<DOC>
<DOCNO>
364
</DOCNO>
<TITLE>
a method for analysing the insulating properties of
the laminar compressible boundary layer .
</TITLE>
<AUTHOR>
libby,pa. and pallone,a.
</AUTHOR>
<BIBLIO>
j. ae. scs. 21, 1954.
</BIBLIO>
<TEXT>
  in some cooling problems associated with high energy flows
it may be convenient to localize strongly the cooling, as for example
by injecting a coolant through an upstream porous strip,
and to depend on the insulating properties of the boundary layer
to reduce, or to eliminate completely the need for further cooling
on the surface downstream of the highly cooled section .  this
upstream cooling technique may be of interest in connection with
optical windows in hypersonic wind tunnels, and on radomes,
wings, and bodies of high-speed aircraft and missiles .
  in this paper a method for investigating the insulating properties
of a laminar compressible boundary layer on a two-dimensional
surface with zero heat transfer is presented .  the physical
situation considered thus corresponds to the case in which the
heat transfer downstream of the strongly cooled section is completely
eliminated .  of practical concern is how the temperature
of the uncooled surface varies in the downstream direction
from its low initial value and thus how the low energy layer
established by the upstream cooling insulates the downstream
surface .
  the karman integral method extended to both the momentum
and energy partial differential equations of the boundary layer
has been used .  the station, at which cooling and or injection
ceases, corresponds to a discontinuity in boundary conditions
and thus in solutions .  at this point the flux of mass, momentum,
and energy within the boundary layer has been made continuous
by the introduction of three additional parameters in the velocity
and stagnation enthalpy profiles .  thus the velocity and stagnation
enthalpy profiles have both been taken as sixth degree
polynomials .  the resulting two integral-differential equations
are then solved for two unknown functions of the distance along
the wall .  these two functions are related to the boundary-layer
thickness and to the wall temperature .  initial conditions corresponding
to a given initial wall temperature and an initial boundary-layer
thickness are prescribed .  exact closed-form solutions
for the case of zero axial pressure gradient are obtained .  for
flows with significant pressure gradients, numerical solutions
are required in general .  several numerical examples of practical
interest are presented .
</TEXT>
</DOC>
