How does tube side heat transfer Coefficient affect selection of Fin Configuration? V.Ganapathy |

Writing the expression for overall heat transfer coefficient on tube inner diameter basis(that makes comparison easy for any fin geometry) and neglecting the effect of fouling factors and tube wall conductivity,we have:

**1/Ui
= 1/hi + (Ai/At)/E ho**

where

Ui=overall
heat transfer coefficient,tube ID basis,Btu/ft^{2}hF

Ai,At
=tube internal and external surface areas,ft^{2}
^{ }E=fin
effectiveness,fraction

ho=gas
side heat transfer coefficient,Btu/ft^{2}hF

(Note
that UiAi=UoAt)

**Example**:
Study the effect of using 2 and 5 fins/in fin geometry on overall heat
transfer when tube side heat transfer coefficient varies: Use 2x.105 in
tubes,29 tubes/row,6 ft long,4 in square pitch,fin height=0.75 in,thickness=0.05
in serrated tubes;turbine exhaust gas flow=150,000 lb/h at 900 F.(surface
area of 2 fins/in tube=2.59 ft^{2}/ft and 5fins/in tube=6.02 ft^{2}/ft).

Using
the equations for finned tubes (see my books for example) or Chart
for finned tube heat transfer coefficient ,we compute ho and Ui for
varying hi values of 20,100 and 2000 Btu/ft^{2}hF for both 2 and
5 fins/in options. The results are shown below.

** Table
showing effect of inside coefficient on overall heat transfer coefficient**

hi,Btu/ft^{2}hF |
20 |
20 |
100 |
100 |
2000 |
2000 |

fins/in |
2 |
5 |
2 |
5 |
2 |
5 |

G,lb/ft^{2}h |
5591 |
6366 |
5591 |
6366 |
5591 |
6366 |

Ai/(EhoAt) |
.01546 |
.00867 |
.01546 |
.00867 |
.01546 |
.00867 |

Uo |
2.73 |
1.31 |
7.03 |
4.12 |
11.21 |
8.38 |

Ui |
15.28 |
17.00 |
39.28 |
53.55 |
62.66 |
109 |

ratio
Ui |
1. |
1.11 |
1 |
1.363 |
1 |
1.74 |

ratio
gas pr drop |
1 |
1.6 |
1 |
1.3 |
1. |
1.02 |

1.As the tube side coefficient increases,the ratio of Ui values(between 5 and 2 fins/in tubes) decreases.With hi=20,the Ui ratio is only 1.11. With a hi=2000,the Ui ratio=1.74. What this means is that as hi decreases,the benefit of adding more finned surface becomes less attractive. With 2.325 times the surface area(6.02/2.59-see above for surface areas of 2 and 5 fins/in tubes)we have only 1.11 fold improvement in Ui. With higher hi of 2000,the increase is a decent 1.74.(because of fin effectiveness,we lose a little and hence not getting the maximum of 2.325).This is the reason we don't use fins in tubular air heaters,where both the gas and air side heat transfer coefficients are on the same order,namely 10 to 15 Btu/ft

2.A simple estimation of tube wall temperature can tell us that higher the fin density,the higher the tube wall temperature.

For hi=100,with 2 fins/in,Ui=39.28. With a gas temperature of 900 F and fluid temperature of say 600 F,the heat flux inside the tube is qi = (900-600)x39.28 =11,784 Btu/ft

With 5 fins/in,Ui=53.55. qi=53.55x(900-600)=16,065. Tube wall temperature= 600+(16,065/100)=761 F. The increase is about 43 F. The fin tip temperature will also be higher with higher tube wall temperature.

3.The ratio of gas pressure drops between the 2 and 5 fins/in designs(after adjusting for the effect of Ui and for same energy transfer values) increases as the tube side coefficient reduces.It is 1.6 for hi=20 and 1.02 for hi=2000.That is,when hi is smaller,it is prudent to use smaller fin surface geometry.

4.Similar conclusions may be drawn when fouling factor inside the tubes is high as discussed in this article.

Hence if one sees a boiler superheater with say 5 or 6 fins/in fin density,the fin selection may be questioned. You may have a much larger surface area than a 2 fins/in design but the tube wall,fin tip temperatures will be running hotter (leading to higher grade tube/fin materials) and probably higher gas pressure drop.You may be unnecessarily paying more $$ for a poor design.Ask for an option with say 2 fins/in design.With economizers and evaporators(where the tube side coefficient is very high),5 or even say 6 fins/in may be used,though this may not be the optimum configuration.

V.Ganapathy's
Home Page(Books,Software,Papers on Boilers,HRSGs)

email Ganapathy