An investigation on thermoelastic interactions under two-temperature thermoelasticity with two relaxation parameters

The present work is concerned with the thermoelastic interactions in a linear, homogeneous, unbounded medium with a cylindrical cavity in the context of the theory of two-temperature thermoelasticity with two relaxation parameters. This theory takes into account that heat conduction in deformable bodies depends on two different temperatures: the conductive temperature and the thermodynamic temperature. The surface of the cavity is assumed to be stress free and subjected to a thermal shock. The problem is formulated on the basis of a thermoelastic model with two relaxation parameters proposed by Green and Lindsay and the two-temperature model suggested by Youssef in a unified way in order to make a detailed comparison between the two models by deriving the short-time approximated solutions for fields analytically. The results are also compared with the earlier findings. Significant dissimilarities among different models of thermoelasticity are pointed out. This study highlights a very significant feature of a two-temperature thermoelastic model.