Neutral inhomogeneities in conduction phenomena

A neutral inhomogeneity in heat conduction is defined as a foreign body which can be introduced in a host solid without disturbing the temperature field in it. The existence of neutral inhomogeneities in conduction phenomena is studied in the present paper. Both the inhomogeneity and the host body are assumed to be isotropic, with the inhomogeneity being either less or more conducting than the surrounding body. The property of neutrality is defined 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 temperature field or the normal component of the heat flux is relaxed. These interfaces are called 'non-ideal interfaces' and represent a thin interphase of low or high conductivity; they are characterized in terms of some scalar interface parameters which usually vary along the interface in order to ensure neutrally. The conditions to be satisfied by the field variables at a non-ideal interface with a variable interface parameter are first derived, and closed form solutions are presented for the interface parameters at neutral inhomogeneities of various shapes. In two-dimensional problems, duality relations are established for composite media with non-ideal interfaces and variable interface parameters. These are implemented in establishing general criteria for neutrality. The terminology of heat conduction is used throughout in the paper but all the results can be directly transferred to the domains of electrical conduction, dielectric behavior or magnetic permeability.