Non-stationary heat transfer in composite membrane with circular inclusions in hexagonal lattice structures

Unsteady heat conduction in fibre composite materials is studied. 2D composite media consist of a matrix with circular inclusions in hexagonal lattice structures. Perfect contact between different materials is assumed on the boundary of the fibres. The temperature field is modelled by a heat equation. Laplace transform and asymptotic homogenization method are used. Then, the original problem for a multi-connected domain is reduced to the recurrent system of boundary value problems in simply connected domains. Employing an additional small parameter and thin layer asymptotics, the analytical solution of the local problem can be obtained. In particular, a closed-form expression for effective heat conductivity is reported. The case of Newton's cooling law is studied separately.