The Effect of Gravity Field on the Plane Waves in a Fiber-Reinforced Two-Temperature Magneto-Thermoelastic Medium Under Lord-Shulman Theory

The aim of the present work is to investigate the influence of the gravity field on the plane waves in a linearly fiber-reinforced magneto-thermoelastic isotropic medium in the context of the two-temperature theory of generalized thermoelasticity under Lord-Shulman model. The problem has been solved numerically using the normal mode analysis together with the eigenvalue approach. Numerical results for the conductive temperature, thermodynamic temperature, displacement components and the stresses are represented graphically and the results are analyzed. The graphical results indicate that the effect of the two-temperature parameter, gravity field and the magnetic field on the plane waves in the fiber-reinforced thermoelastic medium are very pronounced. Comparisons are made with the results in the presence and absence of the two-temperature parameter, gravity field and the magnetic field. Such problems are very important in many dynamical systems.     

A Unified Generalized Thermoelasticity Formulation; Application to Thick Functionally Graded Cylinders

In this article a new unified formulation for the generalized coupled thermoelasticity theories is presented. The generalized coupled thermoelasticity theories proposed by Lord–Shulman, Green–Lindsay, and Green–Naghdi are combined into a unified formulation introducing the unified parameters. The formulation is given for the general anisotropic heterogeneous linear thermoelastic materials and then is reduced to the system of equations for the isotropic heterogeneous materials. As an example, a functionally graded cylinder is considered and the thermoelastic waves based on the new unified formulation, using the generalized theories, are obtained and discussed. Utilizing the transfinite element method, the equations for a long thick circular cylinder are solved in the Laplace domain and the results are inverted to the real time domain using a numerical inversion technique of the Laplace transform. The results for the propagation of thermoelastic waves based on the Lord–Shulman, Green–Lindsay, and Green–Naghdi models are derived and compared.     

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

Abstract

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.     

Two temperature fractional order thermoelasticity theory in a spherical domain

This article is an application of fractional thermoelasticity in association with two-temperature theory. The fractional heat conduction model has been proposed to investigate the thermal variations within the bounded spherical region. The corresponding heat conduction equation has been derived in the context of the generalized two-temperature theory of fractional thermoelasticity. The analytical solutions of thermal variations have been obtained in the Laplace domain, which are inverted using the Gaver–Stehfest algorithm in the time domain. Kuznetsov convergence criterion has been discussed for the bounded variations and stability of the problem. The delay time translations used in the heat flux vector and the temperature gradient result in the finite speed of thermal wave propagation. As a special case of time fractional derivative, the classical and generalized thermoelasticity theories have been recovered.     

Theory of Two-Temperature Thermoelasticity without Energy Dissipation

This paper deals with thermoelastic behavior without energy dissipation; it deals with linear theory of thermoelasticity. In particular, in this work, a new theory of generalized thermoelasticity has been constructed by taking into account two-temperature generalized thermoelasticity theory for a homogeneous and isotropic body without energy dissipation. The new theorem has been derived in the context of Green and Naghdi model of type II of linear thermoelasticity. Also, a general uniqueness theorem is proved for two-temperature generalized thermoelasticity without energy dissipation.     

Eigenfunction expansion method to analyze thermal shock behavior in magneto-thermoelastic orthotropic medium under three theories

This article is concerned with a study of thermal shock response in infinite thermoelastic medium under the purview of Lord–Shulman model, Green–Naghdi theory III, and three-phase-lag model of generalized thermoelasticity. The medium under consideration is assumed to be homogeneous, orthotropic, and thermally conducting. The fundamental equations of the two-dimensional problem of generalized thermoelasticity with three-phase-lag model in an infinite elastic medium under the influence of magnetic field are obtained as a vector–matrix differential equation form using normal mode analysis which is then solved by the Eigenfunction expansion method. Numerical results for the temperature, displacements and thermal stress distribution are presented graphically.     

Generalized Coupled Thermoelasticity of a Layer

The generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Naghdi (GN) theories admit the second sound effect. By introducing some parameters all these theories are combined and a unified set of equations is rendered. These equations are then solved for a layer of isotropic and homogeneous material to study the thermal and mechanical wave propagations. The disturbances are generated by a sudden application of temperature to the boundary. The non-dimensionalized form of the governing equations are solved utilizing the Laplace transform method in time domain. Closed form solutions are obtained for the layer in Laplace transform domain, and a numerical inverse Laplace transform method is used to obtain the temperature, displacement, and stress fields in the physical time domain. The thermo-mechanical wave propagations and reflections from the layer boundaries are investigated.     

Memory response for thermal distributions moving over a magneto-thermoelastic rod under Eringen’s nonlocal theory

Abstract

Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of Lord–Shulman (LS) theory of thermoelasticity based on Eringen’s nonlocal elasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effects of moving heat source speed, time instance, memory-dependent derivative, magnetic field and nonlocality on temperature, stress, and temperature are studied.     

