An O(hN) interface model of a three-dimensional curved interphase in conduction phenomena

A thin isotropic three-dimensional curved interphase of thickness h between two isotropic media is considered in the setting of thermal conduction. This interphase is modelled by a surface between the two neighbouring media, and appropriate interface conditions on it are derived for the temperature and normal heat flux fields. The derivation makes use of Taylor expansions for the fields and is correct to O(h(N)), where h denotes the thickness of the interphase. The jumps for the temperature and normal heat flux in the interface model are given in terms of a. hierarchy of surface differential forms, which depend on the conductivities of the interphase and surrounding media, and involve surface derivatives of the temperature and normal heat flux along the interface. The analysis is directly transferable to the, analogous physical phenomena of electrical conduction, dielectrics, magnetism; diffusion, flow in porous media and anti-plane elasticity.