Mapped transient infinite elements for heat transfer problems in infinite media

Abstract

Based on the fundamental solutions of transient heat transfer problems in infinite media, a mapped transient infinite element is presented and the so-called heat transfer function of the element has been derived in this paper. In order to express the property matrices of the present mapped transient infinite element, a mapping technique, in which the infinite element in a global coordinate system is mapped into a strip element of finite width and infinite length in a local coordinate system, has also been developed. Using the variable substitution technique, the general integral involved in the evaluation of the property matrices of the element has been changed into a standard one for which the conventional Gauss-Legendre integration scheme can be employed. Since the heat transfer function of the present mapped transient infinite element is dependent on both space and time variables, the mechanism of heat transfer problems in infinite media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest in the analysis. Finally, the accuracy and efficiency of the present mapped transient infinite element have been verified through the analysis of a 1D heat conduction problem in a semi-infinite medium and a 2D transient heat transfer problem in a full plane.