A reciprocal theorem in two-dimensional heat transfer and its implications

Reciprocity theorems governing the effective conductivity (thermal or electrical, or permittivity, permeability, diffusion, etc.) of heterogeneous media were first proposed over 25 years ago and since then have been generalized and more rigorously proven. Such theorems were proposed and proved using as the point of departure the view that the results are to be applied to heterogeneous media. The present paper presents reciprocity theorems applicable to heterogeneous bodies, which can then be easily specialized to the cases for which the properties in the large can be consider to be those of a homogeneous medium, enabling the definition of an effective property. The present approach, simplifies the proofs, adds physical insight, and generalizes the application of such results.