Interfacial discontinuities in thermal conductions

Interfacial discontinuities are examined in the context of thermal conductions for generally anisotropic solids. The analysis relies on decomposing a first-rank tensor at an interface into two orthogonal parts, one parallel and one perpendicular to the surface. It is shown that the tangential part of the intensity tensor and the perpendicular part of the heat flux tensor on one side uniquely determine the interfacial quantities on the other side. The relations are linked by two second-rank interfacial operators. Some basic properties of the operators are found. Closely related subjects of the inclusion and inhomogeneity problems are reexamined. Exact results are given for the matrix interfacial quantities under uniform transformation fields in the inhomogeneity and under uniform boundary conditions at infinity.