We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter $epsilon$. We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For $epsilon$ small, we prove that the effective conductivity can be represented as a convergent power series in $epsilon$ and we determine the coefficients in terms of the solutions of explicit systems of integral equations.

We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter epsilon. We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For epsilon small, we prove that the effective conductivity can be represented as a convergent power series in epsilon and we determine the coefficients in terms of the solutions of explicit systems of integral equations.

Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface

Musolino, Paolo
;
2019

Abstract

We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter $epsilon$. We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For $epsilon$ small, we prove that the effective conductivity can be represented as a convergent power series in $epsilon$ and we determine the coefficients in terms of the solutions of explicit systems of integral equations.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10278/3723496
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