On the effective thermal conductivity of dilute suspensions containing highly conducting slender inclusions

Abstract
In this paper we consider the effective thermal conductivity of dilute suspensions containing highly conducting slender inclusions aligned in one direction. By extending the analysis of Rocha & Acrivos (1973b), we solve the temperature field for two aligned particles in an infinite medium by using slender body theory and we calculate the conductivity of a suspension with randomly distributed particles exactly toO(Ф2), where Ф is the volume fraction of the inclusions. The results show that, under these conditions, the coefficient of theO(Ф2) term is significantly lower than that found experimentally by Rocha & Acrivos (1974). This discrepancy is attributed to the fact that, in the experiments of Rocha & Acrivos, the presence of the external magnetic field used to align the particles also induced a non-random particle distribution. A theory is therefore developed to take into account the clustering of the particles during the process of alignment which is found to give values of the coefficient of theO(Ф2) term in good agreement with those obtained experimentally. These findings illustrate the importance of the particle distribution in determining the effective transport coefficient of the composite materials when the interactions between particles are significant.

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