Water enters a double pipe heat-exchanger at 60°C. The water flows on the inside through a copper tube 2.54 cm ID at a velocity of 2 cm/s. Steam flows in the annulus and condenses on the outside of the copper tube at a temperature of 80°C. Calculate the outlet temperature of the water if the heat exchanger is 3-m-long.

Question

GIVEN

• Water flow through a tube in a double pipe heat-exchanger

• Water entrance temperature (Tb,in.) = 60°C

• Inside tube diameter (D) = 2.54 cm = 0.0254 m

• Water velocity (V) = 2 cm/s = 0.02 m/s

• Steam condenses at (Ts) = 0.80°C on the outside of the pipe

• Length of heat exchanger (L) = 3 m

FIND

• Outlet temperature of the water (Tb,out)

ASSUMPTIONS

• Steady state

• Thermal resistance of the copper pipe is negligible

• Pressure in the annulus is uniform therefore, Ts is uniform

• Heat transfer coefficient of the condensing steam is large (see Table 1.4) so its thermal resistance can be neglected

• Outside surface of the heat exchanger is insulated

SKETCH

Answer 1

The Reynolds number is



The thermal entrance length is given



Therefore, the flow is not fully developed and the Sieder and Tale correlation, will be

used



The outlet temperature is given by



Solving for the bulk water outlet temperature



Performing a second iteration using the water properties at the average temperature of 66°C



COMMENTS

The negligible change of Tb,out in the second iteration could be expected because the changes in the

water properties are small.