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 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 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].
Original language | English |
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Pages (from-to) | 24-46 |
Number of pages | 23 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 73 |
Issue number | 1 |
DOIs | |
Publication status | Published - 02 Jan 2013 |
Keywords
- Effective conductivity
- Nonideal contact conditions
- Periodic composite
- Real analytic continuation
- Singularly perturbed domain
- Transmission problem