Bulk thermal conductivity of composites with spherical inclusions

The problem of determining the bulk or effective thermal conductivity of a two-phase composite material whose unit cells contain N(N>1) spherical particles of thermal conductivity αk suspended in a medium of thermal conductivity k has been treated by extending an earlier analysis of McPhedran and Milton [Appl. Phys. A 26, 207 (1981)] who considered the case N=1. The technique is applied to computer-generated two-phase composites with N=16 whose radial distribution functions approximately satisfy the Percus-Yevick equation. The results, which are presented for a wide range of α and φ (the volume fraction of the spheres), are shown to be in good agreement with the experimental values of conductivity of fluidized beds reported by Turner [Chem. Eng. Sci. 31, 487 (1976)].