Thermoelastic Processes by a Continuous Heat Source Line in an Infinite Solid via Moore–Gibson–Thompson Thermoelasticity

Abstract

Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore–Gibson–Thompson equation in cases where some of these models fail to be positive. This thermomechanical model has been constructed in combination with a hyperbolic partial differential equation for the variation of the displacement field and a parabolic differential equation for the temperature increment. The presented model is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source. To solve this problem, together with Laplace and Hankel transform methods, the potential function approach has been used. Laplace and Hankel inverse transformations are used to find solutions to different physical fields in the space–time domain. The problem is validated by calculating the numerical calculations of the physical fields for a given material. The numerical and theoretical results of other thermoelastic models have been compared with those described previously.

The effect of variable properties and rotation in a visco-thermoelastic orthotropic annular cylinder under the Moore–Gibson–Thompson heat conduction model

“…[29][30][31][32][33][34][35] The theoretical study of the thermoelastic and mechanical behavior of different structures have successfully been applied in recent years. [36][37][38][39][40][41][42][43][44][45] Due to a wide variety of microphysical processes, viscoelasticity is of great interest to various applications and can be used as an experimental test for those processes. The Boltzmann superposition theory is extended to the linear viscoelastic governing equations.…”

Solution of Moore–Gibson–Thompson Equation of an Unbounded Medium with a Cylindrical Hole

“…In the context of several mechanical aspects of the flux, this theory started with a third-order differential equation. The MGT thermoelastic model has led to a significant increase in the range of researchers devoted to this theory [17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

“…The Moore-Gibson-Thompson thermoelasticity theory MGTE [15,17] when K * , τ 0 > 0. Case II: Taking into account the effect of diffusion…”

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

“…Since the beginning of Moore-Gibson-Thompson theory, the number of research works aimed at investigating this theory has considerably increased [21][22][23][24][25][26][27]. By implementing the mentioned theories, the mechanical behavior of several structures has been theoretically studied as well [28][29][30][31][32][33][34].…”