| Abstract: | The presentation is devoted to applicability of Fourier law of heat conduction in at nanoscale and in low – dimensional systems. Two main aspects of this problem will be discussed, with brief review of existing analytic, numeric and experimental results. The first aspect is existence (size independence) of the heat conduction coefficient for the case of stationary conduction. Numeric simulations, supported by some analytic evidence, suggest crucial effect of dimensionality – only for 3D systems the heat conduction coefficient reveals size independence. The other aspect is related to the nonstationary heat conduction. In this case, one can demonstrate that for extremely small times or extremely small space scales, the parabolic equation of the heat conduction is no more applicable and hyperbolic models should be used instead. Such models use even more empiric coefficients than the common Fourier law. Applicability of popular hyperbolic extensions of Fourier law (Cattaneo – Vernotte and some others) will be discussed quantitatively and qualitatively |
