Thermal waves in composite membrane with circular inclusions in hexagonal lattice structures
Date
2021Author
Andrianov, I.V.
Awrejcewicz, J.
Starushenko, G.A.
Kvitka, S.A.
Metadata
Show full item recordAbstract
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.