Two-temperature Parameter Research Articles

Rotation and gravitational field on a poroelastic medium under the generalized thermoelasticity theory with two-temperature

The poro-thermoelastic problem with two-temperature, under the influence of the gravitational field and the rotation was investigated. The solution to the problem is presented in the context of lord and Shulman's theory of thermoelasticity with one relaxation time. We applied normal mode analysis to solve the resulting non-dimensional coupled partial differential equations. Effect of rotation, gravitational field, two-temperature parameter and porosity parameter on non-dimensional displacements, thermodynamic temperature, conductive temperature, excess pore water pressure and stresses has been discussed. Numerical analyses are given graphically in the square (2D) to illustrate the effect of these parameters. Some particular cases of interest are deduced from the present investigation.

Piezo-photo-thermoelasticity transport process for hyperbolic two-temperature theory of semiconductor material

A general solution for propagating waves in a generalized piezo-photo-thermoelastic medium for the one-dimensional (1D) problem under the hyperbolic two-temperature theory is investigated. The governing equations of the elastic waves, carrier density (plasma wave), quasi-static electric field, heat conduction equation, hyperbolic two temperature coefficient and constitutive relationships for the peizo-thermoelastic medium are obtained using Laplace transformation method in 1D. On the interface adjacent to the vacuum, mechanical stress loads, thermal and plasma boundary conditions are applied to obtain the main basic physical quantities in the Laplace domain. The inversion of Laplace transform by a numerical method is applied to obtain the complete solutions in the Laplace time domain for the main physical fields in this phenomenon. The effects on the force stress, displacement component, temperature distribution and carrier density of the thermoelastic, thermoelectric and hyperbolic two-temperature parameters by the applied force were graphically discussed.

The Fractional Strain Influence on a Solid Sphere under Hyperbolic Two-Temperature Generalized Thermoelasticity Theory by Using Diagonalization Method

This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere. In the context of the hyperbolic two-temperature generalized thermoelasticity theory, the governing equations have been established. Thermally and without deformation, the sphere’s bounding surface is shocked. The singularities of the functions examined at the center of the world were decreased by using L’Hopital’s rule. Numerical results with different parameter fractional-order values, the double temperature function, radial distance, and time have been graphically illustrated. The two-temperature parameter, radial distance, and time have significant effects on all the studied functions, and the fractional-order parameter influences only mechanical functions. In the hyperbolic two-temperature theory as well as in one-temperature theory (the Lord-Shulman model), thermal and mechanical waves spread at low speeds in the thermoelastic organization.

Thermal-stress analysis of a damaged solid sphere using hyperbolic two-temperature generalized thermoelasticity theory

This work aims to study the influence of the rotation on a thermoelastic solid sphere in the context of the hyperbolic two-temperature generalized thermoelasticity theory based on the mechanical damage consideration. Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed. The governing equations have been written in the context of hyperbolic two-temperature generalized thermoelasticity theory. The bounding surface of the sphere is thermally shocked and without volumetric deformation. The singularities of the studied functions at the center of the sphere have been deleted using L’Hopital’s rule. The numerical results have been represented graphically with various mechanical damage values, two-temperature parameters, and rotation parameter values. The two-temperature parameter has significant effects on all the studied functions. Damage and rotation have a major impact on deformation, displacement, stress, and stress–strain energy, while their effects on conductive and dynamical temperature rise are minimal. The thermal and mechanical waves propagate with finite speeds on the thermoelastic body in the hyperbolic two-temperature theory and the one-temperature theory (Lord-Shulman model).

Photothermal plasma wave in the theory of two-temperature with multi-phase-lag thermo-elasticity in the presence of magnetic field in a semiconductor with diffusion

In the present study, the wave propagation in a magneto-thermodiffusion semiconductor, in the context of a two-temperature generalized theory of thermo-elasticity with triple-phase-lag, is studied. The governing equations in plasma theory, during the photothermal process, are formulated and solved for a plane-wave solution to obtain a velocity equation. The velocity equation indicates the existence of four coupled longitudinal waves and one shear transverse wave, namely coupled mass diffusion (CD) wave, coupled longitudinal displacement (LD), coupled thermal (CT) waves, coupled plasma (CP) waves, and shear transverse (SV) waves. The speeds of these plane waves are computed for silicon material. The effect of the magnetic field parameter, diffusion parameters, two-temperature parameter, phase lag, thermal conductivity, and frequency on the speed of these waves is depicted graphically.

