טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentShvartsman Rina
SubjectNon-Fourier Heat Conduction in One-
Dimensional Microscopic Models of Dielectrics
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

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.