Thermoelastic Damping in Nanomechanical Resonators Based on Two-Temperature Generalized Thermoelasticity Theory

This work is concerned with the study of the thermoelastic damping of nanobeam resonators in the context of the two-temperature generalized thermoelasticity theory. An explicit formula of thermoelastic damping has been derived. Influences of the beam height, the relaxation time parameter, the two-temperature parameter and the isothermal value of frequency have been studied with some comparisons between the Biot model and Lord–Shulman model (L–S). Numerical results show that the values of thermal relaxation parameter and the two-temperature parameter have a strong influence on thermoelastic damping in nanoscales.     

Convolutional Variational Principle,Reciprocal and Uniqueness Theorems in Linear Fractional Two-Temperature Thermoelasticity

Two general models of fractional heat conduction law for non-homogeneous anisotropic elastic solid is introduced and the constitutive equations for the two-temperature fractional thermoelasticity theory are obtained, uniqueness and reciprocal theorems are proved and the convolutional variational principle is established and used to prove a uniqueness theorem with no restrictions imposed on the elasticity or thermal conductivity tensors except symmetry conditions. The two-temperature dynamic coupled, Lord-Shulman and fractional coupled thermoelasticity theories result as limit cases. The reciprocity relation in case of quiescent initial state is found to be independent of the order of differintegration.     

A PROBLEM OF GENERALIZED MAGNETOTHERMOELASTICITY FOR AN INFINITELY LONG,PERFECTLY CONDUCTING CYLINDER

This article concerns the investigation of the stress, temperature, and magnetic field in a transversely isotropic, elastic cylinder of infinite length and perfectly conducting material placed in a primary constant magnetic field when the curved surface of the cylinder is subjected to periodic loading. The analysis encompasses Lord and Shulman and Green and Lindsay theories of generalized thermoelasticity to account for the finite velocity of heat equation. The analysis of the numerical results for stress, temperature, and numerical values of the perturbed magnetic field in the free space is carried out at various points of the cylindrical medium. It is found that the effect of the applied magnetic field is an increase in the elastic wave velocity or, in other words, the increase of the solidity of the body. Furthermore, it has been shown graphically that the stress and perturbed magnetic field are modified due to the thermal relaxation time effect. In the absence of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and classical dynamical thermoelasticity, respectively.     

Thermomechanical Interactions in a Generalized Thermo-Microstretch Elastic Half Space

Interactions caused by thermal and mechanical sources in a generalized thermo-microstretch elastic medium are studied by the use of Laplace-Fourier transform techniques. The formulation is applied to the coupled theory as well as to two generalizations, the Lord-Shulman and the Green-Lindsay theories. The integral transforms are inverted using a numerical technique to obtain the solutions field in the physical domain. Stretch effects lead to the existence of a new wave that is called longitudinal microstretch wave. The results of micropolar generalized thermoelasticity and generalized thermoelasticity are deduced as special cases from the present formulation.     

Electroosmotic flow of a fractional second-grade fluid with interfacial slip and heat transfer in the microchannel when exposed to a magnetic field

We investigated the time-dependent viscoelastic fluid flow through a parallel-plate microchannel under the influence of a transversely applied magnetic field and an axially imposed electric field. We performed the analysis by employing the Poisson-Boltzmann equation under the Debye-Huckel approximation. The generalized second-grade fluid model with a fractional-order time derivative is used to observe the non-Newtonian and fractional behavior rates of deformation employing the Riemann-Liouville fractional operator. We considered the asymmetric zeta potentials and different slip effects at the walls to study the flow behavior near the vicinity of the channel. We obtained an analytical solution in terms of Mittag-Leffler function, applying Fourier and Laplace transformations. We imposed the heat transfer phenomena with the dissipation of energy and Joule heating effects on the model. The governing equations were also solved numerically by employing an implicit finite difference scheme. The numerical solution was compared with the analytical results, considering the influence of the pertinent parameters involved in the problem. The study delineates that the flow rate decreases with a rise in the fractional-order parameter, while the opposite trend is observed with the electroosmotic parameter. Due to the application of sufficient strength of the magnetic field and the Joule heating effects, the temperature increases within the channel.     

INVESTIGATION OF THERMAL RESPONSE CAUSED BY PULSE LASER HEATING

This article identifies models that are suitable for describing thermal transport in metal materials heated by a short-pulse laser. Three two-temperature models (dual-hyperbolic, hyperbolic, and parabolic), two one-temperature models (thermal wave and Fourier conduction), and one ultrafast thermomechanical model are investigated. A finite-difference method is used for solving the heat conduction equations, and a combined finite-difference/finite-element method is developed for solving the coupled thermomechanical equations. The numerical results, performed for gold films, suggest that for pure metals the hyperbolic two-temperature model be used for short-pulse (<1-ns) laser heating, while Fourier's law be used for long-pulse (>1-ns) laser heating. For alloys, the dual-hyperbolic two-temperature model is suggested for short-pulse (<10-ns) laser heating. Due to the high strain rate caused by nanosecond- and shorter-pulse lasers, a coupled thermomechanical model should be considered for more accurately predicting the lattice temperature field.     

