The “equivalent inclusion” method, originally devised by Eshelby for solving the disturbance of a uniform elastic field due to an ellipsoidal inhomogeneity in an otherwise homogeneous elastic medium, is used to estimate the effective thermal conductivity of a multiphase system characterized by a random dispersion of N different sets of arbitrarily oriented ellipsoidal particles in an isotropic matrix. The effect of particle interaction is taken into account with the “mean-field approximation” which has been established in the micromechanics-of-composites area. Simple expressions are derived for the binary systems containing perfectly aligned or randomly oriented fibers or platelets as well as spherical particles. The significance of the present approach is demonstrated in comparison of these expressions with the bounds given by Hashin and Shtrikman. Other existing results including those due to Maxwell and Landauer are also discussed.
