An effective unit cell approach to compute the thermal conductivity of composites with cylindrical particles

This paper introduces a novel method to model the effective thermal conductivity of cylindrical-particle-laden composite materials. This modeling methodology is a combination of the effective medium theory and the finite differences method. Typically the curvature effects of cylindrical or spherical particles are ignored while calculating the thermal conductivity of composites containing such particles through numerical techniques. These particles are modeled as cuboids or cubes. Numerical modeling of circular/spherical geometries as cubes or cuboids will lead to wrong conclusions due to two reasons: (i) It does not capture the effect of curvature on heat flow, i.e., constriction of heat flux lines near the particles due to shape, (ii) It assigns higher effective conductivity to the particles as the cubes or the cuboids have larger volume and surface area. An alternative approach to mesh the particles into small volumes is just about impossible as it leads to highly intensive computational algorithms to get accurate results. On the other hand, effective medium theory takes the effect of curvature into account but it 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.