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The two examples presented below show why fins are used and also the importance of proper fin configuration. More examples can be found in my books.

Extended surfaces make boilers compact,reduce their weight  and gas pressure drop. They are particularly attractive in low gas temperature (low log-mean-temperature difference)applications such as gas turbine or diesel engine exhaust.
The table below compares the design of a bare tube boiler with a finned tube boiler for the same gas temperature drop and duty.
case bare tube finned tube
 gas flow,lb/h 150,000 150,000
gas inlet temp,F 1000 1000
exit gas temp,F 382 382
duty,MM Btu/h 24.25 24.25
steam pressure,psig 150 150
feed water temp,F 240 240
steam flow,lb/h 24,500 24,500
surface area,ft2 11670 20140
U,Btu/ft2hF 12.86 7.17
gas pr drop,in wc 4.5 3.15
no of rows deep 124 21
heat flux,Btu/ft2h 9213 52295
tube wall temp,F 385 484

The finned tube design is compact,as seen by the number of rows deep,only 21 vs 124!
The overall heat transfer coefficient is much lower for the finned tubes hence surface area is larger
Heat flux is much higher with finned tubes due to the large ratio of external/internal surface area
Tube wall temperature is hence much higher with finned tubes

It can also be shown that higher the fin to tube surface,the tube wall and fin tip temperatures will be higher as also the gas pressure drop. Higher the fin density,lower the heat transfer coefficient and vice versa as seen by the chart below for heat transfer in finned tubes.

It can be seen easily that  surface areas with finned tube can be very misleading.A larger surface area in the form of higher fin density does not mean more duty.One has to look at the product of surface area and log-mean temperature difference and not surface area alone! Besides increasing the heat flux,and hence the tube wall,fin tip temperatures and gas pressure drop,improper fin geometry can cost more too though the higher surface area may at first impress a few!!

The example below shows the design of a superheater with different fin geometry. The largest surface area design is not the best. However engineers not familiar with heat transfer may be led to think that it is! See my books for more examples.

gas flow=200,000 lb/h
inlet gas temp=1200 F
gas analysis:% vol CO2=7,H2O=12,N2=75,O2=15
steam flow=100,000 lb/h at 600 psig
tubes:2x0.120 T11;tubes/row=22,length=10ft,square pitch=4 in,fouling factors=0.001(gas/steam)
counter flow configuration . Fin geometry was varied to obtain a duty ranging from 14 to 18 MM Btu/h. Equations used,Calculation procedures are described in my books.

Results of superheater design
case no 1 2 3 4
duty,MM Btu/h 14.14 14.18 17.43 17.39
steam temp out,F 689 689 747 747
gas pr drop,in wc 0.65 1.20 1.15 1.37
gas exit temp,F 951 950 893 893
fins/in x ht x thick 2x0.5x0.075 5x0.75x0.075 2.5x0.75x0.075 4x0.75x0.075
surface area,ft2 2471 5342 5077 6549
tube wall temp,F 836 908 905 931
fin tip temp,F 949 1033 1064 1057
U,Btu/ft2hF 11.79 5.5 8.04 6.23
tube pr drop,psi 9.0 6.5 11.0 9.0
no of rows 6 4 7 6
fin effectiveness,% 84 72 68 70
Cases 1 and 2 have the same duty but due to differences in fin geometry,see the difference in surface area,nearly 2.15 times! As a result of the improper geometry,the tube wall and fin tip temperatures are also higher!
Overall heat transfer coefficient is lower for case 2 versus 1 due to poor fin geometry
Case 3 in fact transfer more duty with lessers surface area compared to case 2.
Cases 3 and 4 also reveal the same trend,namely larger fin surface does not translate to more duty or better design.

Examples on the following topics can be found in my Books "Waste Heat Boiler Deskbook" and "Steam Plant Calculations Manual":
Effect of inline versus staggered arrangement
Solid versus serrated fins-impact on performance
Effect of fouling on boilers with different fin geometries
Optimization of fin geometry considering surface area,gas pressure drop

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