Library Subscription: Guest

ISSN Online: 2377-424X

ISBN Print: 0-89116-130-9

International Heat Transfer Conference 6
August, 7-11, 1978, Toronto, Canada

FINITE-ELEMENT METHOD AND A MATRIX METHOD IN TRANSIENT HEAT-CONDUCTION PROBLEMS

Get access (open in a dialog) DOI: 10.1615/IHTC6.350
pages 251-256

Abstract

The physical meanings of matrices derived from the finite-element method (FEM) for transient heat-conduction problems are discussed "by comparing the matrices with heat balance equations. In this discussion the causes for an unusual oscillatory behavior and a non-convergence of FEM solutions are clarified. Furthermore, a "Matrix Method", which has been developed on the basis of the discussion, is presented with numerical examples. In the proposed method the geometry of the object is divided into suitable elements in which nodal points and nodal domains are designated. The heat balance equations between the nodal domains are expressed in the form of matrix and calculated numerically by the similar technique to FEM. In this calculation a technique is proposed which employs the Crank-Nicholson method in a region and a forward finite difference method in the other region. The proposed Matrix Method can be generally applied to heat-conduction and diffusion problems more easily and more conveniently than FEM.