Problem #1:
Consider a circular steel pipe having an inner diameter of 2.067 in., and wall thickness of
0.154 in. The pipe carrying steam is insulted with 2 in. of 85% magnesia covered in turn
with 2 in. of cork. Estimate the heat loss per hour per foot of pipe if the inner surface of
the pipe is at 250
o
F and the outer surface of the cork is at 90
o
F. The thermal
conductivities (in Btu/hr.ft.F) of the substances concerned are: steel, 26.1; 85% magnesia,
0.04; cork, 0.03.
Answer:
See Example 10.6-1 (or 9.6-1) in the textbook, 2
nd
(or 1
st
) edition, for the notation and the
derivation of the energy equations in terms of temperature for individual layers. The final
forms of these equations are as follow:
(
)
(
)
(
)
1
0
01
0
0
0
1
0
0
01
2
1
12
0
0
1
2
0
0
12
3
2
23
0
0
2
3
0
0
23
Zone 01 (steel):
Zone 12
(magnesia):
Zone 23 (cor
k):
ln
ln
ln
r r
dT
k r
r q
T
T
r q
dr
k
r
r
dT
k r
r q
T
T
r q
dr
k
r
r
dT
k r
r q
T
T
r q
dr
k
−
−
−
=
⇒
−
=
=
⇒
−
=
=
⇒
−
=
Addition of these above equation gives
(
)
(
)
(
)
0
3
0
0
1
0
2
1
3
2
01
12
23
ln
ln
ln
T
T
r q
r r
r
r
r
r
k
k
k
−
=
+
+
Thus, the heat loss over the inner surface of the pipe with an area of
0
2
Lr
π

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