An interface model of a graded three-dimensional anisotropic curved interphase

A three-dimensional, generally curved, constant thickness interphase whose properties vary across its thickness is considered. This graded interphase is modelled by an interface that is located at its mid-surface and which comes now into direct contact with the media that were adjacent to it. The derivation is carried out in the setting of heat conduction, and appropriate jump conditions for the temperature and normal heat flux across the interface are derived, which characterize the interface model. The inhomogeneity of the interphase becomes a major motivation for its replacement by an interface. This representation is expected to simplify significantly the solution of boundary-value problems that involve thin inhomogeneous regions separating two media. Analytical solutions that are not available for a large class of graded interphases can become readily accessible with the derived interface model.