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

Abstract

We consider the steady heat conduction problem within a thermal isotropic and homogeneous square ring composite reinforced by nonoverlapping 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 lengths of the inner square.