<DOC>
<DOCNO>
579
</DOCNO>
<TITLE>
further developments of new methods in heat flow analysis .
</TITLE>
<AUTHOR>
biot,m.a.
</AUTHOR>
<BIBLIO>
j.ae.scs.26, 1959.
</BIBLIO>
<TEXT>
  lagrangian methods in heat-flow problems and transport
phenomena were introduced by the writer in some previous work .
the present paper develops further one particular aspect of the
method,--i.e., the elimination of /ignorable coordinates ./  this
is accomplished by a special choice of generalized coordinates,
each of which is constituted by an arbitrary temperature distribution
and an /associated flow field ./  the latter is a vector
field which is derived from the corresponding scalar field by a variational
method .  the procedure is valid for a certain class of nonlinear
problems, provided we replace the temperature by the heat
content as the unknown .  it is shown that for normal coordinates
derivation of the associated flow field is immediate .  the use
of normal coordinates and their associated flow fields is illustrated
by an example .  introduction of dirac functions and
associated flow fields yields a procedure which constitutes a
generalization of the classical formulation by green's functions
and integral equations .  this is illustrated by application to onedimensional
problems of heating of a homogeneous or composite
slab and directly verified by classical methods in the appendix .
</TEXT>
</DOC>
