Thermoelastic Interactions on Two-Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity

Abstract

The present work is aimed at the study of thermoelastic interactions in an infinite medium with a cylindrical cavity in the context of a theory of generalized thermoelasticity in which the theory of heat conduction in deformable bodies depends on two different temperatures—conductive temperature and dynamic temperature. The cavity surface is assumed to be stress free and is subjected to a thermal shock. In order to make a comparison between the two-temperature generalized thermoelastic model and one-temperature generalized thermoelastic model the problem is formulated on the basis of two different models of thermoelasticity: namely, the Lord–Shulman model and the two temperature Lord–Shulman model in a unified way. Laplace transform technique and decoupling of coupled differential equations are used to derive the solution in transform domain which is then followed by the inversion of Laplace transform by a numerical method to obtain the solutions for field variables in the physical domain. Short-time approximated solutions in the physical domain are also obtained analytically and compared with the earlier findings. Numerical values of physical quantities are computed for copper material, and results obtained by different models are shown graphically for the illustration of the problem.

Keywords:

• Extended thermoelasticity theory
• Generalized thermoelasticity
• Thermoelastic interaction
• Two-temperature generalized thermoelasticity

The authors acknowledge the financial support from the Department of Science and Technology, India.