Systematic study of thermal properties of CNT composites by the fast multipole hybrid boundary node method

Carbon nanotubes (CNTs) are predicted to possess superior heat conductivity, which makes the CNTs promising in development of fundamentally new composite material. With the current advancement in nanotechnology, it is possible to design materials with desired properties for specific applications. On the other hand, the overall properties of CNT composites are usually evaluated using a representative volume element (RVE) with a number of CNTs embedded. For realistic modeling, an RVE including a large number of CNTs, for example, tens or hundreds, is necessary. However, analysis of such an RVE using standard numerical methods faces two severe difficulties: discretization of the geometry into elements and the very large computational scale. In this paper, the first difficulty is alleviated by developing the hybrid boundary node method (HdBNM), which is a boundary-type meshless method. To overcome the second difficulty, a simplified mathematical model for thermal analysis of CNT analysis is first proposed, by which the size of the linear system can be reduced by nearly half. Then, the HdBNM is combined with the Fast Multipole Method (FMM) based on the model to further reduce the computational scale. A variety of RVEs containing different numbers of CNTs, from small to large scales, have been studied in an attempt to investigate the influence of CNT length, distribution, orientation and volume fraction on the overall thermal properties of the composites. Insights have been gained into the thermal behavior of the CNT composite material.