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 $\cont\eps^\alpha$, where $\alpha\in\R$ is a scaling parameter and $\cont>0$ accounts for the imperfect contact. We perform the homogenization for all the scalings $\alpha\in\R$ and we compare the resulting models with the perfect contact transmission case addressed in \cite{Amar:Andreucci:Gianni:Timofte:2019B,Amar:Andreucci:Gianni:Timofte:2019A}, letting $\cont\to 0$, where this is meaningful.

Heat conduction in composite media involving imperfect contact and perfectly conductive inclusions / Amar, M.; Andreucci, D.; Timofte, C.. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - 45:(2022), pp. 11355-11379.

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

M. Amar
;
D. Andreucci;
2022

Abstract

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 $\cont\eps^\alpha$, where $\alpha\in\R$ is a scaling parameter and $\cont>0$ accounts for the imperfect contact. We perform the homogenization for all the scalings $\alpha\in\R$ and we compare the resulting models with the perfect contact transmission case addressed in \cite{Amar:Andreucci:Gianni:Timofte:2019B,Amar:Andreucci:Gianni:Timofte:2019A}, letting $\cont\to 0$, where this is meaningful.
2022
Homogenization, time-periodic unfolding, total flux boundary conditions, imperfect contact conditions, parabolic problems
01 Pubblicazione su rivista::01a Articolo in rivista
Heat conduction in composite media involving imperfect contact and perfectly conductive inclusions / Amar, M.; Andreucci, D.; Timofte, C.. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - 45:(2022), pp. 11355-11379.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1573998
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