A shell-and-tube heat exchanger with two tube passes and a single shell pass is used to heat water by condensing steam in the shell. The flow rate of the water is 15 kg/s and it is heated from 60 to 80°C. The steam condenses at 140°C and the overall heat transfer coefficient of the heat exchanger is 820 W/(m2 K). If there are 45 tubes with an OD of 2.75 cm, calculate the length of tubes required.

Question

GIVEN

• Shell-and-tube heat exchanger with two tube passes and one shell pass

• Water in tubes, condensing steam in shell

• Water flow rate m w= 15 kg/s

• Water temperatures

? Tw,in = 60°C

? Tw,out = 80°C

• Steam temperature (Ts) = 140°C

• Overall heat transfer coefficient (U) = 820 W/(m2 K)

• Number of tubes (N) = 45

• Tube outside diameter (D) = 2.75 cm = 0.0275 m

FIND

• The length of tubes (L)

ASSUMPTIONS

• Counterflow

SKETCH



PROPERTIES AND CONSTANTS

the specific heat of water at the mean temperature of 70°C (cpw)= 4188 J/(kg K)

Answer 1

For counterflow,



Since ?Ta is less than 50% greater than ?Tb, the mean temperature may be used



The rate of heat transfer is given by



Solving for the transfer area



The outside area of the tubes is



If each tube is bent in half to create the two tube passes, than the total tube length is 2 L = 5.6 m