Why Are Fins Not Used in Gas–Gas Exchangers?

Finned surfaces are not used in tubular air heaters as both the air-side and flue gas–side heat transfer coefficients are in the same range. The effect of adding finned surface will not

be reflected in the duty.

Example E.10

Tubes of size 50.8 × 46.4 mm are used in inline arrangement in an air–flue gas exchanger. Three options are reviewed, one with plain tubes and two others with 78 and 197 serrated fins with a fin height of 15 mm and thickness of 1.5 mm and serration width of

4 mm. Calculations for the plain tube exchanger are worked out in Chapter 4 on waste

Appendix E: Calculations with Finned Tubes 441

heat boilers. The finned exchanger performance was obtained by using the procedure discussed earlier. Calculations for the 197 fins/m option are shown later, while results

from computer program are shown for the 78 fins/m case. Fouling factors are 0.0002 m 2

h °C/kcal on air and flue gas sides. S T = 107 mm, S L = 90 mm. Tubes/row = 50 and number deep = 56. Effective length = 2.4 m. See Equations E.1 through E.20 for the calculation procedure. Note that the following is for serrated fins, while calculations for solid fins were shown in Example E.1 (Table E.16).

Solution

A o = d + 2nbh = 0.0508 + 2 × 197 × 0.015 × 0.0015 = 0.05967 m 2 /m

A 2 f = = . 1 34 3 3 m /m

A t = . 1 343 + . 3 14 0 0508 × . × ( − 1 197 0 0015 × . ) = . 1 456 m /m 2

Ratio of external to tube inner surface = 1.456/(3.14 × 0.0464) = 10

2 G 2 = = 35 , 213 = 9 78

50 kg/m h

. kg/m ss

The overall thermal performance, duty, and air–gas exit temperatures with the finned tubes are the same as that with plain tubes. Hence, let us use gas properties at average air temperature of 103°C as follows: C p = 0.2455 kcal/kg °C, µ = 0.0806 kg/m h, k = 0.0282 kcal/m h °C from Appendix F.

Calculation of Heat Transfer Coefficient

Re = 35,213 × 0.0508/0.0806 = 22,193. Compute the constants C 1 –C 6 .

C 3 = . 0 25 0 6 + . exp 

C 5 = 11 . −  . 0 75 1 5 − . exp ( − . 0 7 56 × )  exp ( −× 2 90 107 / ) = . 0 96 005

Average air temperature = 103°C. Assume average fin temperature = 135°C. (These values may be corrected later if necessary, but their effect is small). Convective heat transfer coefficient

h c = 0.00435 × 0.4516 × 0.9605 × [(50.8 + 30)/50.8] 0.5 (376/408) 0.5 × 35,213 × 0.2455

× (0.0282/0.0806/0.02455) 0.67 = 24.93 kcal/m 2 h °C

m = [2 × 24.93 × (0.0015 + 0.004)/(30 × 0.0015 × 0.004)] 0.5 = 39.0 mh = 39.0 × 0.015 = 0.585 tanh (mh) = [(1.796 − .557)/(1.796 + 0.557)] = 0.5265. Fin efficiency E = 0.5265/0.585

= 0.896 Fin effectiveness η = 1 − (1 − 0.896) × 1.343/1.456 = 0.904.

TABLE E.16

Thermal Conductivity of Metals, Btu/ft h °F

Temperature (°F)

Aluminum (annealed) Type 1100-0

Type 3003-0

Type 3004-0

Type 6061-0

Aluminum (tempered) Type 10 (all tempers)

Type 3003 (all tempers)

Type 3004 (all tempers)

Type 6061-T4 and T6

Type 6063-T5 and T6

Type 6063 T42

Cast icon

Carbon steel

u la

Carbon moly steel

tio

Chrome moly steels

n sw

1% Cr, 1 % Mo

inn

2 4 % Cr. 1% Ma

ed T

5% Cr, % Mo

14 15 15 15 16 16 16 16 17 17 17 18 be s

12% Cr

Austenitic stainless steels

Admiralty metal

Naval brass

alc u

Cupper (electrolytic)

Copper and nickel alloys

30% Cu, 70% Ni (Monel)

Nickel–chrome–iron

9.4 9.7 9.9 10 10 11 11 11 12 12 12 13 13 13 ed T

Titanium (or B)

be s

Note: Multiply by 1.489 to obtain values in kcal/m h °C or by 1.732 to obtain values in W/m K.

444 Appendix E: Calculations with Finned Tubes

Neglect nonluminous radiation due to low air temperatures and absence of water vapor and carbon dioxide in air. Using the same h i as in the example shown in Chapter 4 as tube-side flow and tube count are very close, we have

1/U o = 1/(0.904 × 24.93) + 0.0002 + 0.0508 × 10 × ln(50.8/46.4) × /(2 × 30) + 0.0002 × 10 +

(10/49) = 0.04437 + 0.0002 + 0.000767 + 0.002 + 0.204 = 0.2513 or U o = 3.98 kcal/ m 2 h °C

Gas Pressure Drop See Equations E.16 through E.21.

