Effective thermal conductivity of a thin, randomly oriented composite material

The thermal conductivity of a randomly oriented composite material is modeled using a probabilistic approach in order to determine if a size effect exists for the thermal conductivity at small composite thicknesses. The numerical scheme employs a random number generator to position the filler elements, which have a relatively high thermal conductivity, within a matrix having a relatively low thermal conductivity. The results indicate that, below some threshold thickness, the composite thermal conductivity increases with decreasing thickness, while above the threshold the thermal conductivity is independent of thickness. The threshold thickness increases for increasing filler fraction and increasing k/km, the ratio between the filler and matrix thermal conductivities.