Abstract
In this work, the thermo-diffusions interaction in an unbounded material with spherical cavities in the context dual phase lag model is investigated. The finite element technique has been used to solve the problem. The bounding surface of the inner hole is loaded thermally by external heat flux and is traction-free. The delay times caused in the microstructural interactions, the requirement for thermal physics to take account of hyperbolic effects within the medium, and the phase lags of chemical potential and diffusing mass flux vector are interpreted. A comparison is made in the case of the presence and the absence of mass diffusions between coupled, Lord-Shulman and dual phase lag theories. The numerical results for the displacement, concentration, temperature, chemical potential and stress are presented numerically and graphically.
Highlights
The classical thermoelastic theory [1] depends on the Fourier hypothesis of heating conductivity
Lord and Shulman [3] are the two pioneers who contributed most to coupled thermo-elasticity by introducing the generalized theory of thermo-elasticity through alteration of the parabolic nature of the heat conduction equation to a hyperbolic nature. They made this revolutionary change in the nature of the heat conduction equation by incorporating a relaxation time parameter in Fourier’s law of heat conduction and, in doing so, the unrealistic phenomenon of the infinite speed of thermal wave propagation was replaced by practical observation of the finite speed of propagation of thermal waves
Following Sherief et al [7,18], the basic equations for an isotropic, elastic soled with the thermo-diffusions under a dual phase lag model at uniform temperature To in the absence of heating sources and body forces, can be expressed as: The equations of motion as in [7] are μui,jj μ)uj,jj βt T,i
Summary
The classical thermoelastic theory [1] depends on the Fourier hypothesis of heating conductivity. The coupled thermoelastic diffusion theories predict an unrealistic infinite speed of thermal wave propagation Surpassing this impractical generalized thermoelastic diffusion theory, the Lord-Shulman model was first proposed by Sherief, et al [7], introducing a diffusion relaxation parameter into the well-known. Several problems have been raised by generalized thermoelastic models as in [27,28,29,30,31,32,33,34,35,36,37,38,39,40] The aim of this investigation is to introduce e dual phase lag thermo-diffusion formulations instead of Fick’s classical diffusions model by using two diffusion lags. The effects of thermal lags are shown in the different components
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