Mercury flows inside a copper tube 9 m long with a 5.1 cm inside diameter at an average velocity of 7 m/s. The temperature at the inside surface of the tube is 38°C uniformly throughout the tube, and the arithmetic mean bulk temperature of the mercury is 66°C. Assuming the velocity and temperature profiles are fully developed, calculate the rate of heat transfer by convection for the 9 m length by considering the mercury as (a) an ordinary liquid and (b) liquid metal. Compare the results.
GIVEN
FIND
The rate of heat transfer for the 9 m length considering mercury as
(a) an ordinary liquid, and
(b) a liquid metal
ASSUMPTIONS
Steady state
Fully developed flow
SKETCH
PROPERTIES AND CONSTANTS
for mercury at the bulk temperature of 66°C
The Reynolds number is
(a) The mercury will be treated as an ordinary liquid by applying the Dittus-Boelter
The rate of heat transfer is
(b) For liquid metals and a constant surface temperature boundary, the Nusselt number is given by
COMMENTS
Applying the Dittus-Boelter equation, which is valid for Pr > 0.5 only, to mercury (Pr = 0.02) leads to
a 648% overestimation in the rate of heat transfer to the pipe. This shows that application of empirical
outside the limits of experimental verification can lead to serious errors.
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