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.

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

Based on the generalized thermoelastic diffusion theory with fractional order derivative, the dynamic response of an infinite thermoelastic medium with a spherical cavity is investigated. The therm...

Dynamic analysis to the fractional order thermoelastic diffusion problem of an infinite body with a spherical cavity and variable material properties

Investigation of generalized piezoelectric-thermoelastic problem with nonlocal effect and temperature-dependent properties.

Thermal and mass diffusion processes are important issues in a variety of engineering applications and scientific disciplines. The main objective of this research is to develop a new model that demonstrates diffusion in thermoelastic solids and compares the strain/temperature fields and mass diffusion. The proposed model is an extension of the Quintanilla model [1]. In the new model, Fourier’s and Fick’s laws have been improved by including the relaxation times in the Green–Naghdi theory in the framework of Moore–Gibson–Thompson (MGT) heat equation. Based on the introduced model, a one-dimensional half-space problem is considered. The surface surrounding the half-space is exposed to chemical potential and thermal shocks. Our findings indicate that the considered physical fields have a non-zero value only in a limited area and disappear outside this area. This result fully demonstrates the validity of the proposed model because the nature of velocities is limited by heat and diffusive waves.

A new insight into the interaction of thermoelasticity with mass diffusion for a half-space in the context of Moore–Gibson–Thompson thermodiffusion theory

Chunbao Xiong

Papers

Electromagneto-thermoelastic diffusive plane waves in a half-space with variable material properties under fractional order thermoelastic diffusion