cranfield0049

<DOC>
<DOCNO>
49
</DOCNO>
<TITLE>
temperature and velocity profiles in the compressible
laminar boundary layer with arbitrary distribution
of surface temperature .
</TITLE>
<AUTHOR>
chapman,d. and rubesin,m.
</AUTHOR>
<BIBLIO>
j. ae. scs. 16, 1949, 547.
</BIBLIO>
<TEXT>
  an analysis is presented which enables the temperature profiles,
veiocity profiles, heat transfer, and skin friction to be calculated
for laminar flow over a two-dimensional or axially symmetric
surface without pressure gradient but with an arbitrary analytic
distribution of surface temperature .  the general theory is
applicable to a gas of any prandtl number, although the numerical
results given herein have been computed for air .
the predictions of the theory for the special case of constant surface
temperature are compared with the calculations of crocco .
on the basis of this comparison, it is inferred that the present
theory enables heat-transfer and skin-friction calculations accurate
to within about 5 per cent to be made for flight conditions
up to mach numbers near 5 and to within about 1 or 2 per cent
for supersonic wind-tunnel conditions up to considerably higher
mach numbers .
  a particular effort has been made to present the results, which
are simple considering their generality, in a form that can be used
readily in practical applications .  from the mathematical point
of view, the theory is applicable to an arbitrary analytic distribution
of surface temperature, but in any given practical case it is
necessary that the surface-temperature distribution be approximated
by a polynomial .  the only unknowns in the final equations
developed are the coefficients of this polynomial, so that the
work involved in applying the theory in any given case depends
entirely on the work involved in approximating a given surfacetemperature
distribution by a polynomial .
  an example is worked out in detail which illustrates some of the
principal effects of variable surface temperature .  it is shown
that both positively infinite and negatively infinite heat-transfer
coefficients can occur .  the anomaly of infinite and negative
heat-transfer coefficients is discussed and attributed to the customary
definition of the heat-transfer coefficient, which is shown
to be fundamentally inappropriate for flows with variable surface
temperature .  in the particular example considered, a conventional
method for calculating the net heat transferred yields completely
incorrect results .  a brief qualitative discussion of the
possible effects of the heat transfer on flow separation is given .
in order to facilitate the use of the results, all of the principal
equations developed are collected and summarized in the section
entitled /practical use of results ./
</TEXT>
</DOC>