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Chapter 3
Steady Heat Conduction
Review Problems
3152E
Steam is produced in copper tubes by heat transferred from another fluid condensing outside the
tubes at a high temperature. The rate of heat transfer per foot length of the tube when a 0.01 in thick
layer of limestone is formed on the inner surface of the tube is to be determined.
Assumptions
1
Heat transfer is steady since there is no indication of any change with time.
2
Heat
transfer is onedimensional since there is thermal symmetry about the centerline and no variation in the
axial direction.
3
Thermal properties are constant.
4
Heat transfer coefficients are constant and uniform
over the surfaces.
Properties
The thermal conductivities are given to be
k
= 223 Btu/h
⋅
ft
⋅
°F for copper tubes and
k
= 1.7
Btu/h
⋅
ft
⋅
°F for limestone.
Analysis
The total thermal resistance of the new heat exchanger is
(
)
.
Q
T
T
R
R
T
T
Q
new
total,new
total,new
new
4
F
2
10 Btu / h
h. F / Btu
=

→
=

=

°
×
=
°
∞
∞
∞
∞
1
2
1
2
350
250
0 005
After 0.01 in thick layer of limestone forms, the new value of
thermal resistance and heat transfer rate are determined to be
R
r
r
kL
R
R
R
i
limestone,i
total,w/lime
total,new
limestone,i
Btu / h.ft. F)
ft
h F / Btu
h F / Btu
=
=
°
=
°
=
+
=
+
=
°
ln(
/
)
ln( . / .
)
( .
(
)
.
.
.
.
1
2
05 0 49
2
17
1
0 00189
0 005
0 00189
0 00689
π
27%)
of
decline
(a
F/Btu
h
0.00689
F
)
250
350
(
w/lime
total,
2
1
w/lime
Btu/h
10
1.45
4
×
=
°
°

=

=
∞
∞
R
T
T
Q
Discussion
Note that the limestone layer will change the inner surface area of
the pipe and thus the internal convection resistance slightly, but this effect
should be negligible.
3105
T
∞
2
R
total, new HX
T
1
R
limestone
T
2
R
total, new HX
T
1
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View Full DocumentChapter 3
Steady Heat Conduction
3153E
Steam is produced in copper tubes by heat transferred from another fluid condensing outside the
tubes at a high temperature. The rate of heat transfer per foot length of the tube when a 0.01 in thick
layer of limestone is formed on the inner and outer surfaces of the tube is to be determined.
Assumptions
1
Heat transfer is steady since there is no indication of any change with time.
2
Heat
transfer is onedimensional since there is thermal symmetry about the centerline and no variation in the
axial direction.
3
Thermal properties are constant.
4
Heat transfer coefficients are constant and uniform
over the surfaces.
Properties
The thermal conductivities are given to be
k
= 223 Btu/h
⋅
ft
⋅
°F for copper tubes and
k
= 1.7
Btu/h
⋅
ft
⋅
°F for limestone.
Analysis
The total thermal resistance of the new heat exchanger is
(
)
.
Q
T
T
R
R
T
T
Q
new
total,new
total,new
new
4
F
2
10 Btu / h
h. F / Btu
=

→
=

=

°
×
=
°
∞
∞
∞
∞
1
2
1
2
350
250
0 005
After 0.01 in thick layer of limestone forms, the new value of thermal resistance and heat transfer rate
are determined to be
R
r
r
kL
R
r
r
kL
R
R
R
R
i
o
limestone,i
limestone,i
total,w/lime
total,new
limestone,i
limestone,o
Btu / h.ft. F)
ft
h. F / Btu
Btu / h.ft. F)
ft
h. F / Btu
h. F / Btu
=
=
°
=
°
=
=
°
=
°
=
+
+
=
+
+
=
°
ln(
/
)
ln( . /
.
)
( .
(
)
.
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 Spring '08
 BENARD
 Heat Transfer

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