An Effective Unit Cell Approach to Compute the Thermal Conductivity of Composites With Cylindrical Particles

This paper introduces a novel method, combining effective medium theory and the finite differences method, to model the effective thermal conductivity of cylindrical-particle-laden composite materials. Typically the curvature effects of cylindrical or spherical particles are ignored while calculating the thermal conductivity of composites containing such particles through numerical techniques, such that the particles are modeled as cuboids or cubes. An alternative approach to mesh the particles into small volumes is just about impossible, as it leads to highly intensive computations to get accurate results. On the other hand, effective medium theory takes the effect of curvature into account, but cannot be used at high volume fractions because it does not take into account the effects of percolation. In this paper, a novel model is proposed where the cylindrical particles are still treated as squares (cuboids), but to capture the effect of curvature, an effective conductivity is assigned to the particles by using the effective medium approach. The authors call this the effective unit cell approach. Results from this model for different volume fractions, on average, have been found to lie within ±5% of experimental thermal conductivity data.