Homogenization of a heat conduction problem involving tangential operators
We present a model for the heat conduction in a composite having a microscopic
structure arranged in a periodic array made by two phases separated by a
thermally active membrane. The thermal behavior of the membrane is described by a
parabolic equation involving the Laplace–Beltrami operator. Such interface equation
furnishes the contact temperature of the two diffusive phases in terms of the jump of
the heat fluxes at the interface. We obtain the macroscopic behavior of the material
via an homogenization procedure based on the unfolding technique, providing the
equation satisfied by the effective temperature. We are also able to prove an error
estimate on the rate of convergence of the sequence of approximating solutions to the
homogenized solution.
These results are part of a joint research with R. Gianni.