Effect of non-locality in the vibration of a micro-scale beam under two-temperature memory responses

ABSTRACT The vibration of elastic micro-beam is of major significance due to wide applications of ultra-fast lasers, where size effect on heat conduction and elastic deformation increase and classical theory of thermoelastic coupling does not hold any more. Accordingly, the size-dependent thermoelastic model has been developed to deal with higher-order simple material to adopt both size effect of heat conduction and elasticity with the aids of extended irreversible thermodynamics and generalized free-energy. This survey demonstrates the effect of ultra-short-pulsed laser heating in the problem of coupled thermoelastic vibration of a microscale resonator, in which, the non-local heat transport equation is drafted in an integral form of a common derivative on a slipping interval by incorporating the three-phase-lag memory-dependent heat transfer in the context of two-temperature theory. Laplace transform and finite sinusoidal Fourier transform techniques have been employed to determine the lateral vibration of the beam and the scaled thermal moment within the beam. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Specific attention is paid to study the effect of thermal non-local parameter, energy absorption depth, memory-dependent derivative, the two-temperature parameter and delay time also.

A novel theory of generalized thermoelasticity based on thermomass motion and two-temperature heat conduction

The present paper constructs a new theory of two-temperature generalized thermoelasticity based on thermomass motion consideration. The governing equations of the theory are formulated for heterogeneous, anisotropic, and homogenous materials. Moreover, the uniqueness theorem of the equations of the new theory is proved. The theory based on the motion of thermomass predicts the propagation of thermoelastic waves in the micro-scale heat conduction with finite speed. The two-temperature parameter has significant effects on the conductive temperature increment, dynamical temperature increment, strain, displacement, and stress distributions. The two-temperature generalized thermoelasticity with thermomass motion theory introduces a successful thermoelastic model.

A hyperbolic two-temperature photo-thermal interactions in a semiconductor material

This work is concerned with the study of the thermodynamic temperature, conductive temperature, the carrier density, displacement and stress in a semi-infinite semiconductor medium during the photo-thermal process. The medium is considered to be a semiconducting media with an isotropic and homogeneous. Also, the thermal and elastic properties have been considered without neglecting the coupling between the thermoelastic and the plasma waves. The techniques of Laplace transforms are used to get the analytical solutions of the problem in the transformed domain by the eigenvalues method and the inversions of Laplace transformations have been carried numerically. The results are graphically represented to show the effects of the two-temperature parameter.

The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

On the characterization and stability of plane waves under hyperbolic two-temperature generalized thermoelasticity

The propagation and stability (Whitham’s criteria) of harmonic plane waves are described in the context of the hyperbolic two-temperature generalized thermoelasticity in which heat conduction in deformable bodies depends upon the difference between the double derivative of conductive and dynamic temperature. The exact dispersion relation solutions for the longitudinal plane wave are derived analytically. Several characterizations of the wave field, like phase velocity, specific loss, penetration depth, amplitude coefficient factor, and phase shift are examined for the low as well as high frequency asymptotic expansions. For the validity of analytical findings and to study the effect of varying hyperbolic two-temperature parameter on different characterizations, the numerical computation of a particular example is illustrated and displayed graphically. The results of some earlier works have been deduced and discussed from the present investigation as speciallimiting cases.

Characterization of the thermal quality factor of two-temperature micro-viscothermoelastic resonator due to static-pre-stress based on dual-phase-lagging heat conduction

Thermal and mechanical relaxation times play essential roles in the thermal quality factor Q-factorof the micro-resonators, where controls the energy damping through the coupling of thermal and mechanical behavior. In this work, we developed an analytical mathematical model that assumed a pre-stress in a two-temperature micro-viscothermoelastic resonator of silicon to modify the thermal and mechanical relaxation times and thus increase the thermal quality factor. The impacts of length-scale and pre-stress on the thermal quality factor have been discussed. The present model predicts that significant enhancement in terms of thermal quality factors is enabled by tuning the static-pre-stress, the thermal and mechanical relaxation times parameters. The isothermal value of frequency and the two-temperature parameter have impact effects on the thermal quality factor of the micro-resonators.

Reflection of plane waves in magneto-micropolar thermoelastic medium with voids and one relaxation time due to gravity and two-temperature theory

The present model presents the reflection phenomena in a linear and homogenous micropolar thermoelastic isotropic medium with voids. The effects of gravity and magnetic field are investigated in the case of two-temperature theory. The studied problem is investigated, under Lord and Shulman (L–S) theory with one (delay) relaxation time, analytically with constant amplitudes. It is shown that there exist five reflected plane waves: longitudinal, shear, thermal and those due micropolar and voids waves. In addition, the values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of gravity, two-temperature parameter, magnetic field, time, variant angles of incidence and micropolarity with voids. The present results are applicable in many fields such as earthquakes engineering, nuclear physics and manufacturing. It is found that the obtained results are significant.

Waves in generalized thermo-viscoelastic infinite continuum with cylindrical cavity due to three-phase-lag time-nonlocal heat transfer

Generalized thermoelastic interactions due to three-phase-lag time-nonlocal heat transfer in a Kelvin-Voigt type infinitely extended visco-thermoelastic continuum with cylindrical cavity has been investigated. The two-temperature generalized thermoelasticity theory has also been taken into account. The problem has been solved in the domain of Laplace on the assumption that the surface of the cavity is free from traction and is subjected to a smooth and time-dependent-heating effect. Laplace inversion of the transformed solutions has been carried out numerically. The obtained numerical data for different considerations are plotted in graphs to study the effects of time-nonlocal parameter, two-temperature parameter and visco-thermoelastic relaxation parameter on different thermoelastic quantities of physical interest.

Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity

The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the Green- Lindsay (G-L) theory, the coupled (CD) theory, and the Lord-Shulman (L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock. The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.

Two-temperature fractional Green–Naghdi of type III in magneto-thermo-viscoelasticity theory subjected to a moving heat source

In this work, we construct a mathematical model of two-temperature Green–Naghdi (III) magneto-thermo viscoelasticty theory based on the fractional order of heat transfer. Some essential theorems of coupled and generalized thermo-viscoelasticity can be easily obtained. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The resulting formulation is applied to the specific problem of a perfect electrically conducting viscoelastic half-space subjected to a moving heat source with constant velocity and ramp-type heating. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The effects of the heat source speed, the two-temperature parameter, Alfven velocity and the ramping time parameter on a polymethyl methacrylate (Plexiglas) material are discussed.

Effects of Two-Temperature, Rotation, Initial Stressed Magnetic Field on Rayleigh Wave in Half-Plane

Abstract In the present paper, we consider the governing equation for generalized thermoelastic media under the effect of magnetic fleld, rotation, initial stress, and two-temperature parameter for Rayleigh wave in half-space. The secular equation of Rayleigh wave is also deduced using surface wave solution, which also satisfy the radiation condition for thermally insulated/isothermal surface. The velocity and amplitude attenuation factor of Rayleigh wave is also computed for a particular material. The effect of two-temperature, rotation, and initial stress parameters on velocity of propagation and amplitude attenuation factor is shown graphically.

Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responses

This article highlights on the study of coupled plasma, thermal and elastic waves within an orthotropic infinite semiconducting medium in context of photothermal transport process having a spherical cavity under two-temperature theory. The memory-dependent heat transport equation for the present problem is involving the two-temperature dual-phase (DP) lag model of generalized thermoelasticity. The inner boundary of the cavity is stress free and is subjected to an exponentially decaying pulse. Moreover, the carrier density is prescribed on the boundary in terms of the recombination velocity. Employing the Laplace transform as tool, the analytical results for the distributions of the thermophysical quantities have been derived. The numerical inversion of the Laplace transform is carried out using a suitable scheme based on the Riemann-sum approximation technique. Numerical computations for an orthotropic semiconductor are performed and have been demonstrated graphically. The results also demonstrate the effect of coupling between plasma, thermal and elastic waves due to the presence of several kernel functions and response of memory effect. Also, significant differences on the thermophysical quantities are revealed due to the influence of two-temperature parameter, memory effect and time-delay parameter.

Influence of Moving Heat Source on Skin Tissue in the Context of Two-Temperature Caputo–Fabrizio Heat Transport Law

Modeling and understanding heat transport and temperature variations within biological tissues and body organs are key issues in medical thermal therapeutic applications, such as hyperthermia cancer treatment. In this analysis, the bio-heat equation has been studied in the context of a new formulation using Caputo–Fabrizio (CF) heat transport law. The heat equation for this problem involving the Three-Phase (3P)-lag model under two-temperature theory. The Laplace transform technique is implemented to solve the governing equations. The influences of the CF order, the two-temperature parameter and moving heat source velocity on the temperature of skin tissues have been precisely investigated. The numerical inversion of the Laplace transform is carried out using the Zakian method. The numerical outcomes of conductive temperature and thermodynamic temperatures have been represented graphically. Excellent predictive capability is demonstrated for identification of appropriate procedure to select different CF order to reach effective heating in hyperthermia treatment. Significant effect of thermal therapy is reported due to the effect of CF order, the two-temperature parameter and the velocity of moving heat source as well.

The effect of gravity field in a two-temperature fiber-reinforcement thermoelastic half-space with dual-phase-lag model

A new model of generalized thermoelasticity equations for a fiber-reinforced medium with two temperatures under influence of the gravity field and the magnetic field is established. The present model has described both generalizations, Lord–Shulman theory with one relaxation time and dual-phase-lag model instantaneously. The normal mode analysis is used to solve the resulting non-dimensional coupled field equations. Finally, the resulting quantities are depicted graphically to show the effect of the gravity field, two-temperature parameter and the reinforcement on all physical quantities.

Eigenvalue approach on a problem of magneto-thermoelastic rotating medium with variable thermal conductivity: comparisons of three theories

In the present article, we apply the eigenvalue approach on the two-dimension problem of thermoelasticity in the context of the Green-Lindsay theory (G-L) with two relaxation times, coupled theory (CD) and Lord- Shulman theory (L-S) with one relaxation time. The governing equations of the thermoelastic medium with two temperatures are solved for surface wave solutions. The numerical estimates of the quantities of physical interest is obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, two-temperature parameter, rotation, magnetic field, and mechanical force.