[en] Heat conduction in nanosize systems has to be studied in settings involving microscopic details that are not seen in the classical Fourier theory. G. Chen has suggested [Phys. Rev. Lett. 86 (2001) 2297] a combination of the Cattaneo setting in which the velocity of the heat propagation is finite and the kinetic theory setting in which phonons are seen as heat carriers. In this Letter we show that if the Cattaneo and the kinetic theories are combined in a way that preserves the structure expressing their compatibility with thermodynamics (GENERIC structure) then both the Cattaneo and the kinetic equations become modified. The modified Cattaneo equations involve the term introduced by Chen and, in addition, new terms that are nonlinear in quantities that disappear at equilibrium. The kinetic equation is modified by new terms involving gradients of the heat flux and the local temperature.
Disciplines :
Physics
Author, co-author :
Grmela, M.; Ecole Polytechnique de Montreal, C.P.6079 suc. Centre-ville, Montreal, H3C 3A7 Quebec, Canada
Lebon, Georgy ; Université de Liège - ULiège > Services généraux (Faculté des sciences) > Relations académiques et scientifiques (Sciences)
Dauby, Pierre ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Thermodynamique des phénomènes irréversibles
Bousmina, M.; Chemical Engineering, Laval University, Ste-Foy, G1K 7P4 Quebec, Canada
Language :
English
Title :
Ballistic-diffusive heat conduction at nanoscale: GENERIC approach [rapid communication]
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