Boundary integral equation formulations for steady state thermal conduction and their applications in heterogeneities

This paper presents some boundary integral equations of steady state thermal conduction for homogenization of composites based on the generalized self-consistent scheme (GSCS). The proposed formulations only contain the temperature of the interfaces which are easily numerically implemented. A formulation for calculating the heat energy only containing interface integration is also used to determinate the effective thermal conductivity of the composite. The comparison between the results obtained by the present method and the existing counterparts are carried out and the good agreement can be observed. The present method developed here is applicable to various cases of ellipsoidal, spherical and other shapes׳ inhomogeneities.