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National Advisory Committee for Aeronautics, Report - Analysis of Turbulent Heat Transfer, Mass Transfer, and Friction in Smooth Tubes at High Prandtl and Schmidt Numbers

The oppression for eddy difiusioity from a previous analysis
was modified in order to account for the eflect of kinematic
viscosity on the turbulence in the region close to a wall. By
using the modified expression, good agreement was obtained
between predicted and eaperimental results for heat and mass
transfer at Prandtl and Schmidt numbers between 0.5 and 3000.
The ejects of length-to-diameter ratio and of variable viscosity
were also investigated for a wide range of Prandtl numbers.

Most of the existing analyses for turbulent heat and mass
transfer are adequate only for Prandtl and Schmidt numbers
on the order of 1 or less. For instance, the analysis given in
reference 1, although adequate for gases, gives heat— and
mass-transfer coefficients for liquids at high Prandtl or
Schmidt numbers that are higher than those obtained
experimentally. The difference between the experimental
values and the values obtained by the method in reference 1
increases as the Prandtl or Schmidt number increases.

Coefficients obtained from the von Karman analysis (ref. 2)
at high Prandtl or Schmidt numbers are lower than the
experimental values. Rannie’s analysis (ref. 3) gives
coeflicients which are in somewhat better agreement with
the data than either of these analyses, but the coefficients
are again inaccurate at very high Prandtl or Schmidt num—
bers. The analysis of reference 4 agrees with data at
Prandtl or Schmidt numbers of 1 and at very high Prandtl or
Schmidt numbers, but the coefficients are somewhat low at
intermediate values of these numbers. In reference 5,
which was published since the present investigation was
initiated, good agreement was obtained with mass-transfer
data for Prandtl and Schmidt numbers between 0.5 and 3000
by introducing an appropriate amount of turbulence into
the laminar sublayer. In all these analyses, except those in
references 1 and 3, the properties Were constant and the
flow fully developed. The relations among heat transfer,
mass transfer, and fluid friction are discussed in reference 6.