Neutral inhomogeneities in conduction phenomena

A neutral inhomogeneity in heat conduction is defined as a foreign body whi ch can be introduced in a host solid without disturbing the temperature hel d in it. The existence of neutral inhomogeneities in conduction phenomena i s studied in the present paper. Both the inhomogeneity and the host body ar e assumed to be isotropic, with the inhomogeneity being either less or more conducting than the surrounding body. The property of neutrality is define d in this work with respect to an applied constant temperature gradient in the host solid. It is achieved by introducing a non-ideal interface between the two media across which the continuity requirement of either the temper ature field or the normal component of the heat flux is relaxed. These inte rfaces are called 'non-ideal interfaces' and represent a thin interphase of low or high conductivity; they are characterized in terms of some scalar i nterface parameters which usually vary along the interface in order to ensu re neutrality. The conditions to be satisfied by the field variables at a n on-ideal interface with a variable interface parameter are first derived, a nd closed form solutions are presented for the interface parameters at neut ral inhomogeneities of various shapes. In two-dimensional problems, duality relations are established for composite media with non-ideal interfaces an d variable interface parameters. These are implemented in establishing gene ral criteria for neutrality. The terminology of heat conduction is used thr oughout in the paper but all the results can be directly transferred to the domains of electrical conduction, dielectric behavior or magnetic permeabi lity. (C) 1999 Elsevier Science Ltd. All rights reserved.