Heat Conduction through an Inhomogeneous Suspension

The results of Jeffrey (1973) for the calculation of the mean conductivity of a homogeneous suspension of spherical particles to order c² are extended to the case of inhomogeneous suspensions for which the particle probability varies over the length scale of the particle. The averaged-equation approach of Hinch (1977) is used to develop the general theory. Specific results are then calculated in two cases: conduction parallel and perpendicular to a sudden jump in concentration. It is found that the effect of the inhomogeneity of the medium decays proportional to the cube of the ratio of the particle radius to the distance from the inhomogeneity. Thus at distances greater than a few particle radii the homogeneous theory of Jeffrey is applicable.