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

Abstract

The present contribution aims to address a problem of thermoviscoelasticity for the analysis of the transition temperature and thermal stresses in an infinitely circular annular cylinder. The inner surface is traction-free and subjected to thermal shock heating, while the outer surface is thermally insulated and free of traction. In this work, in contrast to the various problems in which the thermal conductivity coefficient is considered to be fixed, this parameter is assumed to be variable depending on the temperature change. The problem is studied by presenting a new generalized thermoelastic model of thermal conductivity described by the Moore–Gibson–Thompson equation. The new model can be constructed by incorporating the relaxation time thermal model with the Green–Naghdi type III model. The Laplace transformation technique is used to obtain the exact expressions for the radial displacement, temperature and the distributions of thermal stresses. The effects of angular velocity, viscous parameter, and variance in thermal properties are also displayed to explain the comparisons of the physical fields.

Thermo-Optical Mechanical Waves in a Rotating Solid Semiconductor Sphere Using the Improved Green–Naghdi III Model

“…This important conclusion demonstrates the importance of the proposed model, in which the problem of the physical inconsistency found in the CPTE and PGN-III models has been solved. This is fully consistent with the claims of Quintanilla [21] and Abouelregal et al [23][24][25][26].…”

“…The energy Equation ( 7), when combined with the enhanced Fourier law presented in (6), has the same flaw as Fourier's normal model, anticipating that the heat waves will spread quickly. After including the relaxation parameter into the GN-III model, Quintanilla [21,22] and Abouelregal et al [23][24][25] developed the suggested updated heat equation. Fourier's law was proposed to be [21,22] 1…”

“…Quintanilla [21,22] is developing a new MGT heat conduction model. After adding the relaxation parameter to the GN-III model, Abouelregal et al [23][24][25] developed the suggested modified heat equation and employed the energy equation. Since the MGT equation was introduced, the number of papers on this idea has exploded [26][27][28][29].…”

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].…”

Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma

“…This theory began with a third-order differential equation created in the context of fluid mechanics. Since the introduction of the MGT theory [ 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 ], many researchers have devoted their efforts to studying this new model.…”