Effect of h i on Fin Selection
Effect of h i on Fin Selection
The tube-side coefficient plays a dominant role in the selection of fin geometry. If the tube- side heat transfer coefficient is small, then it does not pay to use a large fin surface on the tube to take the advantage of finning. For example, in a tubular air heater, both the gas- side and air-side heat transfer coefficients are comparable, and hence, it does not make sense to use fins on the tubes. In a boiler superheater, the tube-side coefficient is reason- ably high but not as much as that in the economizer or evaporator. Hence, we should use low fin density on a superheater. Using 5 or 6 fins/in. does not make sense on a superheater as it unnecessarily increases the heat flux inside the tubes and increases the tube wall tem- perature and reduces the superheater life as shown earlier. In an economizer or evaporator, the tube-side coefficient is very high compared to that on the gas side, and hence, we can afford to use 5 or even 6 fins/in.
The following example shows why the finning is not effective when the tube-side coef- ficient is small.
Example E.4
Over a tube bundle, 150,000 kg/h of flue gas from the combustion of natural gas at
600°C flows. The tube-side coefficient is 150 kcal/m 2 h °C (174 W/m 2 K) in one case and 7000 kcal/m 2 h °C (8140 W/m 2 K) in another case. For both cases, study the performance
using fins of density 216 fins/m versus 78 fins/m. Fin height = 19 mm, serration = 4, thickness = 1.5 mm, staggered tubes. The following conclusions may be drawn (Table E.7):
1. When the tube-side coefficient is very low, it is not productive to use a high fin density. The ratio of U i values between 216 and 78 fins/m (tube-side coefficient)
is only 1.19 with h i = 150 kcal/m 2 h °C when we have used 2.12 times the surface area. That is, if we have 2.12 times increase in surface area, we should get at least some increase in U i close to 2.0. With higher tube-side coefficient, for the surface area increase ratio of 1.46, we get about 1.71 times increase in U i , which is much better. That is, the use of high fin density is justified when tube-side coefficient is high. Else, it is counterproductive.
432 Appendix E: Calculations with Finned Tubes
TABLE E.7
Effect of Tube-Side Coefficient on Finned Bundle Performance
150 Duty, MM kcal/h (MW)
Tube-side coefficient
11.50 11.55 11.5 Gas press. drop, mm wc
106 Tube wall temp., °C
513 Number of rows deep
40.1 56.9 8.45 17.8 Heat flux inside tubes
U o , kcal/m 2 h °C
36,675 Fin density, fins/m
104.4 Ratio U i
U i , kcal/m 2 h °C
1.71 1.19 Ratio ΔP g 1.39 2.07
3,456 Ratio of surface area
Surface area, m 2 1,573
Note: 36 tubes/row, 3.65 m length, S T =S L = 101 mm. Heat flux in
kcal/m 2 h.
2. The gas pressure drop increases by only 1.39 times when h i is 7000 kcal/m 2 h °C, compared to 2.07 times when we have h i = 150 kcal/m 2 h °C. The gas pressure drop increase is too much. 3. The tube wall temperature is also very high when we use fins with h i = 150 kcal/m 2 h °C, which is obvious as the temperature drop across the low tube- side film is much higher.
Tube-side film temperature drop with h i = 150 kcal/m 2 h °C and fins/m of 216 = 42,265/150 = 282°C, while with h i = 7,000 kcal/m 2 h °C, the tube-side film drop =
175,235/7,000 = 25°C only. Thus, tubes also run much hotter when high fin densities are used in low tube-side heat transfer coefficient cases.
The bottom line is as follows: Avoid fins when tube-side coefficients are very low. In
superheaters where h i can be in the range of 1200–1600 kcal/m 2 h °C, use 78–119 fins/m
and not more; otherwise, the heat flux inside the tubes will shoot up, increasing the tube wall temperature and decreasing the life of the superheater. The author has seen several designs of superheaters using 5 fins/in. or even 6. This is a very poor design. Some boiler suppliers do this either without the knowledge of heat flux and tube wall temperatures (whose ill effects will be seen after the warranty period usually!) or with an eye on reducing the number of tubes deep, which reduces the manufacturing costs. The end user is stuck with such poor designs as the life is reduced when superheater tubes operate continuously at a higher temperature.
Effect of Fin Geometry on Heat Transfer Coefficients
When the tube-side heat transfer coefficient is large as in evaporator or economizer, then
a high density makes sense. Here is an example of an evaporator designed with different fin densities. The tube length and spacing were adjusted slightly to obtain the same duty and gas pressure drop.
Appendix E: Calculations with Finned Tubes 433
TABLE E.8
Effect of Fin Geometry in Evaporator
Case 3 Case 4
Gas temperature in, °C
600 Gas temperature out, °C
281 Duty, MM kcal/h (MW)
8.54 8.53 8.52 Gas pressure drop, mm wc
50 48 50 50 Steam flow, kg/h
15,215 Fins/m, height, thickness, serration
157 × 15 × 1.5 × 4 197 × 15 × 1.5 × 4 S T ×S L (staggered)
90 × 90 Tubes/row
20 20 20 20 Number of rows deep
16 13 11 9 Length, m
5 5 5 5.5 Weight of tubes, kg
11,000 U o , kcal/m 2 h °C (W/m 2 K)
49.2 (57.2) 44.6 (51.9) Tube wall temperature, °C
Surface area, m 2 1,075
164,600 Note: Reduce weight of tube bundles using smaller tubes.
Heat flux inside tubes, kcal/m 2 h 102,500
Example E.5
In an HRSG evaporator, 100,000 kg/h of gas turbine exhaust at 600°C is cooled to 281°C.
Tubes are 50.8 × 44 mm. Arrangement is staggered. Steam pressure is 39 kg/cm 2 g (satura- tion temperature is 249°C) and feed water is at 105°C. Fouling factors are 0.0002 m 2 h °C/kcal
on both gas and steam sides. Analysis : All the options have nearly the same weight, duty, and gas pressure drop and
cross section (Table E.8).
• The number of rows deep is lesser when the fin density is higher. Hence, one
can evaluate the cost of the bundle considering material and labor costs and choose the best option. In some locations, cost of labor may be low, and hence, lower fin density option may work out to lower cost as cost of finned tubes will
be lower, and more rows can be assembled at an overall attractive cost. • Surface areas are higher with higher fin density as expected due to the lower
heat transfer coefficients with higher fin densities. • Heat flux inside the tubes is higher with higher fin densities. However, con-
sidering the steam pressure, these heat fluxes are acceptable as discussed in Chapter 2.
• The tube wall temperature is higher with higher fin density due to higher heat
flux. Hence, plant engineers should ask for this information also when obtain- ing quotes from various vendors. It is likely that some vendors may have offered designs with much higher gas velocity and high gas pressure drop with higher heat flux inside the tubes and consequent higher tube wall temperatures.