The influences of thermal relaxation time and varying thermal conductivity in thermoelastic media

Abstract

This study introduces a nonlinear analysis of the transient responses in a thermoelastic medium produced by a thermal shock. The formulations are presented based on a Green-Lindsay (GL) thermoelasticity model with two thermal relaxation times under varying thermal conductivity are included in the governing equations. The finite element process is employed to address the problem without resorting to Kirchhoff transforms, as non-linear formulations pose significant challenges. In the linear case where Kirchhoff's transforms are implemented, the solution to the problem is obtained through Laplace transformations and the eigenvalues technique. The impacts of changing thermal conductivity are examined and contrasted both with and without the use of Kirchhoff transforms. Graphical illustrations of the numerical outcomes display the variations of displacement, temperature, and stress. Compared to the classic thermoelastic (CT) model, the (GL) model excels in accurately depicting the observed waves propagations phenomenon under varying thermal conductivity.

Keywords

• Laplace transforms
• Kirchhoff's transforms
• Eigenvalues approach
• Varying thermal conductivity
• Finite element approach