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Chapter 3
Steady Heat Conduction
3126E
A row of used uranium fuel rods are buried in the ground parallel to each other. The rate of heat
transfer from the fuel rods to the atmosphere through the soil is to be determined.
Assumptions
1
Steady operating conditions exist.
2
Heat transfer is twodimensional (no change in the
axial direction).
3
Thermal conductivity of the soil is constant.
Properties
The thermal conductivity of the soil is given to be
k
= 0.6 Btu/h
⋅
ft
⋅
°F.
Analysis
The shape factor for this configuration is given in
Table 35 to be
5298
.
0
)
ft
12
/
8
(
)
ft
15
(
2
sinh
)
ft
12
/
1
(
)
ft
12
/
8
(
2
ln
)
ft
3
(
2
4
2
sinh
2
ln
2
4
total
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
π
π
π
×
=
⎟
⎠
⎞
⎜
⎝
⎛
π
π
π
×
=
w
z
D
w
L
S
Then the steady rate of heat transfer from the fuel rods
becomes
T
2
= 60
°
F
8 in
T
1
= 350
°
F
15 ft
D
= 1 in
L
= 3 ft
Btu/h
92.2
=
°
−
°
=
−
=
C
)
60
350
)(
F
Btu/h.ft.
6
.
0
)(
ft
5298
.
0
(
)
(
2
1
total
T
T
k
S
Q
&
3127
Hot water flows through a 5m long section of a thin walled hot water pipe that passes through the
center of a 14cm thick wall filled with fiberglass insulation.
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

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