Finite element analysis of a transient 2-dimensional heat conduction problem

Abstract

The analysis of a transient 2-Dimensional heat conduction problem by the Finite Element Method is hereby presented. The solution approach was that of partial discretisation : 4-node isoparametric elements were used in the discretisation of the problem domain in the spatial coordinate, while linear temporal elements are used in the discretisation of the time domain. The Galerkin's Weighted Residual Method was used in the development of the system equation in the space domain, and their transformation into the time domain. The resulting system of equation, which is a two-point recursive relation,was solved using the Gauss - Cholesky Method. The developed algorithm was used on a linear, transient 2-Dimensional problem, and the results obtained were an improvement on those obtained by Bruch, J. C . and Zyvoloski , G.