# Mesoscopic Theories of Heat Transport in Nanosystems by Antonio Sellitto, Vito Antonio Cimmelli, David Jou

By Antonio Sellitto, Vito Antonio Cimmelli, David Jou

This booklet provides generalized heat-conduction legislation which, from a mesoscopic point of view, are correct to new purposes (especially in nanoscale warmth move, nanoscale thermoelectric phenomena, and in diffusive-to-ballistic regime) and while stay alongside of the speed of present microscopic learn. The equations provided within the booklet have compatibility with generalized formulations of nonequilibrium thermodynamics, going past the local-equilibrium. The ebook contains six major chapters, including a preface and a last part dedicated to the longer term views, in addition to an intensive bibliography.

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**Mesoscopic Theories of Heat Transport in Nanosystems**

This booklet provides generalized heat-conduction legislation which, from a mesoscopic viewpoint, are proper to new functions (especially in nanoscale warmth move, nanoscale thermoelectric phenomena, and in diffusive-to-ballistic regime) and while stay alongside of the speed of present microscopic learn.

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A: Math. Gen. 37, 9805–9829 (2004) 7. : Nine-moment phonon hydrodynamics based on the maximum-entropy closure: one-dimensional flow. J. Phys. A: Math. Gen. 38, 8781–8802 (2005) References 27 8. : Chapman-Enskog method for a phonon gas with finite heat flux. J. Phys. A: Math. Gen. ) (2008) 9. : Evaluation of thermal conductivity of porous silicon layers by a photoacoustic method. Appl. Phys. A: Mater. Sci. Process. 64, 155–159 (1997) 10. : Heat capacity of carbon nanotubes. Solid State Commun. 100, 177–180 (1996) 11.

3 for more comments about that equation, here we only observe that Eqs. 28) essentially have the same qualitative behavior both for low, and for very high Knudsen numbers. Several mathematical aspects of Eq. 22) and related ones have been dealt with in Ref. [29]. The idea of a linear hierarchy of evolution equations presented above may be generalized by taking into account that, in the presence of a temperature gradient, the fluxes of order m, m C 1, and m 1 may be coupled not only by the wave-vector k, but also by the temperature gradient itself.

The first were Cattaneo [12, 13] and Vernotte [80] which, basing their analyses on the kinetic theory, proposed a damped version of Eq. 2) to eliminate the paradox of infinite speed of propagation of thermal signals, and to comply with the experimental observations. They generalized Eq. 2) as in Eq. 2 The Guyer-Krumhansl Equation and Phonon Hydrodynamics 33 In fact, for the sake of a formal simplicity, if one assumes that the material functions are constant, then the use of Eqs. 2) instead of Eq.