<DOC>
<DOCNO>
300
</DOCNO>
<TITLE>
on a particular class of similar solutions of the equations
of motion and energy of a viscous fluid .
</TITLE>
<AUTHOR>
reeves,b.l. and kippenhan,c.j.
</AUTHOR>
<BIBLIO>
j. ae. scs. 29, 1962.
</BIBLIO>
<TEXT>
  by introducing the similarity concept to the two-dimensional,
incompressible navier-stokes equations and energy equation, a
particular class of solutions is found .  two general types of flows
are considered ..  (1) laminar free convection--i.e., flows which
take place due to a body force--and (2) laminar forced convection
.
  for free convection on vertical plates, similar solutions are
obtained for two different power-law surface temperature variations,
and it is shown that one of these solutions constitutes a
new type of boundary problem .  results of numerical integrations
of the equations are compared with solutions of the similar
boundary-layer equations for free convection, and it is demonstrated
that a range of surface temperature variations exists for
which the boundary layer equations are no longer valid .
  for forced convection, it is shown that the use of similarity
transformations provides an alternate method of deriving the
ordinary differential equations for some well-known solutions,
such as couette and stagnation point flows .  solutions are obtained
for radial converging or diverging flows between plane
surfaces when the temperatures of the surfaces vary as arbitrary
powers of the distance from the orgin .  results of numerical
integrations of the ordinary differential equations are presented
for prandtl numbers of 0.01 and 1.0 and for linear surface temperature
variations .  some rather surprising results are obtained
for diverging flows when separation occurs and some revealing
comparisons with results from boundary-layer theory are made .
</TEXT>
</DOC>
