131
Hot exhaust gases are used in the reheat section of a Rankine cycle.
Consider a commercial steel tube 5cm
outside diameter, 4.5cm inside diameter used to convey the steam.
The air side heat transfer coefficient is
85 W/m
2
·K, and that of the steam side is 200 W/m
2
·K. Determine:
a. the overall heat transfer coefficient based on the inside tube area (in W/m
2
·K)
b. the overall heat transfer coefficient based on the outside tube area (in W/m
2
·K)
c. the overall heat transfer coefficient based on the inside area if air side fouling is 0.0015 m
2
·K/W and
steam side fouling is 0.0005 m
2
·K/W (in W/m
2
·K).
Approach:
Use Eq. 133 and Eq. 134, which give the overall heat
transfer coefficient in terms of its component parts.
Assumptions:
1. There are no fins.
2. There is no fouling.
Solution:
The overall heat transfer coefficient is calculated with Eq. 133 and Eq. 134:
,
,
,
,
1
1
1
1
i
o
w
i
i
o
o
o i
i
i
o i
i
o o
o
o o
o
o
R
R
R
U A
U A
h A
A
A
h A
η
η
η
η
′′
′′
=
=
+
+
+
+
No fins are used, so
,
,
1
o i
o o
η
η
=
=
.
For a circular tube
(
)
(
)
ln
ln
2
2
o
i
o
i
w
r
r
D
D
R
kL
kL
π
π
=
=
From Appendix A2, the thermal conductivity of commercial steel is
k
= 60.5 W/mK.
The areas are:
and
i
i
o
o
A
D L
A
D L
π
π
=
=
a)
Incorporating the above expressions into the equation for the overall heat transfer coefficient based on the
inside area, noting that the length cancels, and ignoring fouling:
(
)
ln
1
2
i
o
i
i
i
i
i
i
o
o
D L
D
D
A
D L
U
h A
kL
h
D L
π
π
π
π
=
+
+
(
)
(
)
(
)
5
2
2
0.045m ln 0.050 0.045
1
1
1
0.045m
=
+
+
0.005
3.92
10
0.0106
2 60.5W mK
0.050m
200W m K
85W m K
i
U
−
=
+
×
+
2
=64.0W m K
i
U
Answer
b)
The overall heat transfer coefficient based on the outside area is:
2
2
W
0.045
W
64.0
=57.6
0.050
m K
m K
i
o
i
o
A
U
U
A
⎛
⎞⎛
⎞
=
=
⎜
⎟⎜
⎟
⎝
⎠⎝
⎠
Answer
c)
With fouling on both sides of the heat exchanger, we obtain
(
)
(
)
(
)
2
2
2
2
0.045m ln 0.050 0.045
1
1
m K
m K
0.045m
1
0.045m
=
+0.0005
+
+ 0.0005
+
W
2 60.5W mK
W
0.050m
0.050m
200W m K
85W m K
i
U
⎛
⎞⎛
⎞
⎛
⎞
⎜
⎟⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
⎝
⎠
2
=60.3W m K
i
U
Answer
Comment:
The overall heat transfer coefficient is low, so the effect of fouling is small.
If the overall heat transfer coefficient
had been large, then the addition of fouling would have had a much greater effect.
13 1
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132
A two shell pass, eight tube pass heat exchanger with a surface area of 8,300 ft
2
is used to heat 1,700
lbm/min of water from 75
°
F to 210
°
F. Hot exhaust gases enter at 570
°
F and exit at 255
°
F.
Assuming
the exhaust gases have the same properties as air, determine:
a. the overall heat transfer coefficient (in Btu/hr·ft
2
·
°
F)
b. the overall heat transfer coefficient if fouling on both sides equivalent to 0.005 hr·ft
2
·
°
F/Btu is
present in the heat exchanger (in Btu/hr·ft
2
·
°
F).
Approach:
With all temperatures known, along with the area and
one flow rate, sufficient information is given to
evaluate the heat transfer rate and the
LMTD
.
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 Spring '08
 BORCATASCIUC
 Heat Transfer, overall heat transfer

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