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 homo- geneous 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 ε. Under suitable assumptions, we show that the effective conductivity can be continued real analytically in the parameter ε around the degenerate value ε = 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].

A Singularly Perturbed Nonideal Transmission Problem and Application to the Effective Conductivity of a Periodic Composite

Musolino P
2013

Abstract

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 homo- geneous 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 ε. Under suitable assumptions, we show that the effective conductivity can be continued real analytically in the parameter ε around the degenerate value ε = 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].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10278/3723633
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