An air-cooled low-pressure-steam condenser is shown in following figure.

Question

An air-cooled low-pressure-steam condenser is shown in following figure.

The tube bank is four rows deep in the direction of air flow and there are total of 80 tubes. The tubes have ID = 2.2 cm and OD 2.5 cm and are 9-m-long with circular fins on the outside. The tube-plus-fin area is 16 times the bare tube area (i.e., the fin area is 15 times the bare tube area, neglect the tube surface covered by fins). The fin efficiency is 0.75. Air flows past the outside of the tubes. On a particular day, the air enters at 22.8°C and leaves at 45.6°C. The air flow rate is 3.4 × 105 kg/h. The steam temperature is 55°C and has a condensing coefficient of 104 W/(m2 K). The steam-side fouling coefficient is 104 W/(m2K). The tube wall conductance per unit area is 105 W/(m2K). The air-side fouling resistance is negligible. The air-side-film heat transfer coefficient is 285 W/(m2K). (Note this value has been corrected for the number of transverse tube rows.) (a) What is the log-mean temperature difference between the two streams? (b) What is the rate of heat transfer? (c) What is the rate of steam condensation? (d) Estimate the rate of steam condensation if there were no fins.

GIVEN

• The condenser shown above

• Number of tubes (N) = 80 and number of rows (Nr) = 4 (in air flow direction)

• Tube diameters Di = 2.2 cm = 0.022 m Do = 2.5 cm = 0.025 m

• Tube length (L) = 9 m

• Air temperature Ta,in = 22.8°C Ta,out = 45.6°C

• Air flow rate m a= 3.4 × 105 kg/h = 94.4 kg/s

• Steam temperature = 55°C (constant)

• Fin area = 15 (tube area)

• Fin efficiency (?f) = 0.75

• Steam side

Transfer coefficient h i= 104 W/(m2 K)

Fouling coefficient (1/Ri) = 104 W/(m2 K)

• Tube wall conductance per unit area (1/Rk) = 105 W/(m2 K)

• Air side: Transfer coefficient h o= 285 W/(m2 K)

• Fouling resistance on the air side is negligible

FIND

(a) The log-mean temperature difference(LMTD)

(b) The rate of heat transfer (q)

(c) The rate of steam condensation m

(d) Estimate the rate of steam condensation if there were no fins 2cm

ASSUMPTIONS

• Air side transfer coefficient is the same with or without fins

• Tube surface covered by the fins is negligible

PROPERTIES AND CONSTANTS

for dry air at the average temperature of 34.2°C,

the specific heat (cpa) = 1013 J/(kg K),

for steam at a saturation temperature of 55°C,

the heat of vaporization (hfg) = 2600 (kJ/kg)

Answer 1

(a)



(b) The overall heat transfer coefficient for the base tube area



The rate of heat transfer for the bare tubes above is



If the entire fin area was at the same temperature as the exterior of the tube wall, the rate of heat transfer from the fin would be



The actual rate of heat transfer from the fins is



The actual rate of heat transfer from the fins is



(c) The rate of condensation is



(d) If there were no fins, the rate of heat transfer would be that from the bare tube alone. Therefore



COMMENTS

The rate of condensate flow without the fins is only 8% of that with fins.