This paper is concerned with thermoelastic material behavior whose constitutive response functions possess thermal features that are more general than in the usual classical thermoelasticity. After a general development of the constitutive equations in the context of both nonlinear and linear theories, attention is focused on the latter. In particular, the one-dimensional version of the equation for the determination of temperature in the linearized theory provides an easy comparative basis of its predictive capability: In one special case where the Fourier conductivity is dominant, the temperature equation reduces to the classical Fourier law of heat conduction, which does not permit the possibility of undamped thermal waves; however,'in another special case in which the effect of conductivity is negligible, the equation has undamped thermal wave solutions without energy dissipation.

On undamped heat waves in an elastic solid

Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of applicability, and can be applied to both weakly and strongly coupled systems. In its modern formulation, relativistic viscous hydrodynamics can directly be solved numerically. This has been useful for the problem of ultrarelativistic heavy-ion collisions, and I will review the setup and results of a hydrodynamic description of experimental data for this case.

http://personalpages.to.infn.it/~alberico/QGP2008/Romatschke/Romatschke-lectures.pdf

New Developments in Relativistic Viscous Hydrodynamics

The conduction of heat in two dimensions displays a wealth of fascinating phenomena of key relevance to the scientific understanding and technological applications of graphene and related materials Here, we use density-functional perturbation theory and an exact, variational solution of the Boltzmann transport equation to study fully from first-principles phonon transport and heat conductivity in graphene, boron nitride, molybdenum disulphide and the functionalized derivatives graphane and fluorographene In all these materials, and at variance with typical three-dimensional solids, normal processes keep dominating over Umklapp scattering well-above cryogenic conditions, extending to room temperature and more As a result, novel regimes emerge, with Poiseuille and Ziman hydrodynamics, hitherto typically confined to ultra-low temperatures, characterizing transport at ordinary conditions Most remarkably, several of these two-dimensional materials admit wave-like heat diffusion, with second sound present at room temperature and above in graphene, boron nitride and graphane

/pdf/phonon-hydrodynamics-in-two-dimensional-materials-bx11pq6elo.pdf

Phonon hydrodynamics in two-dimensional materials

A new formulation of nonequilibrium thermodynamics, known as extended irreversible thermodynamics, has fuelled increasing attention. The basic features of this formalism and several applications are reviewed. Extended irreversible thermodynamics includes dissipative fluxes (heat flux, viscous pressure tensor, electric current) in the set of basic independent variables of the entropy. Starting from this hypothesis, and by using methods similar to classical irreversible thermodynamics, evolution equations for these fluxes are obtained. These equations reduce to the classical constitutive laws in the limit of slow phenomena, but may also be applied to fast phenomena, such as second sound in solids, ultrasound propagation or generalised hydrodynamics. In contrast with the classical theory, extended thermodynamics leads to hyperbolic equations with finite speeds of propagation for thermal and viscous signals. Supplementary information about the macroscopic parameters is provided by fluctuation theory. The results of the macroscopic theory are confirmed by the kinetic theory of gases and nonequilibrium statistical mechanics. The theory is particularly useful for studying the thermodynamics of nonequilibrium steady states and systems with long relaxation times, such as viscoelastic media or systems at low temperatures. There is no difficulty in formulating the theory in the relativistic context. Applications to rigid electrical conductors as well as several generalisations including higher-order fluxes are also presented. A final section is devoted to the formulation of extended irreversible thermodynamics within the framework of the so-called rational thermodynamics.

REVIEW ARTICLE: Extended irreversible thermodynamics

This work examines the lagging behavior for heat transport in small-scale and fast-transient processes. The experimental result by Qiu et al. for the femtosecond transient response in gold films and that by Bertman and Sandiford for the temperature pulse traveling through superfluid liquid helium are re-examined with emphasis on the lagging behavior. The model employing the phase-lag concept provides as competent or even better results when describing the special response observed in these experiments.

Experimental support for the lagging behavior in heat propagation

An experiment on temperature pulse propagation in a bcc crystal of $^{3}\mathrm{He}$ grown at 959 atm shows the existence of second sound in the solid below about 058\ifmmode^\circ\else\textdegree\fi{}K In the temperature range $042\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}lTl058\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$, reflections of the received pulses were observed In the range $058\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}lTl12\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$, the temperature pulses were observed to propagate diffusively

Second Sound in Solid Helium

Temperature pulses in dielectric solids

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Second Sound in Solid Helium

Temperature pulses in dielectric solids