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June  2018, 23(4): 1739-1756. doi: 10.3934/dcdsb.2018078

## Laplace-Beltrami operator for the heat conduction in polymer coating of electronic devices

 1 Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy 2 Dipartimento di Matematica ed Informatica, Università di Firenze, Via Santa Marta 3, 50139 Firenze, Italy

* Corresponding author

Received  June 2016 Revised  July 2017 Published  March 2018

In this paper we study a model for the heat conduction in a composite having a microscopic structure arranged in a periodic array. We obtain the macroscopic behaviour of the material and specifically the overall conductivity via an homogenization procedure, providing the equation satisfied by the effective temperature.

Citation: Micol Amar, Roberto Gianni. Laplace-Beltrami operator for the heat conduction in polymer coating of electronic devices. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1739-1756. doi: 10.3934/dcdsb.2018078
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##### References:
Left: the periodic cell $Y$. ${E_{{\rm{int}}}}$ is the shaded region and ${E_{{\rm{out}}}}$ is the white region. Right: the region
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