<DOC>
<DOCNO>
542
</DOCNO>
<TITLE>
biot's variational principle in heat conduction .
</TITLE>
<AUTHOR>
lardner,t.j.
</AUTHOR>
<BIBLIO>
a.i.a.a. j. 1963, 196.
</BIBLIO>
<TEXT>
  biot's variational principle is applied to a number of different
one-dimensional heat conduction problems .  these problems
show the applicability of the variational principle to problems
involving prescribed heat flux boundary conditions and to those
with temperature-dependent material properties .
  a method is introduced for including boundary conditions
when these are expressed as prescribed heat fluxes .  the idea
behind this is overall energy balance within the body, which is a
constraint condition to be satisfied by the time histories of the
generalized coordinates .
  the variational principle is then applied to the well-known
problem of constant surface heat flux in order to present the
technique and provide a basis for the remaining sections .  the
equivalence of the result obtained in applying the variational
principle for a prescribed surface temperature history to that obtained
for a prescribed heat flux is also pointed out .  radiation
cooling due to fourth power radiation from semi-infinite solids
and finite slabs together with radiation according to newton's
law of cooling is then treated .  finally, the introduction of temperature-dependent
material properties is discussed and the determination
of the temperature distribution in a semi-infinite
solid with variable properties is investigated .
</TEXT>
</DOC>
