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A phenomenological scaling approach for heat transport in nano-systems. (English) Zbl 1081.80001
Summary: A phenomenological approach of heat transfer in nano-systems is proposed, on the basis of a continued-fraction expansion of the thermal conductivity, obtained within the framework of extended irreversible thermodynamics. Emphasis is put on the transition from the diffusive, collision-dominated heat transport to the ballistic heat transport, as a function of the mean free path and the length of the system.

80A20 Heat and mass transfer, heat flow (MSC2010)
82B35 Irreversible thermodynamics, including Onsager-Machlup theory
Full Text: DOI
[1] Joshi, A.; Majumbar, A., Transient ballistic and diffusive phonon heat transport in thin films, J. appl. phys., 74, 31-39, (1993)
[2] Hill, T.L., Thermodynamics of small systems, (1994), Dover New York · Zbl 0115.23003
[3] Chen, G., Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles, J. heat transfer., 118, 539-545, (1996)
[4] Jou, D.; Casas-Vázquez, J.; Lebon, G., Extended irreversible thermodynamics, Rep. prog. phys., 51, 1105, (1988), Springer Berlin, 62 (1999) 1035 · Zbl 0974.74003
[5] Jou, D.; Casas-Vázquez, J.; Criado-Sancho, M., Thermodynamics of fluids under flow, (2000), Springer Berlin · Zbl 0806.76002
[6] Tzou, D.Y., Macro to microscale heat transfer. the lagging behaviour, (1997), Taylor and Francis New York
[7] Aoki, H.; Kusnezov, D., Fermi-pasta-Ulam model: boundary jumps, fourier’s law, and scaling, Phys. rev. lett., 86, 4029-4032, (2001)
[8] Giardinà, C.; Livi, R.; Politi, A.; Vassalli, M., Finite thermal conductivity in 1D lattices, Phys. rev. lett., 84, 2144-2147, (2000)
[9] Garrido, P.L.; Hurtado, P.I.; Nadrowski, B., Simple one-dimensional model of heat conduction which obeys fourier’s law, Phys. rev. lett., 86, 5486-5489, (2001)
[10] Dhar, A., Heat conduction in the disordered harmonic chain revisited, Phys. rev. lett., 86, 5882-5885, (2001)
[11] Chapman, S.; Cowling, T.G., The mathematical theory of non-uniform gases, (1970), Cambridge University Press Cambridge · Zbl 0098.39702
[12] Dedeurwaerdere, T.; Casas-Vázquez, J.; Jou, D.; Lebon, G., Foundations and applications of a mesoscopic thermodynamic theory of fast phenomena, Phys. rev. E, 53, 498-506, (1996)
[13] Dreyer, W.; Struchtrup, H., Heat pulse experiments revisited, Continuum mech. thermodyn., 5, 3-50, (1993)
[14] Chen, G., Ballistic-diffusive equations for transient heat conduction from nano to macroscales, J. heat transfer, 124, 320-328, (2002)
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