Relaxation Time Of Heat Flux Research Articles

Analytical Analysis of The Dual-phase-lag Heat Transfer Equation in a Finite Slab with Periodic Surface Heat Flux (RESEARCH NOTE)

This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the first time, the analytical solution of DPL model of heat conduction equation is obtained adopting Laplace transform method and inversion theorem. The temperature profiles at the front and rear surfaces of the slab are calculated for various temperature gradient relaxation time. The phase and amplitude difference between the front and the rear surface are calculated numerically as a function of the temperature gradient relaxation time, which are reported previously as a function of the heat flux relaxation time. The results demonstrate that increasing on the temperature gradient relaxation time leads to the lower phase difference and upper amplitude difference between the temperature responses of the front and rear surfaces.

Analysis of thermoelastic damping in micro- and nanomechanical resonators based on dual-phase-lagging generalized thermoelasticity theory

In this work the thermoelastic damping of a micro-beam resonator is analyzed by the generalized thermoelasticity theory based on the dual-phase-lagging thermal conduction model. An explicit formula of thermoelastic damping has been derived. Influences of the beam height, aspect ratio and the ratio of temperature relaxation time to the heat flux relaxation time are examined. Numerical results show that the thermoelastic damping at nano-scales based on the non-Fourier theory may exceed the maximum values of Lifshitz–Roukes’ model and Zener’s approximation. Values of thermal relaxation constants and their ratio have strong influence on thermoelastic damping at nano-scales. This work may bring new insights to the exploration of thermoelastic damping in micro resonators on the submicrometer or nanometer scales.

Influence of the properties of a ferromagnetic metal on the spectrum of Rayleigh waves excited by pulsed laser radiation

A solution to the problem of laser generation of Rayleigh wave pulses in ferromagnetic metals is theoretically studied. The spectra of acoustic pulses are determined in the thermoelastic approximation taking into account a finite value of the heat-flux relaxation time, the metal absorption coefficient, and a change in the thermal linear expansion coefficient. An estimate is obtained for the maximum excess temperature in a half-space upon absorption of an optical pulse.

The nonequilibrium thermodynamic conditions and properties of materials

The basic principles for classifying the properties of materials, measured under nonequilibrium thermodynamic conditions, are formulated. It is proposed to supplement the nonlinear nonequilibrium thermodynamic mode of operation by new submodes, the area of action of which is determined by the dimensionless criteria introduced. The heat flux relaxation time and the temperature gradient time are considered as new nonlinear properties.

A criterion of applicability of the parabolic heat conduction equation

A criterion (KMCV) of applicability of the parabolic heat conduction equation to isotropic materials is proposed that quantitatively determines the conditional boundary between linear and nonlinear regimes of nonequilibrium thermodynamics in the one-dimensional formulation of some heat transfer problems. The criterion is related to the heat flux relaxation time τr. Once this characteristic time is known, the condition KMCV = 0 implies validity of the parabolic heat conduction equation. If τr is unknown, the adequacy of the parabolic heat conduction model can be judged from the absence of a temporal variation of the KMCV/τr ratio under the main condition that the heat source power is independent of the time.

Transient Fourier-law deviation by molecular dynamics in solid argon.

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.