Abstract
In the current article, in the presence of thermal and diffusion processes, the equations governing elastic materials through thermodiffusion are obtained. The Moore–Gibson–Thompson (MGT) equation modifies and defines the equations for thermal conduction and mass diffusion that occur in solids. This modification is based on adding heat and diffusion relaxation times in the Green–Naghdi Type III (GN-III) models. In an unbounded medium with a cylindrical hole, the built model has been applied to examine the influence of the coupling between temperature and mass diffusion and responses. At constant concentration as well as intermittent and decaying varying heat, the surrounding cavity surface is traction-free and is filled slowly. Laplace transform and Laplace inversion techniques are applied to obtain the solutions of the studied field variables. In order to explore thermal diffusion analysis and find closed solutions, a suitable numerical approximation technique has been used. Comparisons are made between the results obtained with the results of the corresponding previous models. Additionally, to explain and realize the presented model, tables and figures for various physical fields are presented.
Highlights
The theory of thermoelasticity has received a lot of interest from researchers and scientists due to its many applications in different fields
The model and equations derived and obtained in the second section of this paper are valid for many special cases that can be inferred from our constructed model
A new generalized thermoelastic diffusion model has been derived in the present paper, connecting heat and mass flux in elastic materials
Summary
The theory of thermoelasticity has received a lot of interest from researchers and scientists due to its many applications in different fields. Researchers provided alternative theories of coupled thermoelasticity, which became widely known as a general thermoelastic theory This concept has been gaining fame in recent years because its aim is to solve the contradiction of the unlimited heat propagation rate. Quintanilla [15] has built a new model of thermoelastic heat conduction (called “MGT thermoelasticity”) based on the Moore–Gibson– Thompson equation Another new thermoelastic model with two temperatures, in which heat conduction was described as the historical MGT version, was given by Quintanilla [16], which emerged from the development of the theory of Green–Naghdi Type III by adding a relaxation factor. A new theory of thermal diffusion is formulated in this present work, in which the Moore–Gibson–Thompson equation defines the heat conduction and diffusion formulae This model was designed to explore the interaction between elasticity, heat, and the mechanisms of diffusion of elastic materials that allow the propagation of thermal waves at finite rates. Numerical values have been provided in figures and tables to illustrate the comparisons between the physical fields in order to allow a distinction between the results we obtained and the corresponding results in other special models
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