  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.
