<DOC>
<DOCNO>
395
</DOCNO>
<TITLE>
new methods in heat flow analysis with application
to flight structures .
</TITLE>
<AUTHOR>
biot,m.a.
</AUTHOR>
<BIBLIO>
j. ae. scs. 24, 1957.
</BIBLIO>
<TEXT>
  new methods are presented for the analysis of transient heat
flow in complex structures, leading to drastic simplifications in
the calculation and the possibility of including nonlinear and surface
effects .  these methods are in part a direct application of
some general variational principles developed earlier for linear
thermodynamics .  they are further developed in the particular
case of purely thermal problems to include surface and
boundary-layer heat transfer, nonlinear systems with temperature-dependent
parameters, and radiation .  the concepts of
thermal potential, dissipation function, and generalized thermal
force are introduced, leading to ordinary differential equations
of the lagrangian type for the thermal flow field .  because of the
particular nature of heat flow phenomena, compared with dynamics,
suitable procedures must be developed in order to formulate
each problem in the simplest way .  this is done by treating a
number of examples .  the concepts of penetration depth and
transit time are introduced and discussed in connection with onedimensional
flow .  application of the general method to the
heating of a slab, with temperature-dependent heat capacity,
shows a substantial difference between the heating and cooling
processes .  an example of heat flow analysis of a supersonic wing
structure by the present method is also given and requires only
extremely simple calculations .  the results are found to be in
good agreement with those obtained by the classical and much
more elaborate procedures .
</TEXT>
</DOC>
