By Antonio Sellitto, Vito Antonio Cimmelli, David Jou
This ebook provides generalized heat-conduction legislation which, from a mesoscopic standpoint, are appropriate to new functions (especially in nanoscale warmth move, nanoscale thermoelectric phenomena, and in diffusive-to-ballistic regime) and whilst stay alongside of the velocity of present microscopic study. The equations provided within the booklet have compatibility with generalized formulations of nonequilibrium thermodynamics, going past the local-equilibrium. The e-book contains six major chapters, including a preface and a last part dedicated to the long run views, in addition to an in depth bibliography.
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Additional info for Mesoscopic Theories of Heat Transport in Nanosystems
However, since we are assuming that the quantity driving the heat flow is ˇ rather than T, we have substituted T with ˇ into the Newton cooling law. The comparison of results from Eqs. ˇ ˇenv / provide the best description of heat transfer in fast processes. , ˇP D 0) by Eq. 41) it follows that Tenv Á ˇenv , which is assumed to be constant, as well as in Eq. 61). Combining Eqs. 70) R r instead of Eq. 62). It is important to note the difference between Eqs. 70), since the term in T= Eq. 62) is absent in Eq.
In Eqs. 13) U0 is given by Eq. U0 Tcv /. 3 The Nonlinear MCV and GK Equations 37 In other words, Eq. 12) points out that a small heat pulse, moving in the same direction of the heat flow, will travel with a velocity which differs from the speed of propagation of pulses in opposite direction, given by Eq. 13). In particular, the theoretical model in Eq. 10) prescribes that the former speed is smaller than the latter one [22, 23]. A similar result has been obtained in Ref.  and in Ref.  by applying different approaches.
Rep. Prog. Phys. 62, 1035–1142 (1999) 55. : A phenomenological scaling approach for heat transport in nano-systems. Appl. Math. Lett. 18, 963–967 (2005) 56. : Extended irreversible thermodynamics of heat transport. A brief introduction. Proc. Est. Acad. Sci. 57, 118–126 (2008) 57. : Nonequilibrium temperatures and second-sound propagation along nanowires and thin layers. Phys. Lett. A 373, 4386–4392 (2009) 58. : Extended Irreversible Thermodynamics, 4th revised edn. Springer, Berlin (2010) 59. : Heat fluctuations and phonon hydrodynamics in nanowires.