We analyze thermal transport in three-dimensional (3D) nano-composites composed of carbon nanotube (CNT) dispersions to investigate percolation effects on the effective thermal conductivity of these composites. Thermal transport simulations for the randomly distributed nanotubes inside the host substrate are based on the diffusive Fourier conduction theory. The numerical model incorporates the effect of substrate-CNT conductivity ratio and the interfacial resistance due to tube-tube and tube-substrate contact, which are the most critical parameters governing thermal transport properties. Numerical predictions of effective thermal conductivity are in excellent agreement with the linear response theory and effective medium approximation (EMA) when assumptions of theory are incorporated in the model. The trends for the variation of effective thermal conductivity with increasing nanotube density are in broad agreement with previous experimental observations. Our numerical results also show that the onset of thermal percolation is gradual and largely dependent on the tube-to-substrate conductivity ratio and interfacial resistance at tube-tube and tube-substrate contact.
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