### Abstract

© 2015 Elsevier B.V. All rights reserved. Non-local effects in generalized heat-transport equations provide a mesoscopic approach to phonon hydrodynamics. In contrast to usual phonon hydrodynamics with non-slip heat flow, we consider, in analogy to rarefied gas dynamics, a slip heat flow along the walls. This way the effective thermal conductivity behaves as Kn-1 instead of as Kn-2, which is the behavior in usual phonon hydrodynamics, Kn being the Knudsen number, i.e., the ratio between the mean-free path of the heat carriers and a characteristic size of the system. Here we revisit previous formulations to provide a more explicit and clearer interpretation of the differences between the effective mean-free path in the non-local term of the generalized transport equation for q, and that in the thermal conductivity.

Original language | English |
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Pages (from-to) | 2652-2656 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 379 |

DOIs | |

Publication status | Published - 23 Oct 2015 |

### Keywords

- Effective phonon mean-free path
- Effective thermal conductivity
- Phonon-walls collisions
- Silicon nanowires

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## Cite this

Carlomagno, I., Sellitto, A., & Jou, D. (2015). Effective phonon mean-free path and slip heat flow in rarefied phonon hydrodynamics.

*Physics Letters, Section A: General, Atomic and Solid State Physics*,*379*, 2652-2656. https://doi.org/10.1016/j.physleta.2015.05.044