Thermoelastic interactions in an unbounded solid due to a continuous heat source using the modified TPL G–N model

Abstract

This article exhibits the thermoelastic interactions because of a consistent heat source in an isotropic, homogeneous, unbounded elastic solid with regards to the modified theory of thermoelasticity without energy dissipation. A novel modification for the three-phase-lag Green–Naghdi (TPL G–N) heat conduction equation is proposed for this purpose. A new potential function is employed to help in solving the present problem together with Laplace and Hankel transforms. After inverting Laplace transforms, the small-time approximated solutions are used to obtain expository expressions for the field variables inside the medium. The trend of variations in all quantities past the elastic wavefront to the heat wavefront is investigated. The quantities suddenly bounce to a high worth just previously the situation of the heat wavefront and from that point hop again to zero qualities.

KEYWORDS:

• Green–Naghdi III
• three-phase lags
• unbounded solid disk
• continuous heat source

Acknowledgment

This project was funded by the Deanship of the Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant number (DF-255-130-1441). The authors, therefore, gratefully acknowledge DSR technical and financial support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project was funded by the Deanship of the Scientific Research (DSR), King Abdulaziz University, Jeddah, under [grant number DF-255-130-1441].