Analysis of a recent heat conduction model with a delay for thermoelastic interactions in an unbounded medium with a spherical cavity

In this work, we study the thermoelastic interactions in an unbounded medium with a spherical cavity in the context of a very recently proposed heat conduction model established by Quintanilla (2011). This model is a reformulation of three-phase-lag conduction model and is an alternative heat conduction theory with a single delay term. We make an attempt to study the thermoelastic interactions in an isotropic elastic medium with a spherical cavity subjected to three types of thermal and mechanical loads in the contexts of two versions of this new model. Analytical solutions for the distributions of the field variables are found out with the help of the integral transform technique. A detailed analysis of analytical results is provided by short-time approximation concept. Further, the numerical solutions of the problems are obtained by applying numerical inversion of Laplace transform.We observe significant variations in the analytical results predicted by different heat conduction models. Numerical values of field variables are also observed to show significantly different results for a particular material. Several important points related to the prediction of the new model are highlighted

Magneto-thermoelastic waves induced by a thermal shock in a finitely conducting elastic half space

The propagation of magneto-thermoelastic disturbances produced by a thermal shock in a finitely conducting elastic half-space in contact with vacuum is investigated. The boundary of the half-space is subjected to a normal load. Lord-Shulman theory of thermoelasticity [1] is used to account for the interaction between the elastic and thermal fields. Laplace transform on time is used to obtain the short-time approximations of the solutions because of the short duration of 'second sound' effects. It is found that in the half-space the displacement is continuous at the modified dilational and thermal wavefronts, whereas the perturbed magnetic field, stress and the temperature suffer discontinuities at these locations. The perturbed magnetic field, is, however, discontinuous at the Alf'ven-acoustic wavefront in vacuum

On the existence and decay in a new thermoelastic theory with two temperatures

In this work, we study a new two-temperatures thermoelastic model. Both thermodynamic and conductive temperatures are included, being related by means of an elliptic or parabolic equation. Then, two problems are considered assuming the dependence or not on the rate conductivity temperature. Existence of solutions for the three-dimensional setting and the exponential energy decay in the one-dimensional case are shownPeer ReviewedPostprint (author's final draft

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

The generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermo-visco-elastic plane waves of assigned frequency in an infinite visco-elastic solid of Kelvin-Voigt type, when the entire medium rotates with a uniform angular velocity. A more general dispersion equation is deduced to determine the effects of rotation, visco-elasticity, and relaxation time on the phase-velocity of the coupled waves. The solutions for the phase velocity and attenuation coefficient are obtained for small thermo-elastic couplings by the perturbation technique. Taking an appropriate material, the numerical values of the phase velocity of the waves are computed and the results are shown graphically to illustrate the problem