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National Advisory Committee for Aeronautics, Technical Notes - Measurements of Recovery Factors and Coefficients of Heat Transfer in a Tube for Subsonic Flow of Air

Measurements of heat flow to air at subsonic velocities
and at substantially constant Reynolds number show that the
heat—transfer coafficient he, based on the difference be—
tween the temperature of the heated wall and the adiabatic
wall temperature, is independent of this difference. In
order to determine the adiabatic wall temperature. recovery
factors were measured at the pipe Wall for adiabatic flow.
The recovery factor averages 0.88 and is substantially in—
dependent of Mach number in the range from 0.2 to l. The"
coefficient of heat transfer he, based on the difference

betWeen the temperature of the heated wall and the mean
stagnatiOn temperature of the stream, is not independent_ofm
this temperature difference unless the temperature differ—
ence is large compared with the difference between stagna-
tion temperature and mean stream temperature. The conven-
tional heat-transfer coefficient hm varies even more with
temperature difference. The preferred Stanton number
he/chv where cp is specific heat at constant pressure
and G is mass velocity, is nearly independent of average
Mach number in the range frOm 0.1 to 0.75, and varies with
Reynolds number substantially in the manner characteristic
of turbulent flow of incompressible fluids in pipes.

Published data for flow of air at high Mach numbers in—
volve such large temperature differences that they throw no
light on whether he or h3 should be employed for heat—
transfer calculations. They are used here tO'extend the
present conclusiOns to much higher Reynolds numbers and tem-
perature differences, leading to the relation
where D is the inside diameter and ”m is the absolute
viscosity of air at average mean stream temperatures.

In heat transfer to or from a stream of incompressible
fluid the coefficient of heat transfer is defined as the
rate of heat transfer per unit of surface area per unit dif:
ference between the temperature of the surface and the mean_
stream temperature at the cross section in question.
(All symbols are defined in the appendix.) The value of
this coefficient is found to be substantially independent of
the temperature difference except for large temperature dif—
ferences.