The equation was recommended by H. Hausen (Zeitschr. Ver. Deut. Ing., Belherft No. 4, 1943) for forced-convection heat transfer in fully developed laminar flow through tubes. Compare the values of the Nusselt number predicted by Hausen’s equation for Re = 1000, Pr = 1, and L/D = 2, 10 and 100, respectively, with those obtained from two other appropriate equations or graphs in the text.
GIVEN
• Fully developed laminar flow through a tube
• The Nusselt number correlation shown above
• Reynolds number (Re) = 1000
• Prandtl number (Pr) = 1
• Length divided by diameter (L/D) = 2, 10, or 100
FIND
• The Nusselt number (Nu) from the above correlation and two others from the text
ASSUMPTIONS
• ?b / ?s ? 1.0
• Constant wall temperature
SKETCH
Using the Hausen correlation and L/D = 2
can also be used to estimate the Nusselt number. The velocity entrance region for this
calculated
The thermal entrance for this problem can be calculated
Therefore, in the first case, the temperature and velocity profiles are not fully developed and the ‘short
duct approximation’ curve will be used
From
for a parabolic velocity distribution, Nu ? 7.5
for a parabolic velocity distribution, Nu ? 4.1
Finally, the Sieder and Tate correlations contained can be applied (since
Pr = 1 implies that the fluid is a liquid)
Similarly for
Tabulating the results
COMMENTS
The agreement among the three correlations is within the accuracy of empirical correlations.
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