Rensselaer Polytechnic Institute

MANE 4020

13-1 Hot exhaust gases are used in the reheat section of a Rankine cycle. Consider a commercial steel tube 5-cm outside diameter,
4.5-cm inside diameter used to convey the steam. The air side heat transfer coefficient is 85 W/m2·K, and that of the steam
side is 200 W/m2·K. Determine:
a. the overall heat transfer coefficient based on the inside tube area (in W/m2·K)
b. the overall heat transfer coefficient based on the outside tube area (in W/m2·K)
c. the overall heat transfer coefficient based on the inside area if air side fouling is 0.0015 m2·K/W and steam side
fouling is 0.0005 m2·K/W (in W/m2·K).
Approach:
Use Eq. 13-3 and Eq. 13-4, 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. 13-3 and Eq. 13-4:
, , , ,
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
η η o i o o = = .
For a circular tube ln ln ( ) ( )
2 2
o i o i
w
r r D D
R
π π kL kL
= =
From Appendix A-2, the thermal conductivity of commercial steel is k = 60.5 W/mK.
The areas are: and
A D L A D L i i o o = = 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:
1 ln ( )
2
i i o i i
i i i o o
A D L D L D D
U h A kL h D L
π π
π π
= + +
( ) ( )
( )
5
2 2
1 1 0.045m ln 0.050 0.045 1 0.045m
= + + 0.005 3.92 10 0.0106
200 W m K 85 W m K 2 60.5 W mK 0.050 m
Ui
-
= + × +
=64.0 W m K 2
Ui Answer
b) The overall heat transfer coefficient based on the outside area is:
2 2
W 0.045 W
64.0 =57.6
m K m K 0.050
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
1 1 m K m K 0.045m 1 0.045m 0.045m ln 0.050 0.045
= +0.0005 + + 0.0005 +
200 W m K W 2 60.5 W mK W 0.050 m 0.050 m 85 W m K
Ui
    
    
    
=60.3W m K 2
Ui 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.
13-3 In a desalination plant, salt water is used to create pure water. Salt water is boiled, and salt concentrates in the boiler; the salt
water solution is drained from the boiler, and the pure water vapor is condensed for use. Condensing vapor at a high pressure
is used to boil salt water at a lower pressure. Consider an experiment on a single tube; condensing steam at 105 ºC inside the
tube is used to boil salt water at 85 ºC. The 304 stainless steel tube is 3-m long, 2.5-cm inside diameter, and 2-mm thick.
The overall heat transfer coefficient based on the inside area is 830 W/m2·K, and the condensing coefficient is 1500 W/m2·K.
Determine the heat transfer coefficient of the boiling salt water (in W/m2·K)