Application of the Finite-Element Method to Heat-Transfer Problems. Part II. Transient Two-Dimensional Heat Transfer with Convection and Radiation Boundary Conditions.
Technical rept. Aug 70-May 71,
ARMY WEAPONS COMMAND ROCK ISLAND ILL RESEARCH DEVELOPMENT AND ENGINEERING DIRECTORATE
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The transient two-dimensional heat-conduction analysis was prepared by a variational principle and finite-element synthesis. This provided for the use of arbitrary geometry, combination of orthotropic materials, and general boundary-conditions. The finite-element difference expression and the ordinary finite-difference formulas for the Laplacian term were derived. A particular finite-difference formula for the Laplacian term was chosen to bring the difference expressions of finite element, finite difference, and method of weighted residuals Galerkin into the same format. The stability criteria were established for all three techniques by use of the general stability, von Neumann, and Dusinberre concepts. The oscillation characteristics were derived for all three techniques. Various iteration techniques were investigated to represent nonlinear boundary-conditions radiation. Author
- Numerical Mathematics