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.
Autori: | |
Data di pubblicazione: | 2019 |
Titolo: | Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface |
Rivista: | ASYMPTOTIC ANALYSIS |
Digital Object Identifier (DOI): | http://dx.doi.org/10.3233/ASY-181495 |
Volume: | 111 |
Appare nelle tipologie: | 2.1 Articolo su rivista |
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