; however, the numerical solution was
continued throughout the subsequent thawing period.
Figure 10.37 One-dimensional column with nodes used in solv-
ing Aldrich (1956) problem.
6
4
2
0
10.11.1 Solving Complex Coupled Heat Flow Problems
There is a wide variety of example problems involving heat
flow that could be solved for illustration purposes; however,
only the above few examples have been presented. It is also
possible to couple heat flow with the flow of air and/or water;
however, these topics are outside the scope of this topic. Other
phase flows require the coupling (or simultaneous solution)
of more than one partial differential equation.
2
4
6
0
30
60
90 120 150 180 210
Time (days)
240 270 300 330 360 390
Figure 10.38
Temperature conditions applied on upper boundary.
8
5.0 m
4.0 m
6
0.01 m
0.2 m
0.4 m
3.0 m
4
2.0 m
2
1.4 m
2.0 m
0
1.2 m
1.0 m
0.8 m
2
0.6 m
0.4 m
4
0.2 m
0.1 m
6
0
30
60
90
120
150
180 210
Time (days)
240
270
300
330
360
390
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