### Abstract

We consider the problem of exactly determining the effective thermal conductivity, σ^{eff}, of a composite material consisting of periodic or random arrays of spheres which possess superconducting interfaces. This requires the solution of the local temperature field in which there is a jump in the normal component of the heat flux across the sphere-matrix interface. The strength of this interface is characterized by a dimensionless parameter (7-40 such that C -0 corresponds to the usual perfect interface case. An approximate formula for the effective conductivity, creff, compares favourably with our results for a wide range of sphere volume fractions, phase conductivity ratios, and values of the interfacial strength C.

Original language | English (US) |
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Pages (from-to) | 1331-1344 |

Number of pages | 14 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 453 |

Issue number | 1961 |

DOIs | |

State | Published - Jan 1 1997 |

### All Science Journal Classification (ASJC) codes

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