Heat transfer models for two-component media with interfacial jump

Abstract

The paper deals with the asymptotic behaviour of the heat transfer in a bounded domain having an -periodic structure formed by two interwoven components separated by an interface on which the heat flux is continuous and the temperature subjects to a first-order jump condition. We study the cases when the orders of magnitude with respect to of the ratio between the two conductivities and of the jump transmission coefficient are, respectively, and , with and . We derive the macroscopic laws and the effective coefficients obtained by the two-scale convergence technique of the homogenization theory.

Keywords:

• Homogenization
• heat conduction
• first-order jump interface
• two-scale convergence

AMS Subject Classifications:

• 35B27
• 80M40
• 76M50

Acknowledgements

This work has been accomplished during the visit of D. Poliševski at the I.R.M.A.R.’s Department of Mechanics (University of Rennes 1), whose support is gratefully acknowledged.

Notes

No potential conflict of interest was reported by the authors.