M.Sc Student | Shvartsman Rina |
---|---|

Subject | Non-Fourier Heat Conduction in One- Dimensional Microscopic Models of Dielectrics |

Department | Department of Mechanical Engineering |

Supervisor | Professor Oleg Gendelman |

Full Thesis text |

Fourier equation of heat conduction admits the paradox of infinite velocity of heat propagation. To avoid this unphysical outcome, non Fourier models of heat transfer were proposed. The best known equation of this sort is Cattaneo-Vernotte (CV) equation.

In this work, the non stationary conduction problem is investigated from the microscopic point of view, In order to assess the phenomena of the non-Fourier heat conduction and the validity of the CV equation for microscopic models of dielectrics. Frenkel- Kontorova model of one-dimensional chain of particles has been used. Relaxation to equilibrium for various spatial modes of the temperature distribution was studied numerically with the help of Runge - Kutta method.

The simulations
demonstrate that the effects of the non-stationary heat conduction can be
easily revealed in simple one - dimensional models of dielectrics. There exists
a critical modal wavelength *l*^{*} which separates between
oscillating and diffusive relaxation of the temperature field; existence of
such critical scale is inconsistent with Fourier law. So, if the size of the
system is close to this critical scale, more exact models should be used for
computation of the non-stationary heat flow. The critical size decreases with
the temperature increase. In the vicinity of the critical scale the relaxation
behavior is inconsistent with the - second order Cattaneo - Vernotte law and
thus more elaborate higher - order approximations should be used.