Our purpose is to model heat transport at micro- and nano-scales. At these scales, the mechanism of transport is not only diffusive, i.e. dominated by multiple scattering of phonons, but includes also a ballistic contribution due to collisions of phonons with the boundaries. To takes these effects into account, we follow the line of thoughts of Extended Irreversible Thermodynamics. The original idea underlying the present paper is to assume the coexistence of two kinds of heat carriers, namely ballistic and diffusive phonons, which are obeying different time-evolution equations: the diffusive collisions are described by a Cattaneo equation and ballistic interactions by a Guyer–Krumhansl like equation. The model is applied to the problem of transient heat transport in microfilms and the results are compared with earlier descriptions.

Published online: 2011-04-21
DOI: 10.1016/j.crme.2011.03.009

@article{CRMECA_2011__339_5_324_0,
     author = {Georgy Lebon and Miroslav Grmela and Charles Dubois},
     title = {From ballistic to diffusive regimes in heat transport at nano-scales},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {324--328},
     publisher = {Elsevier},
     volume = {339},
     number = {5},
     year = {2011},
     doi = {10.1016/j.crme.2011.03.009},
     language = {en},
}

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Georgy Lebon; Miroslav Grmela; Charles Dubois. From ballistic to diffusive regimes in heat transport at nano-scales. Comptes Rendus. Mécanique, Thermodiffusion and coupled phenomena, Volume 339 (2011) no. 5, pp. 324-328. doi : 10.1016/j.crme.2011.03.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.03.009/