Thermoelasticity with Second Sound: A Review

Chandrasekharaiah, D. S.

doi:10.1115/1.3143705

Cited by 808 publications

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“…However, determining u and for arbitrary t is a tedious task. Since the second-sound effects are short lived [4], it may be sufficient to obtain and analyse the solutions for small t. This is done by taking s to be large.…”

Section: Transform Solutionmentioning

confidence: 99%

“…In view of the experimental evidence available in favour of finiteness of heat propagation speed, generalized thermoelasticity theories are considered to be more realistic than the conventional thermoelasticity theory in dealing with practical problems involving very large heat fluxes at short intervals, like those occurring in laser units and energy channels. For a review of the relevant literature, see [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…We solve the governing equations by employing the Laplace transform technique. Since the second sound effects are short-lived [4], we perform the inverse Laplace transform operation for small time and derive expressions for displacement, temperature and radial and hoop stress fields. We find that the thermoelastic interactions consist of two coupled waves propagating with finite speeds, of which one is predominantly elastic and the other predominantly thermal, and that neither of these waves experiences attenuation.…”

Section: Introductionmentioning

confidence: 99%

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Chandrasekharaiah

Srinath²

1997

Journal of Elasticity

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Abstract. The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions in a homogeneous and isotropic unbounded body containing a cylindrical cavity. The interactions are supposed to be due to a constant step in radial stress or temperature applied to the boundary of the cavity, which is maintained at a constant temperature or zero radial stress (as the case may be). By using the Laplace transform technique, it is found that the interactions consist of two coupled waves both of which propagate with a finite speed but with no attenuation. The discontinuities that occur at the wavefronts are computed. Numerical results applicable to a copper-like material are presented.Mathematics Subject Classifications (1991): 73B30, 73D10, 73D15.

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Section: Transform Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chandrasekharaiah

Srinath²

1997

Journal of Elasticity

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“…However, it is well-known that due to its parabolic character it implies infinite speed of the signal propagation and thus should be modified if very large gradients or extremely small scales are involved [17][18][19][20]. On macroscopic level, numerous modifications were suggested to recover the hyperbolic character of the heat transport equation [19][20][21][22]. Perhaps, the most known is the lowest -order approximation known as CattaneoVernotte (CV) or telegraphist (TE) law [23,24].…”

Section: Introductionmentioning

confidence: 99%

Nonstationary heat conduction in one-dimensional models with substrate potential

et al. 2012

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The paper investigates non-stationary heat conduction in one-dimensional models with substrate potential. In order to establish universal characteristic properties of the process, we explore three different models -Frenkel-Kontorova (FK), phi4+ (φ 4 +) and phi4-(φ 4 −). Direct numeric simulations reveal in all these models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with parabolic Fourier equation of the heat conduction and clearly demonstrates the necessity of hyperbolic models. The crossover wavelength decreases with increase of average temperature. The decay patterns of the temperature field almost do not depend on the amplitude of the perturbations, so the use of linear evolution equations for temperature field is justified. In all model investigated, the relaxation of thermal perturbations is exponential -contrary to linear chain, where it follows a power law. However, the most popular lowest-order hyperbolic generalization of the Fourier law, known as Cattaneo-Vernotte (CV) or telegraph equation (TE) is not valid for description of the observed behavior of the models with on-site potential. In part of the models a characteristic relaxation times exhibit peculiar scaling with respect to the temperature perturbation wavelength. Quite surprisingly, such behavior is similar to that of well-known model with divergent heat conduction (Fermi-Pasta-Ulam chain) and rather different from the model with normal heat conduction (chain of rotators). Thus, the data on the non-stationary heat conduction in the systems with on-site potential do not fit commonly accepted concept of universality classes for heat conduction in one-dimensional models.

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“…These nonclassical theories are often regarded as the generalized dynamic theory of thermoelasticity. Brief reviews of this topic have been reported by Chandrasekharaiah [4]. The phenomenon of reflection of pure elastic waves may be found in many references [1,2,5,6,10,13].…”

Section: Introductionmentioning

confidence: 99%

The reflection phenomena of SV‐waves in a generalized thermoelastic medium

Abd-alla

Al-Dawy

2000

International Journal of Mathematics and Mathematical Sciences

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Abstract. We discuss the reflection of thermoelastic plane waves at a solid half-space nearby a vacuum. We use the generalized thermoelastic waves to study the effects of one or two thermal relaxation times on the reflection plane harmonic waves. The study considered the thermal and the elastic waves of small amplitudes in a homogeneous, isotropic, and thermally conducting elastic solid. The expressions for the reflection coefficients, which are the ratio of the amplitudes of the reflected waves to the amplitude of the incident waves are obtained. It has been shown, analytically, that the elastic waves are modified due to the thermal effect. The reflection coefficients of a shear wave that incident from within the solid on its boundary, which depend on the thermoelastic coupling factor and included the thermal relaxation times, have been found in the general case. The numerical values of reflection coefficients against the angle of incidence for different values of thermal relaxation times have been calculated and the results are given in the form of graphs. Some special cases of reflection have also been discussed, for example, in the absence of thermal effect our results reduce to the ordinary pure elastic case.

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Thermoelasticity with Second Sound: A Review

Cited by 808 publications

References 0 publications

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Nonstationary heat conduction in one-dimensional models with substrate potential

The reflection phenomena of SV‐waves in a generalized thermoelastic medium

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