It is proposed to preheat the water for a boiler with flue gases from the boiler stack. The flue gases are available at the rate of 0.25 kg/s at 150°C, with a specific heat of 1000 J/(kg K). The water entering the exchanger at 15°C at the rate of 0.05 kg/s is to be heated at 90°C. The heat exchanger is to be of the reversed current type with one shell pass and 4 tube passes. The water flows inside the tubes which are made of copper (2.5 cm-ID, 3.0 cm-OD). The heat transfer coefficient at the gas side is 115 W/(m2 K), while the heat transfer coefficient on the water side is 1150 W/(m2 K). A scale on the water side offers an additional thermal resistance of 0.002 (m2 K)/W. (a) Determine the overall heat transfer coefficient based on the outer tube diameter. (b) Determine the appropriate

Question

mean temperature difference for the heat exchanger. (c) Estimate the required tube length. (d) What would be the outlet temperature and the effectiveness if the water flow rate is doubled, giving a heat transfer coefficient of 1820 W/(m2 K)?



GIVEN

• Reverse current heat exchanger - 1 shell pass , 4 tube passes

• Water in tubes, flue gases in shell

• Copper tubes

? Inside diameter (Di) = 2.5 cm = 0.025 m

? Outside diameter (Do) = 3.0 cm = 0.03 m

• Specific heat of gases (cpg) = 1000 J/(kg K)

• Gas inlet temperature

? Tg,in = 150°C

• Water temperatures

? Tw,in = 15°C

? Tw,out = 90°C

• Gas flow rate ( m g) = 0.25 kg/s

• Water flow rate ( m w)= 0.05 kg/s

• Tubes are copper

• Gas side heat transfer coefficient ( )ch = 115 W/(m2 K)

• Water side heat transfer coefficient ( )ih = 1150 W/(m2 K)

• Scaling resistance on the water side (Ri) = 0.002 (m2 K)/W

FIND

(a) The overall heat transfer coefficient (Uo) based on the outside tube diameter

(b) The appropriate mean temperature difference (?Tmean)

(c) The required tube length (L)

(d) The outlet temperature and effectiveness if the water flow rate were doubled, making ih = 1820 W/(m2 K)

SKETCH



PROPERTIES AND CONSTANTS

the specific heat of water at the average temperature of 52.5°C (cpw) =4179 J/kg K

the thermal conductivity of copper (k) = 392 W/(m K) at 127°C

Answer 1

(a) The overall heat transfer coefficient is



(b) The outlet temperature of the gases can be determined from an energy balance



for a simple counterflow heat exchanger



This must be corrected using



F = 0.78



(c) The rate of heat transfer is



Length of each tube pass = L/4 = 9.9 m

(d) For a doubled water flow rate, hi = 1820 W/(m2 K) similarly to part (a)



The heat capacity rates are



The number of transfer units is



The outlet temperature can be calculated