Abstract
In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining the Green–Naghdi Type III and Lord–Shulman models. Eringen’s non-local theory has also been applied to demonstrate the effect of thermoelastic materials which depends on small scale. Some special cases as well as previous thermoelasticity models are deduced from the presented approach. In the domain of the Laplace transform, the system of equations is expressed and the problem is solved using state space method. The converted physical expressions are numerically reversed by Zakian’s computational algorithm. The analysis indicates the significant influence on field variables of non-local modulus and magnetic field with larger values. Moreover, with the established literature, the numerical results are satisfactorily examined.
Highlights
In-depth investigation on the mechanical and thermal interactions within a solid medium is of great interest in various scientific fields
This paper presents a thermoelastic investigation of a half-space medium based on the Eringen’s non-local theory
The non-local models non-local Moore–Gibson–Thompson thermoelasticity (NMGTE) and NLS follow a similar pattern in the distribution of temperature variation and studied physical variables
Summary
In-depth investigation on the mechanical and thermal interactions within a solid medium is of great interest in various scientific fields. The theories of a non-local elasticity state that the stress at any arbitrary point depends on the strain at other points, whereas the classical continuum mechanics suggests that the stress at a certain location is only related to the strain at that specific local point In this model, the equilibrium law includes the non-local field residues, and such residues are associated with the constitutive equations in which the stabilization and thermodynamic restriction requirements are balanced. As far as we know, there is hardly an effort to analyze the non-local fractures of the preheated materials, which is extremely important for the handling and/or manufacturing of advanced materials, because the material adjacent to the surface approaches to its melting temperature In these cases, the theoretical model of non-local effect and fractional order incorporating the amended Fourier law is necessary to establish the thermoelastic responses of micro/nanoscale structures. The effects of heat source strength, non-local parameter and the magnet field are considered and discussed
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