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National Advisory Committee for Aeronautics, Technical Notes - Slip-Flow Heat Transfer from Cylinders in Subsonic Streams

Over 1000 measured convective heat—transfer coefficients for normal
cylinders in subsonic slip flow have been correlated by using Nusselt
number as a function of Reynolds and Knudsen (or Mach) numbers. The ex-
perimental range corresponds to the following dimensionless groups: Mach
number M, 0.05 to 0.80; Reynolds number Re, 1 to 75; Knudsen number
Kn, 0.009 to 0.077. Air temperatures between 0° and 280° F and cylinder
temperatures between 54° and 620° F were used. At Kn = 0.009, the
Nusselt number (Nu) correlation extrapolated smoothly into continuumr
flow empirical curves, which show Nu as a function of iTE with a
small, regular variation in Nu from compressibility or Mach number
effects. The data showed increasing sensitivity to Kn as it increased
to 0.077. The experimental Nu curves at Kn = 0.077 qualitatively
verified two characteristics predicted by free—molecular—flow theoretical
analysis. These are a shift to first—power dependence on Re and large
separation of constant Mach number parametric curves due to rarefied gas—
flow phenomena. Therefore, the experimental slip—flow correlation served
as a bridge between continuum empirical relations and free—molecular
theoretical results, but data between 0.10 < Kn < 2 are required to com—
plete this general correlation.

A complicated nonlinear dependence of the heat—transfer coefficient
to the difference between cylinder and recovery temperature AT is re-
ported. The heat—transfer coefficient h. increased with increasing
AT for Kn < 0.02; while for Kn > 0.02, h decreased with increasing
AT. The MaCh number had a secondary effect on this AT phenomenon.
For cylinders operated at AT >-200° F and over the entire range of
this research, an increase in air temperature increased the heat-transfer
coefficient. The preceding were secondrorder effects that caused devia-
tions of up to 20 percent from the general correlation.

Fine metal wires, 0.00005 to 0.001 inch in diameter, have been
widely used in aerodynamic research as anemometers. The use of hot-wire
anemometers for mean flow measurements began with the early work of King
(ref. 1), while the investigation of fluctuations in airflows started
with the classical research of Dryden and Kuethe (ref. 2). In every
application, the sensitivity of the electrically heated anemometer to
the flow properties is determined by the heat-transfer characteristics
of cylinders in forced convection.