Generalized Thermoelastic Interactions Using an Eigenvalue Technique in a Transversely Isotropic Unbounded Medium with Memory Having a Line Heat Source

Abstract

The present article looks over thermoelastic interactions in a homogeneous, linear, transversely isotropic unbounded continuum with the aid of memory-dependent derivatives in the presence of a line heat source. The exploration has been unifiedly carried out in the context of Green-Lindsay and Lord-Shulman models. A cylindrical polar coordinates system has been used to describe the problem and the eigenvalue technique has been adopted to solve the governing field equations in the transformed domain of Laplace. The solution for different thermophysical quantities is obtained in the real space-time domain using the Stehfest method for numerical Laplace inversion. The obtained numerical data for different thermophysical quantities are plotted in graphs to investigate the impacts of the time delay parameter, and the different kernel functions, and a comparison between the considered models has been accomplished. It is worth mentioning that the results of an analogous problem for isotropic material can be easily deduced from the corresponding results of this article. The adoption of generalized thermoelastic theory with memory-dependent derivative along with eigenvalue technique in analyzing the thermoelastic interactions is relatively fresh.

Keywords

• memory-dependent derivative
• eigen value approach
• vector-matrix differential equation
• stehfest method