The effective thermal conductivity of a suspension (Q1083334)

The effective thermal conductivity of an inhomogeneous suspension is considered for the case of low and moderate volume densities of randomly distributed spherical particles. A mathematical apparatus of convolutions of the \(\Lambda\)-functions is developed enabling closed formulas to be derived for the dipole moment of a particle in the system. An exact expression for the dipole moment averaged over the ensemble that is accurate to terms of the order of the square of the particle density is given for a spatially homogeneous distribution of particles. The effective thermal conductivity of the suspension is calculated to the same approximation. It is shown that when the region occupied by the spherical particles represents an ellipsoid of revolution and the temperature gradient away from this region tends to a given constant value, the effective thermal conductivity becomes independent of the ratio of the ellipsoid semiaxes, i.e. independent of the form of the region occupied by the system.