Thermoelastic Diffusion Media Research Articles

Effect of three-phase-lag thermal and three-phase-lag diffusion models on waves at the boundary of elastic and thermoelastic diffusion medium

In this paper, we discuss the reflection and refraction of an incident P wave or [Formula: see text] wave at the interface of a plane. The plane, which is divided into two halves, is an elastic medium [Formula: see text] having an incident wave and a thermoelastic diffusion medium [Formula: see text] with TPLT (i.e., three-phase-lag thermal) and TPLD (i.e., three-phase-lag diffusion) models. It has been noticed that two waves are reflected and four are refracted in an isotropic thermoelastic diffusion medium. Out of the four refracted waves, three are longitudinal waves: a quasi-longitudinal wave [Formula: see text] a quasi-mass diffusion wave [Formula: see text], a quasi-thermal wave [Formula: see text] and one is a transverse wave [Formula: see text]. If we consider the above waves first, the amplitude and energy ratio are calculated by using the surface boundary conditions and then graphically represented to compare the change in energy and amplitude ratio with the change in incident angle for three particular cases. The conservation of energy is depicted by verifying that all the energy sums up to unity. The considered problem has its application in earthquake engineering, astronautics, rocket engineering, seismology and many more engineering areas.

Reflection of plane waves in an orthotropic micropolar thermoelastic diffusive medium with two-temperature

Reflection of plane waves in an orthotropic micropolar thermoelastic diffusive medium with two-temperature

Thermoelastic waves in a fractional-order initially stressed micropolar diffusive porous medium

The research article is the analysis of wave propagation in an initially stressed micropolar fractional-order derivative thermoelastic diffusion medium with voids. The governing equations in the context of generalized fractional-order derivative thermo-elasticity are formulated and the velocity equations are obtained. The plane wave solution of these equations indicates the existence of six plane waves, namely coupled longitudinal displacement (cL), coupled thermal (cT), coupled mass diffusion (cMD), coupled longitudinal void volume fraction (cV), coupled transverse displacement (cTD), and coupled transverse micro-rotational (cTM) waves. The sets of coupled waves (cL), (cT), (cMD) and (cV) are found to be dispersive, attenuating and influenced by the presence of thermal, diffusion and voids parameters in the medium. The speeds of coupled transverse displacement (cTD), and coupled transverse micro-rotational (cTM) waves are not affected by thermal, diffusion and void parameters. The speeds of the plane waves, cL,cT,cMD,andcVare computed for a particular material and plotted against the thermal parameter, frequency, initial stress, diffusion and void parameters.

Wave propagation in an initially stressed rotating thermo-diffusive medium with two-temperature and micro-concentrations

PurposeThe purpose of this paper is to study the reflection of plane waves in an initially stressed rotating thermoelastic diffusive medium with micro-concentrations and two-temperature.Design/methodology/approachA two-dimensional model of generalized thermoelasticity is considered. The governing equations are transformed into the non-dimensional forms using the dimensionless variables. Then, potential functions are introduced for the decoupling of the waves. Further, appropriate boundary conditions are assumed to completely solve the problem. Finally, numerical computations are performed using MATLAB.FindingsThe problem is solved analytically and it is found that there exist five coupled waves in addition to an independent micro-concentration wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have also been computed numerically for a specific material.Originality/valueThe modulus values of amplitude ratios are presented graphically to exhibit the effects of angular velocity, initial stress, two-temperature, diffusion and micro-concentration parameters. The expressions of energy ratios obtained in explicit form are also depicted graphically as functions of angle of incidence. The law of conservation of energy at the free surface during reflection phenomenon is also verified.

Reflection of plane waves in a thermoelastic diffusive medium under the effect of microtemperatures

The present analysis is aimed to model and study the characteristics of various reflected waves in a homogeneous and isotropic thermoelastic diffusive half-space with microtemperatures. It is shown that there exist four kinds of coupled longitudinal waves in addition to transverse and microtemperature waves in such type of medium. The reflection coefficients and energy ratios of these reflected waves have been computed numerically with the help of MATLAB programing when (i) a set of coupled longitudinal waves is made incident and (ii) a transverse wave is made incident. The numerical values of modulus of reflection coefficients are presented graphically to depict the effect of thermodiffusive parameter. It has been verified that there is no dissipation of energy at the free plane boundary during reflection phenomena.

