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How does tube side heat transfer         Coefficient affect selection of Fin  Configuration?   V.Ganapathy
Tube side heat transfer coefficient has an important influence on proper selection of fin configuration in boiler superheaters,evaporators and economizers.Assuming finned tubes may be used,a low fin density on the order of  1 to 2 fins/in (or low external surface area) is  recommended when the tube side heat transfer coefficient is low as in superheaters,while a high fin density such as 4 to 6 fins/in may be used in evaporators and economizers; of course we are assuming that the gas stream is clean and this aspect is not influencing fin geometry selection.
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/ft2hF
Ai,At =tube internal and external surface areas,ft2
 E=fin effectiveness,fraction
ho=gas side heat transfer coefficient,Btu/ft2hF
(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 ft2/ft and 5fins/in tube=6.02 ft2/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/ft2hF 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/ft2hF 20 20 100 100 2000 2000
fins/in 2 5 2 5 2 5
G,lb/ft2h 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
(Please see my book "Steam plant calculations manual",for detailed calculations and more examples)
Conclusions
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/ft2hF.Fins are attractive only when the tube side coefficient is very large compared to gas side coefficient.
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/ft2h.The temperature drop across the tube side film (hi=100)=11,784/100=118 F.Hence the wall temperature (neglect fouling etc) is about 600+118=718 F.
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.

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