Chapter 3
Steady Heat Conduction
3172
Steam is flowing inside a steel pipe. The thickness of the insulation needed to reduce the heat loss by
95 percent and the thickness of the insulation needed to reduce outer surface temperature to 40
°
C are 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 conductivities are constant.
4
The thermal contact resistance at the interface is
negligible.
Properties
The thermal conductivities are given to be
k
= 61 W/m
⋅
°C for steel and
k
= 0.038 W/m
⋅
°C for
insulation.
Analysis
(
a
) Considering a unit length of the pipe, the inner and the outer surface areas of the pipe and the
insulation are
2
3
3
3
3
2
2
2
1
m
1416
.
3
m)
1
(
m
3770
.
0
m)
1
(
m)
12
.
0
(
m
3142
.
0
m)
1
(
m)
10
.
0
(
D
D
L
D
A
L
D
A
L
D
A
o
i
=
π
=
π
=
=
π
=
π
=
=
π
=
π
=
R
i
T
∞
1
R
2
R
o
T
∞
2
R
1
The individual thermal resistances are
C/W
02274
.
0
0.23876
)
12
.
0
/
ln(
03079
.
0
02274
.
0
0.23876
)
12
.
0
/
ln(
00048
.
0
03031
.
0
C/W
22026
.
0
18947
.
0
00048
.
0
03031
.
0
C/W
02274
.
0
)
m
1416
.
3
(
C)
.
W/m
14
(
1
1
C/W
18947
.
0
)
m
3770
.
0
(
C)
.
W/m
14
(
1
1
C/W
0.23876
)
12
.
0
/
ln(
)
m
1
(
C)
W/m.
038
.
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat, Heat Transfer, Ri, ho Ao

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