Model for the effective thermal conductivity of carbon nanotube composites

We present a novel model of the effective thermal conductivity for carbon nanotube composites by incorporating the interface thermal resistance with an average polarization theory. The dependence of the effective thermal conductivity on nanotube length, diameter, concentration, and interface thermal resistance has been taken care of simultaneously in our treatment. The model predicts that the large length of the carbon nanotubes embedded plays a key role in the thermal conductivity enhancement, while the large interface thermal resistance across the nanotube-matrix interface causes a significant degradation. Interestingly, the model predicts that the nanotube diameter has a very small effect on the thermal conductivity enhancement of the nanotube composites. In addition, the model predicts that the thermal conductivity enhancement of nanotube composites increases rapidly with decreasing the thermal conductivity of the matrix and increases with increasing the thermal conductivity of the carbon nanotube. Predictions from the novel model are in excellent agreement with the experimentally observed values of the effective thermal conductivity of carbon nanotube nanofluids which the classical models have not been able to explain.