Evaluation of effective thermal conductivity of CNT‐based nano‐composites by element free Galerkin method

Abstract

Purpose

The purpose of this paper is to evaluate the thermal properties of carbon nanotube composites via meshless element free Galerkin (EFG) method.

Design/methodology/approach

The EFG method is based on moving least square approximation, which is constructed by three components: a weight function associated with each node, a basis function and a set of non‐constant coefficients. In principle, EFG method is almost identical to finite element method. The EFG method does not require elements for the interpolation (or approximation) of field variable, but only requires a set of nodes for the construction of approximation function.

Findings

The equivalent thermal conductivity of the composite has been calculated, and plotted against nanotube length, nanotube radius, RVE length, and RVE radius. Temperature distribution has been obtained and plotted with RVE length. An approximate numerical formula is proposed to calculate the equivalent thermal conductivity of CNT‐composites. Present computations show that the addition of 6.2 per cent (by volume) of CNT in polymer matrix increases the thermal conductivity of the composite by 42 per cent, whereas 16.1 per cent of CNT addition increases the thermal conductivity of the composite by 352 per cent.

Research limitations/implications

An ideal model, i.e. representative volume element containing single CNT has been taken to evaluate the thermal properties of CNT‐composites.

Practical implications

A simplified approach based on EFG method has been developed to evaluate the overall thermal conductivity of the CNT‐composites.

Originality/value

Continuum mechanics‐based mesh‐free EFG method has been successfully implemented for the thermal analysis of CNT‐composites.

Citation

Singh, I.V., Tanaka, M., Zhang, J. and Endo, M. (2007), "Evaluation of effective thermal conductivity of CNT‐based nano‐composites by element free Galerkin method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 No. 8, pp. 757-769. https://doi.org/10.1108/09615530710825756