Determine the rate of heat transfer per meter length to a light oil flowing through a 2.5 cm-ID, 60 cm-long copper tube at a velocity of 0.03 m/s. The oil enters the tube at 16°C and the tube is heated by steam condensing on its outer surface at atmospheric pressure with a heat transfer coefficient of 11.3 kW/( m2 K). The properties of the oil at various temperatures are listed in the accompanying tabulation

Question

GIVEN

• Oil flowing through a copper tube with atmospheric pressure steam condensing on the outer surface

• Oil properties listed above

• Inside diameter (D) = 2.5 cm = 0.025 m

• Tube length (L) = 60 cm = 0.6 m

• Oil velocity (V) = 0.03 m/s

• Inlet oil temperature (Tb,in) = 16°C

• Heat transfer coefficient on outside of pipe ( ,c o h )= 11.3 kW/(m2 K)

FIND

• The rate of heat transfer (q) to the oil

ASSUMPTIONS

• Steady state

• The thermal resistance of the copper tube is negligible

• Constant wall temperature

• The tube wall is thin

SKETCH



PROPERTIES AND CONSTANTS

At atmospheric pressure, steam condenses at a temperature (Ts) of 100°C.

Answer 1

The Reynolds number for the oil flowing through the pipe is



Using the oil properties at the inlet temperature of 16°C



The thermal entrance length is given by



Therefore, the temperature profile is not fully developed and the Hausen correlation will be used (assuming the wall temperature ? Ts for ?s)



The thermal circuit for heat flow from the steam to the oil is shown below



If the tube wall is thin, Ao ? Ai = ?DL = ?(0.025 m)(0.6 m) = 0.047 m2 and the thermal resistance is



The outlet temperature can be calculated by replacing hcA by 1/ARtotal in



This is a significant change in the oil temperature and warrants another iteration using the properties

of the oil at the average bulk temperature of 22.4°C. Interpolating the oil properties from the given

data



The rate of heat transfer is given substituting 1/A Rtotal for hc



COMMENTS

Note that 99% of the thermal resistance is on the inside of the pipe.