Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach

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.

On a mixture of an MGT viscous material and an elastic solid

“…where 3 , and W 1,2 0 (B) and L 2 (B) are the usual Sobolev spaces. Let us denote an element U ∈ H by U = (u, v, z, w, y), and define the operators:…”

“…On the other hand, in the last decade great interest has been developed to understand the so-called Moore-Gibson-Thompson equation which was first used in fluid mechanics. Recently, this equation has been considered as a heat equation (and then, to analyze the Moore-Gibson-Thompson thermoelasticity) [1][2][3]5,6,13,14,16,22,23,28,31] and a new kind of viscous elastic materials [12,13,27]. In this work, we want to consider a mixture of a viscous solid of Moore-Gibson-Thompson type and an elastic material.…”

Fractional derivative Moore‐Gibson‐Thompson heat equation without singular kernel for a thermoelastic medium with a cylindrical hole and variable properties

“…The number of publications devoted to MGT theory has grown substantially since its inception [22][23][24][25][26][27]. The thermal and mechanical behavior of many structures has been effectively studied theoretically in recent years [29][30][31][32][33][34][35]. Quintanilla [21] modified equation for thermal conductivity is as follows:…”

Viscoelastic stressed microbeam analysis based on Moore–Gibson–Thompson heat equation and laser excitation resting on Winkler foundation

“…The combination of amended Fourier law and the energy equation has proved that the continuity of the points results in a number of components so that the real component is infinitely dependent and thus dependence on solutions continues to fail. 51 In recent years, a significant number of studies were based on research and understanding of the Moore-Gibson-Thompson (MGT) equation. [52][53][54][55] This theory was derived from a differential equation of the third order, integrated into the importance of some aspects of fluid dynamics.…”

“…The combination of amended Fourier law and the energy equation has proved that the continuity of the points results in a number of components so that the real component is infinitely dependent and thus dependence on solutions continues to fail. 51…”