Effective conductivity of periodic arrays of spheres with interfacial resistance

H. Cheng; Salvatore Torquato

doi:10.1098/rspa.1997.0009

Effective conductivity of periodic arrays of spheres with interfacial resistance

H. Cheng, Salvatore Torquato

Research output: Contribution to journal › Article

104 Scopus citations

Abstract

We consider the problem of analytically determining the effective thermal conductivity of a composite material consisting of periodic arrays of spheres with interfacial resistance. We applied Rayleigh's method which has been used extensively for such calculations in the perfect interface case, i.e. no jump in the temperature across the interface. Results are presented for simple, body-centred and face-centred cubic arrays, and each for a wide range of volume fractions. Our calculations were based on very accurate lattice sums in all three lattice cases and temperature fields were resolved to very high multipole moments, including all azimuthal terms. In the case of zero interfacial strength, our formulation recovers all previously reported benchmark results.

Original language	English (US)
Pages (from-to)	145-161
Number of pages	17
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	453
Issue number	1956
DOIs	https://doi.org/10.1098/rspa.1997.0009
State	Published - Jan 1 1997

All Science Journal Classification (ASJC) codes

Mathematics(all)
Engineering(all)
Physics and Astronomy(all)

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10.1098/rspa.1997.0009

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Cheng, H., & Torquato, S. (1997). Effective conductivity of periodic arrays of spheres with interfacial resistance. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 453(1956), 145-161. https://doi.org/10.1098/rspa.1997.0009

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