6533b872fe1ef96bd12d2e64
RESEARCH PRODUCT
Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface
Roman PukhtaievychPaolo MusolinoMatteo Dalla RivaMatteo Dalla Rivasubject
Materials scienceasymptotic expansionGeneral MathematicsThermal resistanceInterface (computing)Composite numberperiodic dilute compositeConductivityEffective conductivitySettore MAT/05 - Analisi MatematicaPhase (matter)Mathematics (all)non-ideal contact conditionComposite materialSeries expansionsingularly perturbed domainasymptotic expansion; Effective conductivity; non-ideal contact condition; periodic dilute composite; singularly perturbed domain; Mathematics (all)description
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 ?. 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 ? small, we prove that the effective conductivity can be represented as a convergent power series in ? and we determine the coefficients in terms of the solutions of explicit systems of integral equations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-02-13 |