Abstract
Abstract In the past few decades, many models have been proposed to address the shortcomings found in the classical theories of thermoelasticity and to allow limited speeds of heat waves. In this context, in the current paper a new generalized model of thermoelasticity based on the Moore–Gibson–Thompson (MGT) equation has been introduced. This new model can be derived by introducing the relaxation time factor into the third type of Green–Naghdi model (GN-III). In contrast to the previous works, it was taken into account that the physical properties of the material are dependent on temperature and on the viscous type. The viscoelastic medium has been assumed to obey the Kelvin–Voigt model. On the basis of the present model, thermo-viscoelastic interactions have been investigated in an unbounded orthotropic body with a cylindrical cavity. The surface of the cavity is restricted and exposed to a pulse-formed heat flow that dissolves exponentially. The characteristic thermal modulus of the material is assumed to be a linear function of temperature. The Laplace transform can be used to eliminate time dependency from control equations. Using a suitable approximate method, the transformed equations have been finally inverted by numerical inversion of the Laplace transform. Certain comparisons have been introduced to estimate the effects of the viscosity, pulsed heat, and thermal temperature-independent properties on all studied fields. A comparison with previous models of thermoelasticity is also performed in tables to verify the accuracy of the proposed model. We found from the results that the physical fields strongly depend on the viscoelastic parameter, the change of the thermal conductivity, and pulsed heat, so it is not possible to neglect their effect on the manufacturing process of machines and devices.
Highlights
In materials science, research and electronics, building insulation, and related fields, thermal conductivity is important, when achieving high temperatures
We found from the results that the physical fields strongly depend on the viscoelastic parameter, the change of the thermal conductivity, and pulsed heat, so it is not possible to neglect their effect on the manufacturing process of machines and devices
Alloys reduce the change in electrical conductivity, so the thermal conductivity of temperature increases in proportion to the temperature
Summary
Research and electronics, building insulation, and related fields, thermal conductivity is important, when achieving high temperatures. This suggestion is generally modified and a relaxing factor is included to solve this problem [23] In this presented work, we will present a new effort to remove the paradox inherent in the classical coupled theory that is based on Fourier’s law of thermal conductivity as well as the third type of Green and Naghdi theories. The study of thermal conductivity, especially if it depends on a change in temperature, is very important in many areas of physical, chemical, engineering, and other applications For this reason thermal and mechanical reactions were studied inside an elastic, viscous, infinite body with a cylindrical cavity, taking into account that the coefficient of thermal conductivity is dependent on the change of temperature. The results showed that the new MGT thermoelasticity model fits the experimental data and physical phenomena better in contrast to the traditional thermoelastic models
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