A singularity perturbed nonideal transmission problem and application to the effective conductivity of a periodic composite

We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. The diameter of each inclusion is assumed to be prop...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 73; no. 1; pp. 24 - 46
Main Authors Dalla Riva, Matteo, Musolino, Paolo
Format Journal Article
LanguageEnglish
Published Society for Industrial and Applied Mathematics 2013
Subjects
Mathematics
Numerical Analysis
periodic composite
real analytic continuation
singularly perturbed domain
transmission problem
nonideal contact conditions
effective conductivity
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Summary:We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. The diameter of each inclusion is assumed to be proportional to a positive real parameter $\epsilon$ . Under suitable assumptions, we show that the effective conductivity can be continued real analytically in the parameter around the degenerate value $\epsilon= 0$, in correspondence of which the inclusions collapse to points. Part of the results presented here have been announced in [M. Dalla Riva and P. Musolino, AIP Conf. Proc. 1493, American Institute of Physics, Melville, NY, 2012, pp. 264-268].
ISSN:0036-1399
DOI:10.1137/120886637