Variational principles for heat transfer
Abstract
Variational principles are described with respect to applicability in heat transfer problems. Frechet derivatives determine if a given differential or integral equation has a variational principle, i.e., a real number can be assigned to each function for a given class of functions. The establishment of boundary conditions and characterization of variations for steadystate, linear heat conduction is detailed. The procedures are expanded to steadystate nonlinear, unsteady state linear and unsteadystate heat conduction problems. The variational method is asserted to be equivalent to the Galerkin method unless no variational principle exists. Finally, quasivariational and restricted variational principles are considered.
 Publication:

Numerical Properties and Methodologies in Heat Transfer
 Pub Date:
 1983
 Bibcode:
 1983npmh.book...17F
 Keywords:

 Conductive Heat Transfer;
 Variational Principles;
 Differential Equations;
 Galerkin Method;
 Laplace Transformation;
 Linearity;
 Fluid Mechanics and Heat Transfer