Comptes Rendus
From ballistic to diffusive regimes in heat transport at nano-scales
Comptes Rendus. Mécanique, Volume 339 (2011) no. 5, pp. 324-328.

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:
DOI: 10.1016/j.crme.2011.03.009
Keywords: Diffusion, Heat transport, Irreversible thermodynamics, Nano-systems

Georgy Lebon 1; Miroslav Grmela 2; Charles Dubois 2

1 Université de Liège, Département dʼAstrophysique, Géophysique et Océanographie, 17, allée du 6 Août, B-4000 Liège, Belgique
2 École Polytechnique, Center for Applied Research on Polymers and Composites, Montreal, Canada
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Georgy Lebon; Miroslav Grmela; Charles Dubois. From ballistic to diffusive regimes in heat transport at nano-scales. Comptes Rendus. Mécanique, 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/

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[3] G. Lebon; D. Jou; J. Casas-Vazquez Understanding Non-Equilibrium Thermodynamics, Springer, Berlin, 2008

[4] C. Cattaneo Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena, Volume 3 (1948), pp. 3-21

[5] X. Alvarez; D. Jou Memory and nonlocal effects of heat transport: from diffusive to ballistic regimes, Appl. Phys. Lett., Volume 90 (2007), p. 083108

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