A memory response on the elasto-thermodiffusive interaction subjected to rectangular thermal pulse and chemical shock

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of elasto-thermodiffusion to investigate the transient phenomena for an isotropic three-dimensional thermoelastic medium subjected to permeating gas induced by a rectangular thermal pulse, where the heat conduction equation is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The chemical potential is also assumed to be known on the bounding plane. Employing the Laplace transform and double-Fourier transform techniques, the problem has been solved analytically in the transformed domain. Numerical inversion of the Laplace transform and double-Fourier transforms are carried out using a Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative, the effect of delay time and thermodiffusion also.

Keywords:

• Thermoelastic diffusion
• memory dependent derivative
• double Fourier transform
• Laplace transform
• three-phase-lag thermoelastic model

Acknowledgements

The author would like to thank the Editor and the anonymous referees for their comments and suggestions on this paper.

Conflict of interest

The author declares that there is no Conflict of interest.

Additional information

Funding

The author received no financial support for the research.