Elastodynamic interactions of laser pulse in microstretch thermoelastic mass diffusion medium with dual phase lag

The aim of the present investigation is to study the effects of laser heat source and phase lags on a microstretch thermoelastic mass diffusion medium including dual phase lag model. The normal mode analysis technique has been adopted to obtain the components of displacement, microrotation, microstress, mass concentration and temperature distribution due to the presence of ultra-laser heat source. The numerical computation has been performed (using Matlab software) on the resulting quantities. The computed numerical results are shown graphically to depict the effect of laser heat source and diffusion phase-lags. Some particular cases of interest are also deduced from the present investigation.

A problem of thick circular plate in modified couple stress thermoelastic diffusion with phase-lags

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.

Elastodynamic Response of Thermal Laser Pulse in Micropolar Thermoelastic Mass Diffusion Medium

The present investigation deals with the deformation in micropolar thermoelastic diffusion medium due to inclined load subjected to thermal laser pulse. Normal mode analysis technique is used to solve the problem. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The closed form expressions of normal stress, tangential stress, couple stress, temperature distribution, and mass concentration are obtained. A computer program has been developed to derive the physical quantities numerically. The variation of normal stress, tangential stress, coupled stress, temperature change, and mass concentration is depicted graphically to show the effect of relaxation times and mass concentration. Some particular cases of interest are deduced from the present investigation.

Effect of phase-lags on Rayleigh wave propagation in thermoelastic medium with mass diffusion

Purpose– The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion.Design/methodology/approach– 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.Findings– 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.Originality/value– 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.

A study of plane wave and fundamental solution in the theory of microstretch thermoelastic diffusion solid with phase-lag models

Purpose – 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. Design/methodology/approach – Wave propagation technique along with the numerical methods for computation using MATLAB software has been applied to investigate the problem. Findings – 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. Originality/value – Basic properties of the fundamental solution are established by introducing the dual-phase-lag diffusion (DPLD) and dual-phase-lag heat transfer (DPLT) models.

Dual-Phase-Lag Model of Wave Propagation at the Interface Between Elastic and Thermoelastic Diffusion Media

A dual-phase-lag diffusion model, augmenting the Fick law by the inclusion of the delay times of the mass flow and the potential gradient at the interface between two media into it, is proposed. The effects of reflection and refraction of plane waves at the interface between an elastic and a thermoelastic diffusion media were investigated with the use of this model. It was established that the ratios between the amplitudes and energies of the waves reflected and refracted at the interface between the indicated media are determined by the angle of incidence of radiation on this interface, the frequency of the incident wave, and the thermoelastic and diffusion properties of the media. Expressions for the ratios between the energies of different reflected and refracted waves and the energy of the incident were derived. The variation in these ratios with change in the angle of incidence of radiation on the indicated interface was calculated numerically and represented graphically.

Plane wave propagation in an anisotropic dual-phase-lag thermoelastic diffusion medium

Purpose– 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.Design/methodology/approach– 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.Findings– 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.Originality/value– Introduction of a new model of DPLD in the equation of mass diffusion.

Wave propagation at the boundary surface of an elastic and thermoelastic diffusion media with fractional order derivative

The purpose of this research is to study the reflection and refraction of obliquely incident plane wave at the interface of elastic and thermoelastic diffusion media with fractional order derivative. Lord–Shulman [1] theory of thermoelasticity using the methodology of fractional calculus is used to investigate the problem. It is noticed that three type of longitudinal waves and one transverse wave propagate in an isotropic thermoelastic diffusion medium. The amplitude and energy ratios of various reflected and refracted waves are obtained and it is found that these are the functions of incidence angle and frequency of that incident wave. The variation of modulus of amplitude ratios and energy ratios with the angle of incidence for different fractional orders are computed numerically using continuous boundary conditions for the copper material. The computed numerical results are depicted graphically for the variation of energy ratios with the angle of incidence. It has been verified that the sum of energy ratios is equal to unity at the interface. Some particular cases of interest are also deduced from the present investigation.

Numerical analysis of the propagation characteristics of Stoneley waves at an interface between microstretch thermoelastic diffusion solid half spaces

This paper is concerned with the study of propagation of Stoneley waves at the interface of two dissimilar isotropic microstretch thermoelastic diffusion medium in the context of generalized theories of thermoelasticity. The dispersion equation of Stoneley waves is derived in the form of a determinant by using the boundary conditions. The dispersion curves giving the phase velocity and attenuation coefficients with wave number are computed numerically. Numerically computed results are shown graphically to depict the diffusion effect alongwith the relaxation times in microstretch thermoelastic diffusion solid half spaces for thermally insulated and impermeable boundaries, respectively. The components of displacement, stress, couple stress, microstress, and temperature change are presented graphically for two dissimilar microstretch thermoelastic diffusion half-spaces. Several cases of interest under different conditions are also deduced and discussed.

