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Summary: NON FOURIER HEAT CONDUCTION IN MICROSCOPIC MODELS OF
DIELECTRICS
Oleg Gendelman
Faculty of Mechanical Engineering, Technion Israel Institute of Technology
ovgend@techunix.technion.ac.il
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. Fermi Pasta
Ulam ,Frenkel- Kontorova and coupled rotators models were used for direct molecular
dynamics simulations.
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
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