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

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  • 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.

    Mathematics Subject Classification: Primary: 35B27; Secondary: 35Q79, 35K20.


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  • Figure 1.  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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