Solutions for homework Set #6:
Problem #1
:
Solve problem 10.A.1 in BSL
Answer:
See Example 10.6-1 in BSL 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
(
)
(
)
(
)
(
)
0
3
0
0
0
1
0
2
1
3
2
01
12
23
2
2
ln
ln
ln
L T
T
Q
Lr q
r r
r
r
r
r
k
k
k
π
π
−
=
=
+
+
Or the heat loss per hour per foot of the pipe

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