Application of integral equations to simulate local fields in carbon nanotube reinforced composites

TL;DR

This paper develops a boundary integral equation method to simulate steady heat conduction in a composite material reinforced with randomly distributed carbon nanotubes, providing a new computational approach for analyzing thermal behavior.

Contribution

It introduces a boundary integral equation approach to model heat transfer in CNT-reinforced composites with complex boundary conditions.

Findings

Effective simulation of heat conduction with various CNT distributions

Demonstrated accuracy through numerical examples

Applicable to composites with different geometries

Abstract

We consider the steady heat conduction problem within a thermal isotropic and homogeneous square ring composite reinforced by non-overlapping and randomly distributed carbon nanotubes (CNTs). We treat the CNTs as rigid line inclusions and assume their temperature distribution to be fixed to an undetermined constant value along each line. We suppose also that the temperature distribution is known on the outer boundary and that there is no heat flux through the inner square. The equations for the temperature distribution are governed by the two-dimensional Laplace equation with mixed Dirichlet- Neumann boundary conditions. This boundary value problem is solved using a boundary integral equation method. We demonstrate the performance of our approach through four numerical examples with small and large numbers of CNTs and different side length of the inner square.