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The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion.

The field equations for the linear theory of homogeneous isotropic thermoelastic diffusion medium are taken into consideration by using dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. This equation is converted into a polynomial form of higher degree.

From the polynomial equation, Rayleigh wave root is found. The secular equation is resolved into a polynomial form to find the roots and therefore to find the existence and propagation of Rayleigh wave. The existence of Rayleigh wave in the assumed model depends on the values of various parameters involved in the secular equation. These roots are resolved for phase velocity and attenuation of the inhomogeneous propagation of Rayleigh wave. Behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. Particular cases of the interest are also deduced from the present investigation.

Governing equations corresponding to DPLT and DPLD models of thermoelastic diffusion are formulated to study the wave propagation and their dependence on various material parameters. In this paper effects of thermal and diffusion phase lags on the phase velocity, attenuation and on particle paths are observed and depicted graphically.

The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material symmetry. A generalized form of mass diffusion equation is introduced instead of classical Fick's diffusion theory by using two diffusion phase-lags, one phase-lag of diffusing mass flux vector, represents the delayed time required for the diffusion of the mass flux and the other phase-lag of chemical potential, represents the delayed time required for the establishment of the potential gradient. The basic equations for the anisotropic thermoelastic diffusion medium in the context of dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models are presented. The governing equations for transversely isotropic and isotropic case are also reduced. The different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically. Numerically computed results are depicted graphically for anisotropic, transversely isotropic and isotropic medium. The effect of diffusion and thermal phase-lags are shown on the different characteristic of waves. Some particular cases of result are also deduced from the present investigation.

The governing equations of thermoelastic diffusion are presented using DPLT model and a new model of DPLD. Effect of phase-lags of thermal and diffusion is presented on different characteristic of waves.

The effect of diffusion and thermal phase-lags on the different characteristic of waves is appreciable. Also the use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient.

Introduction of a new model of DPLD in the equation of mass diffusion.

The purpose of this paper is to depict the effect of time and thermal and diffusion phase-lags due to axisymmetric heat supply in a ring. The problem is discussed within the context of dual-phase-lag heat transfer and dual-phase-lag diffusion models. The upper and lower surfaces of the ring are traction free and subjected to an axisymmetric heat supply.

The solution is found by using Laplace and Hankel transform technique and a direct approach without the use of potential functions. The analytical expressions of displacements, stresses and chemical potential, temperature and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of time and diffusion and thermal phase-lags are shown on the various components. Some particular cases of result are also deduced from the present investigation.

It is observed that change in time changes the behaviour of deformations of the various components of stresses, displacements, chemical potential function, temperature change and mass concentration. The authors find that for t=0.2, trends are oscillatory in all the cases whereas for t=0.1, trends are quite different. A sound impact of diffusion and thermal phase-lags on the various quantities is observed. A lot of difference in the trends of single phase lag and dual phase lag is observed. The use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient.

This problem is totally new because dual phase lag is applied in heat conduction and diffusion equation while considering the problem of plate in axisymmetric heat supply.

The purpose of this paper is to study of propagation of plane wave and the fundamental solution of the system of differential equations in the theory of a microstretch thermoelastic diffusion medium in phase-lag models for the case of steady oscillations in terms of elementary functions.

Wave propagation technique along with the numerical methods for computation using MATLAB software has been applied to investigate the problem.

Characteristics of waves like phase velocity and attenuation coefficient are computed numerically and depicted graphically. It is found that due to the presence of diffusion effect, these characteristics get influenced significantly. However, due to decoupling of CD-I and CD-II waves from rest of other, no effect on these characteristics can be perceived.

Basic properties of the fundamental solution are established by introducing the dual-phase-lag diffusion (DPLD) and dual-phase-lag heat transfer (DPLT) models.

The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model.

The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique.

The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter.

Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.