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National Advisory Committee for Aeronautics, Technical Notes - Analytical and Experimental Investigation of Fully Developed Turbulent Flow of Air in a Smooth Tube with Heat Transfer with Variable Fluid Properties

A previous analysis of turbulent flow and heat transfer in smooth
tubes with variable fluid properties was modified in order to bé'appli~
cable to air which has a Prandtl number slightly less than unity (0.75).
In order to verify the analysis, tests were conducted to determine
local heat—transfer coefficients and friction factors for fully developed
turbulent flow of air in a smooth electrically heated tube having an
inside diameter of 0.87 inch and a length of 87 inches. The tests were
conducted at high ratios of wall to fluid bulk temperature. Velocity
and temperature profiles were measured for some conditions.

The analytically predicted results were found to agree closely with
the experimental. Both the analytical and experimental results indi—
cated that the effects of ratio of wall to bulk temperature on the
Nusselt number correlation can be eliminated by evaluating the fluid
properties, including density, in the Reynolds and Russelt numbers at
a temperature close to the average of the wall and bulk temperatures.

In order for this correlation to apply it is necessary to assume con—
stant Prandtl number and constant specific heat in calculating both the
experimental and analytical results.

The effects of variation of shear stress and heat transfer across
the tube on the velocity and temperature distributions were analytically
investigated and found to be small for turbulent flow with variable
fluid properties. The effects of molecular shear stress and heat trans-
fer in the region at a distance from.the wall were also investigated
and found to be small.

In an experimental investigation of average heat transfer and
friction coefficients for air flowing in smooth tubes (reference 1), it
was found that the ratio of wall to fluid bulk temperature has an appre-
ciable effect on the heat-transfer and friction correlations. A theo-
retical analysis given in reference 2 indicates a similar effect for local
coefficients. For verification of the analysis given in reference 2, it
is desirable to Obtain local rather than average heat-transfer coeffi-
cients and friction factors and.measurements of radial velocity and tem-
perature distributions for large heat-transfer rates. Local rather than
average coefficients are desirable because average coefficients include
possible effects of flow development near the tube entrance and of heat
loss at the ends of the tube.