An exact mathematical formulation and associated parallel computational scheme is developed by use of regular harmonics and the addition theorem for the harmonics to calculate the effective thermal conductivity of discretely inhomogeneous media consisting of spherical particles embedded in a continuous matrix. Exact calculations of the temperature field and heat transfer (with high harmonics orders of sphere interactions) are performed in various particulate configurations in which the number of particles is sufficiently large to represent a continuous inhomogeneous medium. Effective medium principles are applied to determine the effective conductivity of the medium. Reported experimental results in the literature are compared with the results from our analytical formulation.

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