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 steady-state, linear heat conduction is detailed. The procedures are expanded to steady-state nonlinear, unsteady state linear and unsteady-state heat conduction problems. The variational method is asserted to be equivalent to the Galerkin method unless no variational principle exists. Finally, quasi-variational 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