Effective thermal conductivity of periodic composites with highly conducting imperfect interfaces

The purpose of this work is to determine the effective conductivity of periodic composites accounting for highly conducting imperfect interfaces between the matrix and inclusions phases and to study the dependencies of the effective conductivity on the size and distribution of inhomogeneities in the matrix phase in different cases: squared, hexagonal, cubic and random inclusion distributions. The local solution of the periodic conduction problem is found in Fourier space by using the Green operators and closed-form expressions of factors depending on the size and shape of the inclusions. The numerical results of size-dependent effective thermal conductivity are finally compared with an analytical estimation obtained from the generalized self-consistent model. The method elaborated and results provided by the present work are directly applicable to other physically analogous transport phenomena, such as electric conduction, dielectrics, magnetism, diffusion and flow in porous media and to the mathematically identical phenomenon of anti-plane elasticity.