A three-phase-lag model of the linearized theory of coupled thermoelasticity is formulated by considering the heat condition law that includes temperature gradient and the thermal displacement gradient among the constitutive variables. The Fourier law is replaced by an approximation to a modification of the Fourier law with three different translations for the heat flux vector, the temperature gradient and also for the thermal displacement gradient. The model formulated is an extension of the thermoelastic models proposed by Lord–Shulman, Green–Naghdi and Tzou.

On A Thermoelastic Three-Phase-Lag Model

https://www.math.uni-konstanz.de/~racke/dvidat/m32.pdf

A note on stability in three-phase-lag heat conduction

We consider a thermoelastic theory where the heat conduction is described by the Moore–Gibson–Thompson equation. In fact, this equation can be obtained after the introduction of a relaxation parame...

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Moore–Gibson–Thompson thermoelasticity:

http://kops.uni-konstanz.de/bitstream/handle/123456789/636/research_paper_248.pdf;sequence=1

Ill-posed problems in thermomechanics

This study is concerned with the mixed initial boundary value problem for a dipolar body in the context of the thermoelastic theory proposed by Green and Naghdi. For the solutions of this problem we prove a result of Holder’s-type stability on the supply terms. We impose middle restrictions on the thermoelastic coefficients, which are common in continuum mechanics. For the same conditions we propose a continuous dependence result with regard to the initial data.

The effect of a dipolar structure on the Hölder stability in Green–Naghdi thermoelasticity

Electro-magneto-thermo-elastic plane waves in rotating media with thermal relaxation

The propagation of harmonically time-dependent thermo-elastic plane waves of assigned frequency in infinite rotating media is studied using the theory of thermo-elasticity recently proposed by Green and Lindsay. A more general dispersion equation is deduced to determine the effect of rotation and relaxation times on the phase velocity of the coupled waves. The solutions for the phase velocity and the attenuation coefficient are obtained for small thermo-elastic coupling by a perturbation technique. Cases of low and high frequencies are also studied to determine the effect of rotation, the relaxation parameters and thermo-elastic coupling on the phase velocity and the attenuation coefficient of the waves.

Effect of rotation and relaxation times on plane waves in generalised thermo-elasticity

Magnetoelastic Plane Waves in Infinite Rotating Media

The propagation of magneto-thermoelastic disturbances produced by a thermal shock in a finitely conducting elastic half-space in contact with a vacuum is investigated. The temperature-rate dependent theory of thermoelasticity proposed by Green and Lindsay is employed. Because of the short duration of the “second sound” effects, short-time approximations of the solutions are studied using a Laplace transform on time. It is found that the temperature and deformation are discontinuous at the wave fronts whereas the perturbed magnetic fields suffer delta function singularity at these locations.

S. K. Roy Choudhuri

Papers

On A Thermoelastic Three-Phase-Lag Model

Electro-magneto-thermo-elastic plane waves in rotating media with thermal relaxation

Effect of rotation and relaxation times on plane waves in generalised thermo-elasticity

Magnetoelastic Plane Waves in Infinite Rotating Media

Temperature-rate dependent magnetothermoelastic waves in a finitely conducting elastic half-space