BOUNDS ON THE EFFECTIVE THERMAL-CONDUCTIVITY OF A DISPERSION OF FULLY PENETRABLE SPHERES

The author evaluates upper and lower bounds on the effective thermal conductivity K//e of a model of two-phase composite materials in which one of the phases consists of inclusions (or voids), of conductivity K//2 and volume fraction phi //2, dispersed throughout a matrix phase of conductivity K//1 and volume fraction phi //1. This problem is mathematically equivalent to finding the effective electrical conductivity, dielectric constant, or magnetic permeability of the composite medium, or the diffusion coefficient associated with flow past the fixed inclusions.