Effective thermal conductivity of a thin, randomly oriented composite material

The thermal conductivity of a randomly oriented composite material is model ed using a probabilistic approach in order to determine if a size effect ex ists for the thermal conductivity at small composite thicknesses. The numer ical scheme employs a random number generator to position the filler elemen ts, which have a relatively high thermal conductivity, within a matrix havi ng 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 i s independent of thickness. The threshold thickness increases for increasin g filler fraction and increasing k(f)/k(m), the ratio between the filler an d matrix thermal conductivities.