Thermal waves in composite membrane with circular inclusions in hexagonal lattice structures

Abstract

Non-stationary heat conduction in the fibre composite materials is studied. 2D сomposite media consists of matrix with circular inclusions in hexagonal lattice structures. The perfect contact between different materials is assumed on the boundary of the fibres. The local temperature field in the unit cell is modeled by the heat equation. Time variable excludes from the original boundary value problem using of Laplace transform. Asymptotic homogenization method allows to reduce original problem for multiply-connected domain to the sequence of boundary value problems in simply-connected domains. Composite material is supposed densely-packed with a high-contrast. In this case, the local boundary value problem includes a small parameter equal to the ratio of the distance between the inclusions to the characteristic cell size. Using of additional small parameter and thin layer asymptotics allows to solve local problem analytically. Closed form expression for effective heat conductivity is obtained.