C 2 0 11 14 . 22193 04 = . . + × − = . 0 1355 .† Spacing between fins S = 1/n – b = (1/197) − 0.0015 = 0.003576

= . 0 3851 C 2

0 11 0 × . 015 0 003576 0 15 /.  C .

6 = 16 . − . 0 75 1 5 − . exp ( − . 0 7 57 × ) exp    − 0 . 2 × ( / 90 107 )  = . 0 94 9 9

 f = 0.1355 × 0.3851 × 0.949 × (80.8/50.8) × (376/408) 0.25 = 0.0771 (average air temperature is

103°C (376 K) and average fin temperature is 135°C (408 K).

B 2 =  ( . 0 107 − . 0 05967 ) /. 0 107  = . 0 1957

a = ( + 1 0 1957 0 1957 . × . )( × 181 25 − )( / × 4 57 )( / 376 ) = . 0 00189 .

Gas dens 3 iity = = . 0 93 kg/m

∆P g (

) × . 9 78 × 56 † = 93 mm wc

Checking the Duty Apply the NTU method for the cross-flow exchanger performance. See Appendix A for

equations for various types of exchangers. The air side is mixed while the flue gas is not.

C max = 225 000 0 279 , × . = , 62 775 .† C min = 200 000 0 246 0 99 48 708 , × . × . = ,

C = 48,708/62,775 = 0.7759. A = 1.456 × 50 × 56 = 9784 m 2 . NTU = 3.98 × 9,784/(200,000 × .99 × 0.2455) = 0.801

 −− { 1 ex p NTU C ( − ×

∈=− exp

Hence, Q T = 0.449 × 48,708 × (375 − 25) = 7.65 MM kcal/h (8.9 MW). Results for all the cases are shown in Table E.17. The following observations may be made.

Appendix E: Calculations with Finned Tubes 445

TABLE E.17

Performance of Air Heater with and without Fins

Air Flow

Inlet air temperature, °C 25 25 25 Exit air temperature, °C

181 Duty, MM kcal/h

7.69 7.67 7.64 Air-side pressure drop, mm wc

U o , kcal/m 2 h °C

9,772 Flue gas flow, kg/h

Surface area, m 2 1,360

225,000 Flue gas temperature in, °C

375 Flue gas temperature out, °C

253 Flue gas pressure drop, mm wc

30 28 26 Fins/m

0 78 197 Tubes/row

50 50 50 Number of rows deep

57 57 56 Length, m

3 2.55 2.4 Transverse pitch, mm

82 97 107 Longitudinal pitch, mm

70 90 90 Ratio of external to internal surface area

1.09 4.48 10 Weight, kg

The cross section of the exchanger, duty, and pressure drops on air and gas sides are same. However, the surface area of the finned exchangers are much more and also their weight. We are adding weight and cost to the exchanger for the same duty, which is fool- ish. Hence, the cost of the finned bundle will also be higher. One can see how low the U o value is reduced as the fin density increases. Hence, finned tubes are not used when the tube-side heat transfer coefficient is comparable with the tube outside coefficient.

A summary of important points about finned tubes is given in Table E.18.

TABLE E.18

What You Should Know about Finned Tubes The higher the fin surface area, the lower will be the heat transfer coefficient. One should not evaluate finned

surfaces by surface area alone. Product of (UA) should be compared and not A alone, which is what many do! Surface areas in boiler components can vary by 50%–100% for the same duty due to improper selection of fin

geometry! Higher fin surface also results in higher heat flux inside tubes and hence higher tube wall and fin tip temperatures. Life of superheaters is affected by poor selection of fin geometry. Use smaller fin density when tube-side coefficient is small. For superheaters, 78–117 fins/m is adequate, while for evaporators and economizers, 157–255 fins/m may be fine. Staggered arrangement is slightly better than inline for finned tubes. Smaller-diameter tubes with same fin configuration results in a less heavy tube bundle compared to a larger

tube diameter bundle. Fouling inside the tubes impacts finned tubes more than plain tubes through lower duty and higher tube wall

temperatures. Serrated fins give a slightly higher heat transfer coefficient and also higher gas pressure drop. Using thick fins increases the tube wall temperature while decreasing the fin tip temperature. The duty

increases slightly. Hence, fin thickness may be limited to 1.5–1.9 mm. The use of 3 mm or thicker fins may be permitted for a row or two to limit the fin tip temperature but not for the entire HRSG.

446 Appendix E: Calculations with Finned Tubes

References

1. V. Ganapathy, Industrial Boilers and HRSGs, CRC Press, Boca Raton, FL, 2003. 2. ESCOA Corp., ESCOA Fin Tube Manual, Tulsa, OK, 1979. 3. Fin Tube Technologies, Tulsa, OK. 4. V. Ganapathy, Applied Heat Transfer, Pennwell Books, Tulsa, OK. 1982, p501. 5. V. Ganapathy, Evaluated extended surfaces carefully, Hydrocarbon Processing, Oct. 1990, p65. 6. V. Ganapathy, Understand finned heat exchangers, Chemical Engineering, Sept. 2013, p62.

Why Are Fins Not Used in Gas–Gas Exchangers?