Memory response for thermal distributions moving over a magneto-thermoelastic rod under Eringen’s nonlocal theory

Abstract

Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of Lord–Shulman (LS) theory of thermoelasticity based on Eringen’s nonlocal elasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effects of moving heat source speed, time instance, memory-dependent derivative, magnetic field and nonlocality on temperature, stress, and temperature are studied.

Keywords:

• Laplace transform
• Lord–Shulman model
• magneto-thermoelasticity
• memory-dependent derivative
• moving heat source
• nonlocal

Acknowledgments

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

Disclosure statement

The author declares that he has no conflict of interest.

Funding

The author received no financial support for the research.

Table 1. Data table corresponding to Figure 6 for the temperature, displacement, and stress distribution at t = 3 and v = 2 in the local medium.

Table 2. Data table corresponding to Figure 7 for the temperature, displacement, and stress distribution at t = 1 and v = 4 in the local medium.