Two-Temperature Generalized Thermoelasticity with Variable Thermal Conductivity

In this work, the consideration of variable thermal conductivity as a linear function of temperature has been taken into account in the context of two-temperature generalized thermoelasticity (Youssef's model). The governing equations have been derived and used to solve the one-dimensional problems of an elastic half-space. The governing equations have been cast into a matrix form by using Bahar–Hetnarski method, and Laplace transform is used to get the general solution for any set of boundary conditions. The solution has been applied for a thermally shocked medium that has no strain on its bounding plane. The numerical inversion of the Laplace transform has been calculated by using the Riemann-sum approximation method. The distribution of the conductive temperature, the thermo-dynamical temperature, the strain, the displacement, and the stress have been shown graphically with some comparisons.     

Dispersion Analysis of Generalized Magneto-Thermoelastic Waves in a Transversely Isotropic Cylindrical Panel

In this article the three-dimensional dispersion analysis of a homogeneous transversely isotropic magneto generalized thermoelastic cylindrical panel is discussed in the context of the linear theory of generalized thermoelasticity. Three displacement potential functions are introduced to uncouple the equations of motion. A Bessel function solutions with complex argument is used directly to analyze the frequency equations with traction-free boundary conditions and the special cases have also been deduced for magneto-elastic, thermoelastic and elasto-kinetic at various levels from the present analysis. Finally the numerical example demonstrates the present method and is studied for the material magnetostrictive cobalt iron oxide (CoFe₂O₄). The computed non-dimensional phase velocity, attenuation coefficient, specific loss and thermo-mechanical coupling factor are plotted in the form of dispersion curves with the support of MATLAB.     

On the Fundamental Solutions of Generalized Thermoelasticity with Three Phase-Lags

The aim of the present work is to derive the fundamental solutions in the linear theory of generalized thermoelasticity with three phase-lags, recently introduced by Roychoudhuri (2007). We consider the case of homogeneous and isotropic bodies and present a solution of the Galerkin-type of field equations. The solution is then used to determine the effects of concentrated loads and heat sources in an unbounded medium. The fundamental solutions of the field equations in case of steady vibrations are also derived.     

Fractional Ultrafast Laser–Induced Thermo-Elastic Behavior In Metal Films

In this work, a new mathematical model of modification heat conduction for an isotropic generalized thermoelasticity is derived using the methodology of fractional calculus. Some theorems of generalized thermoelasticity follow as limit cases. An ultrafast fractional thermoelasticity model utilizing the modified hyperbolic heat conduction model and the generalized fractional thermoelastic theory was formulated to describe the thermoelastic behavior of a thin metal film irradiated by a femtosecond laser pulse. The temporal profile of the ultrafast laser was regarded as being non-Gaussian. An analytical–numerical technique based on the Laplace transform was used to solve the governing equations and the time histories of the temperature, displacement and stress in a gold film were analyzed. Some comparisons have been shown in figures to estimate the effects of the relaxation time and fractional order parameter α on all the studied fields.     

A Two-Dimensional Generalized Electromagneto-Thermoelastic Problem for a Half-Space

A two-dimensional coupled problem in electromagneto-thermoelasticity for a thermally and electrically conducting half-space solid whose surface is subjected to a time-dependent heat is studied in this paper. The problem is in the context of the Green and Lindsay's generalized thermoelasticity theory with two relaxation times. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deforms because of heat, and due to the application of the magnetic field, there results an induced magnetic field and an induced electric field in the medium. The Maxwell's equations are formulated and the electromagneto-thermoelastic coupled governing equations are established. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium.     

Normal Mode Method for Two-Temperature Generalized Thermoelasticity Under Thermal Shock Problem

The theory of two-temperature generalized thermoelasticity, based on Youssef's theory, was used to solve boundary value problems of one-dimensional generalized thermoelasticity half-space by heating its boundary with different types of heating. The governing equations are solved using new mathematical methods within the purview of the Lord-?hulman (L-S) theory and the classical dynamical coupled theory (CD). The general solution obtained is applied to a specific problem of a half-space subjected to one type of heating—thermal shock type. The separation of variables method is used to get the exact expressions for distributions of displacement, the stresses, and temperature distribution. Variations of the considered functions through the horizontal distance are illustrated graphically. Comparisons are made with results between the two theories. Numerical work is also performed for a suitable material and results are discussed, specifically the conductive temperature, the dynamical temperature, and the stress and strain distributions are shown graphically when discussed.