Numerical Model for Thermal Transport in 3-D Nanotube Composites

The effective thermal conductivity of three dimensional (3-D) nanocomposites composed of carbon nanotube (CNT) dispersions is computed using Fourier conduction theory. The random ensemble of nanotubes is generated numerically and each nanotube is discretized using a finite volume scheme. The background substrate mesh is also discretized using a finite volume scheme. We incorporate all parameters crucial for thermal transport studies, i.e. tube aspect ratio, tube density, composite sample size, substrate-CNT conductivity ratio and the interfacial resistance due to tube-tube and tube-substrate contact. Two-dimensional (thin film) nanocomposites are also simulated for comparison. Numerical predictions of effective thermal conductivity are in excellent agreement with the effective medium approximation (EMA) for both 2-D and 3-D nanocomposites at low tube densities, but depart significantly from EMA predictions when tube-tube interaction becomes significant. It is found that the effect of tube-tube contact on effective thermal conductivity is more significant for 2-D composites than 3-D composites. Hence percolation effects may play a more significant role in thermal transport in 2-D nano-composites.