Transfinite element methodology for nonlinear/linear transient thermal modelling/analysis - Progress and recent advances

The 'transfinite element method' (TFEM) proposed by Tamma and Railkar (1987 and 1988) for the analysis of linear and nonlinear heat-transfer problems is described and demonstrated. The TFEM combines classical Galerkin and transform approaches with state-of-the-art FEMs to obtain a flexible hybrid modeling scheme. The fundamental principles of the TFEM and the derivation of the governing equations are reviewed, and numerical results for sample problems are presented in extensive graphs and briefly characterized. Problems analyzed include a square plate with a hole, a rectangular plate with natural and essential boundary conditions and varying thermal conductivity, the Space Shuttle thermal protection system, a bimaterial plate subjected to step temperature variations, and solidification in a semiinfinite liquid slab.