Fundamental Solution for the Plane Problem in Magnetothermoelastic Diffusion Media

The aim of the present paper is to study the fundamental solution in orthotropic magneto- thermoelastic diffusion media. With this objective, firstly the two-dimensional general solution in orthotropic magnetothermoelastic diffusion media is derived. On the basis of thegeneral solution, the fundamental solution for a steady point heat source in an infinite and a semi- infinite orthotropic magnetothermoelastic diffusion material is constructed by four newly introduced harmonic functions. The components of displacement, stress, temperature distribution and mass concentration are expressed in terms of elementary functions. From the present investigation, some special cases of interest are also deduced and compared with the previously obtained results. The resulting quantities are computed numerically for infinite and semi-infinite magnetothermoelastic material and presented graphically to depict the magnetic effect.

Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with a fractional order derivative

In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.

Numerical study of wave propagation in thermoelastic diffusive medium by using differential quadrature method

PurposeThe purpose of this paper is to study the wave propagation in thermoelastic diffusive medium.Design/methodology/approachThe present paper deals with the numerical study of wave propagation in coupled thermoelastic diffusive medium by using DQ method together with fourth‐order Runge‐Kutta method.FindingsThe paper finds solutions of displacements, temperature change and concentration.Research limitations/implicationsThe paper can be sued to solve non‐linear partial differential equations.Originality/valueThe solutions of displacements, temperature change and concentration are illustrated graphically. Numerical examples show that the method yields very good results.

A study of influence of diffusion inside a spherical shell under thermoelastic diffusion with relaxation times

The present work is concerned with the elasto-thermo-diffusion interactions inside a spherical shell whose inner and outer boundaries are traction free and are subjected to a step input in temperature under generalized thermoelastic diffusion. The chemical potential is also assumed to be a function of time on the boundaries of the shell. The problem is studied by employing three different theories of thermoelastic diffusion in a unified way. The integral transform technique is used to obtain the general solution. Using a numerical method and computer programming, the final solution in the physical domain is obtained. The results corresponding to thermoelastic medium, that is, in the absence of diffusion, are also found in a particular case. The influence of diffusion on variation of physical fields due to the cross effects arising from the coupling of temperature, diffusion and strain fields inside the shell is analyzed with the help of graphically plotted results of different field variables in the thermoelastic medium and thermoelastic diffusive medium. The variation of this influence with time under different theories is also discussed. The significant points are highlighted.

Analysis of plane waves in anisotropic thermoelastic diffusive medium

This paper concentrates on the study of the propagation of harmonic plane waves in a homogeneous anisotropic thermoelastic diffusive medium in the context of different theories of thermoelastic diffusion. It is found that five types of waves propagate in an anisotropic thermoelastic diffusive medium, namely a quasi-elastodiffusive (QED-mode), two quasi-transverse (QSH-mode and QSV-mode), a quasi-mass diffusive (QMD-mode) and a quasi-thermo diffusive (QTD-mode) wave. The governing equations for homogeneous transversely isotropic diffusive medium in different theories of thermoelastic diffusion are taken as a special case. It is noticed that when plane waves propagate in one of the planes of transversely isotropic thermoelastic diffusive solid, purely quasitransverse wave mode(QSH) decouples from rest of the motion and is not affected by the thermal and diffusion vibrations. On the other hand, when plane waves propagate along the axis of solid, two quasi-transverse wave modes (QSH and QSV) decouple from the rest of the motion and are not affected by the thermal and diffusion vibrations. From the obtained results, the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically for a single crystal of magnesium. The effects of diffusion and relaxation times on phase velocity, attenuation coefficient, specific loss and penetration depth has been studied. Some particular cases are also discussed.

A study of axi-symmetric waves through an isotropic thermoelastic diffusive medium

The paper deals with the propagation of axial symmetric cylindrical surface waves in a cylindrical bore through a homogeneous isotropic thermoelastic diffusive medium of infinite extent. The three theories of thermoelasticity namely, Coupled Thermoelasticity (CT), Lord and Shulman (L-S) and Green and Lindsay (G-L) are used to study the problem. The frequency equations, connecting the phase velocity with wave number, radius of bore and other material parameters, for empty and liquid filled bore are derived. The numerical results obtained have been illustrated graphically to understand the behaviour of phase velocity and attenuation coefficient versus wave number of a wave. A particular case of interest has also been deduced from the present investigation.