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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on May 15, 2009
The Quarterly Journal of Mechanics and Applied Mathematics 2009 62(3):235-262; doi:10.1093/qjmam/hbp010
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© The author 2009. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Effective conductivity of unidirectional cylinders with interfacial resistance

P. Drygas{dagger}

( Department of Mathematics, University of Rzeszow, ul. Rejtana 16a, 35-959 Rzeszow, Poland )

V. Mityushev{ddagger}

( Department of Mathematics, Pedagogical University, ul. Podchorazych 2, 30-084 Krakow, Poland )

{dagger} Corresponding author. <drygaspi{at}univ.rzeszow.pl>

{ddagger} <vmityu{at}yahoo.com>

Received 29 June 2008. Revise 26 November 2008. Revise 1 March 2009. Accepted 30 March 2009.


  Abstract

We investigate the effective conductivity tensor for unidirectionally arbitrary distributed cylinders when the contact between the components is not perfect. The corresponding boundary value problem is reduced to a system of functional-differential equations, which is solved using symbolic computations. The major advantage of the method presented here is to provide approximate analytical expressions for the local thermal flux and for the effective conductivity in a systematic manner in terms of the concentration of inclusions, of the contrast parameter, of the thermal resistance and of the location of the parallel fibres.


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