An extended thermodynamic model of transient heat conduction at sub-continuum scales

in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2011), 467

A thermodynamic description of transient heat conduction at small length and timescales is proposed. It is based on extended irreversible thermodynamics and the main feature of this formalism is to ... [more ▼]

A thermodynamic description of transient heat conduction at small length and timescales is proposed. It is based on extended irreversible thermodynamics and the main feature of this formalism is to elevate the heat flux vector to the status of independent variable at the same level as the classical variable, the temperature. The present model assumes the coexistence of two kinds of heat carriers: diffusive and ballistic phonons. The behaviour of the diffusive phonons is governed by a Cattaneo-type equation to take into account the high-frequency phenomena generally present at nanoscales. To include non-local effects that are dominant in nanostructures, it is assumed that the ballistic carriers are obeying a Guyer–Krumhansl relation. The model is applied to the problem of transient heat conduction through a thin nanofilm. The numerical results are compared with those provided by Fourier, Cattaneo and other recent models. [less ▲]

Ballistic-diffusive heat conduction at nanoscale: GENERIC approach [rapid communication]

in Physics Letters A (2005), 339

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 ... [more ▼]

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. [less ▲]

Coupled buoyancy and thermocapillary convection in a viscoelastic Maxwell fluid

in Journal of Physics : Condensed Matter (1993), 5