Heat conduction in composite media involving imperfect contact and perfectly conductive inclusions

We study the thermal properties of a composite material made up of a medium hosting an $eps$-periodic array of perfect thermal conductors. The thermal potentials of the two phases are coupled across the interface through a non-standard imperfect contact transmission condition, involving the external thermal flux and a proportionality coefficient $conteps^alpha$, where $alphainR$ is a scaling parameter and $cont>0$ accounts for the imperfect contact. We perform the homogenization for all the scalings $alphainR$ and we compare the resulting models with the perfect contact transmission case addressed in [Amar:Andreucci:Gianni:Timofte:2019B] and [Amar:Andreucci:Gianni:Timofte:2019A], letting $cont o 0$, where this is meaningful