Transient Fourier-law deviation by molecular dynamics in solid argon

Abstract

Using a molecular-dynamics (MD) numerical simulation, we test the validity of the generalized Fourier law predicted by Cattaneo and Vernotte (CV) and theoretically established in the extended irreversible thermodynamics. The numerical experiments are achieved at constant and high density in a Lennard-Jones (6-12) solid argon. The temperature domain is restricted to the so-called kinetic region where the thermal conductivity \ensuremath{\lambda}\ensuremath{\sim}${\mathit{T}}^{\mathrm{\ensuremath{-}}1}$. It was found that the heat flux relaxation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{V}}$ and the phonon mean relaxation time are numerically equal with a good accuracy, in agreement with the consequence of the phonon transfer equation at macroscopic equilibrium. For nonequilibrium regimes, we study the thermal response of the lattice to a temperature disturbance of low or high magnitude. Stress effects were detected and excluded from the kinetic temperature measurement. Finally, a thermal energy analysis shows that the time transition to the Fourier regime is well predicted by the MD value of ${\mathrm{\ensuremath{\tau}}}_{\mathit{V}}$, but a large disagreement is found between the MD data and the hyperbolic model solution before that time. As a conclusion, the CV law is confirmed when considering heat flux fluctuations at equilibrium, but nonequilibrium situations with macroscopic temperature gradients are badly represented by the hyperbolic model. \textcopyright{} 1996 The American Physical Society.