An integral method theorem for heat conduction

Abstract

A MATHEMATICAL solution existence and uniqueness theorem has been developed for applying the classical Goodman heat balance integral (HBI) method to a class of one-dimensional heat conduction problems. This Synoptic presents the theorem and points out its significance and uses. The theorem applies to the class of problems in which a heat flux load is imposed on a semi-infinite solid with temperaturedependent properties. It includes new mathematical conditions which test whether the HBI method can rigorously handle nonlinearities in the heat loads and material properties of a particular problem. Examples show that violation of the new conditions can lead to mathematical/numerical solutions which become unexpectedly singular under the HBI method, even though the original problem under study may be physically sound.