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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 10.61 (or 9.61) 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:
( )
()
10
0
1
00
0
1
01
21
1
2
1
2
12
32
23
0
0
2
3
0
0
23
Zone 01 (steel):
Zone 12
(magnesia):
Zone 23 (cor
k):
ln
ln
ln
rr
dT
k r
rq
T
T
dr
k
dT
T
T
dr
k
dT
T
T
dr
k
−
−
−
=⇒
−
=
−
=
−
=
Addition of these above equation gives
03
01
12
23
ln
ln
ln
TT
kkk
−
=
++
Thus, the heat loss over the inner surface of the pipe with an area of
0
2
Lr
π
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()
03
00
0
10
21
32
01
12
23
2
2
ln
ln
ln
LT
T
QL
r
q
rr
kkk
π
−
==
++
Or the heat loss per hour per foot of the pipe
( )
0
01
12
23
2
ln
ln
ln
TT
Q
L
−
=
The r
i
for this problem are
1
2
3
2.067/ 2
1.0335 in.
1.0335
0.154
1.19 in.
1.19
2
3.19 in.
3.19
2
5.19 in.
o
r
r
r
r
=+=
=+
=
=
Insertion of numerical values into the above formula gives:
24.58
Btu/hrfoot
o
Q
L
=
Problem # 2:
An oil is acting as a lubricant for a pair of cylindrical surfaces such as those shown in
Fig. 9.41 (see section 94 in the textbook, 1
st
edition) or Fig.10.41 (2
nd
edition). The
angular velocity of the outer cylinder is 7908 rpm. The outer cylinder has a radius of 5.06
cm, and the clearance between the cylinders is 0.027 cm. What is the maximum
temperature in the oil if both wall temperatures are know to be 158
o
F? The physical
properties of the oil are assumed constant at the following values:
Viscosity: 92.3 cp
Density: 1.22 g/cm
3
Thermal conductivity: 0.0055 cal/s.cm.C
Answer:
The parallelplate approximation in Example 10.4 in the textbook (or 9.4 in the 1
st
edition) is used here to estimate the temperature rise. Multiplication of Eq. 10.49 (or 9.4
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 Fall '08
 Peters

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