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This paper is concerned with the influence of memory-dependent heat transport law on rotating thermoelastic medium with voids via three-phase-lag. The entire pervious medium is rotating with a invariant angular haste, where the bounding airplane is subordinated to a thermal shock and is free of tractions. By employing the normal mode analysis, the exact expressions for the displacement components, stresses, temperature distribution and change in volume fraction field have been depicted graphically in the presence and the absence of gyration and memory-dependent outgrowth. The effect of the voiding is also bandied in the literature review. [ABSTRACT FROM AUTHOR]

Enlightened by the memory dependent derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of the magnetic field and moving heat source in a rod in the context of three-phase lag theory of thermoelasticity based on Eringen's nonlocal elasticity. Both ends of the rod were fixed, and heat is insulated. Employing Laplace transform as a tool, the problem was transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain was obtained by applying the inverse Laplace transform. Numerical calculation for temperature, displacement and stress within the rod was carried out and displayed graphically. The effect of the moving heat source speed, time instance, memory dependent derivative, magnetic field and nonlocality on temperature, displacement, and stress was studied. Finally, three animated were added for easy understanding of the effect of moving the heat source on the studied fields. As per authors concern, the concept of the animated has been presented for the first time in this kinds of literature till now. [ABSTRACT FROM AUTHOR]

The main concern of this article is to deal with the thermoelastic interaction in a functionally graded thermoelastic rod being enlightened by the memory-dependent derivative. This article investigates the transient phenomena due to the influence of an induced magnetic field of constant intensity and due to the presence of a moving heat source of constant velocity in the context of three-phase lag model of generalized thermoelasticity. Employing the Laplace and the Fourier transforms as tool, the problem has been constructed in the transformed domain. The inversions of the Fourier transform have been carried out using residual calculus whereas the numerical inversions of the Laplace transform have been performed employing the Riemann sum approximation method. Numerical computations for stress, displacement, and temperature within the rod are carried out and have been demonstrated graphically. The results also demonstrate how the nonhomogeneity parameter and the speed of the moving heat source influence the thermophysical quantities. It is observed that the temperature, thermally induced displacement, and stress of the rod are found to decrease at large source speed. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field, nonhomogeneity, and memory effect also. [ABSTRACT FROM AUTHOR]

The model of the equations of generalized thermoelasticity based on the Lord–Shulman's theory with nonlocal elasticity effect is used to study the photothermal waves in a semiconducting medium. The exact expressions for the displacement components, temperature, carrier density, and stress components are obtained by using normal mode analysis. Numerically simulated results are obtained and presented graphically for silicon. The comparisons are shown graphically to explore the effects of the time and the elastic nonlocal parameter on the different physical quantities. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The present article is aimed at studying the effect of an induced magnetic field in an initially stressed homogeneous, isotropic, thermoelastic half-space. The corresponding mathematical modeling has been formulated in the context the memory-dependent heat transport equation in the context of three-phase lag model of generalized thermoelasticity involving two-temperature theory. The bounding plane of the medium is subjected to different types of prescribed temperature and variable mechanical loading. Employing the Laplace transform, the analytical results for the distributions of the thermophysical quantities have been derived and the corresponding vector-matrix differential equation is solved with the help of state space approach. The numerical inversion of the Laplace transform is carried out with the help of an efficient and pragmatic algorithm based on the Riemann-sum approximation technique. Numerical computations for a copper material is performed and have been demonstrated graphically. The result provides a motivation to investigate the problem and draw conducting remarks due to the influence of the magnetic field, memory effect and time-delay parameter also. [ABSTRACT FROM AUTHOR]

The analysis of fracture is very important along with the miniaturization of the device and wide application 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. Due to these, size-dependent thermoelastic model have been introduced for higher order simple material to adopt both the size effect of heat conduction and elasticity with the aids of extended irreversible thermodynamics and generalized free energy. With this motivation, the present study is now formulated to provide the nonlocal phenomena of a homogeneous, isotropic infinite space weakened by a finite linear mode I crack. The boundary of the crack is subjected to prescribed temperature and stress. The governing equations have been solved on employing the Laplace and the Fourier transforms, which reduces to four dual integral equations, the solution of which is equivalent to solving the Fredholm's integral equation of the first kind. The Bellman method has been used to compute numerical inversion of the Laplace transform. The result provides the direction how the nonlocality and size-dependence can control the fracture and what is the significant effect of various kernel functions and the effect of memory is also reported. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This present study deals with a novel mathematical model of generalized thermoelasticity in a fiber-reinforced, isotropic unbounded thermoelastic solid due to the presence of a continuous line heat source under the influence of magnetic field. The derivative is defined in an integral form of a common derivative on a slipping interval by incorporating memory-dependent heat transfer. Employing both Laplace and Hankel transforms as tools, analytical results for distributions of different fields have been derived with the help of potential function approach. The inversion of Hankel transform is performed analytically, whereas the numerical inversion of Laplace transform is carried out employing Zakian method and the method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory to exhibit the significance of the kernel functions and the time-delay parameter is constructed. The significant differences of the two different numerical schemes have also explained. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of reinforcement and magnetic field. Also, significant differences due to the choice of linear and nonlinear kernels in the heat equation is elaborated. [ABSTRACT FROM AUTHOR]

This present survey deals with a novel mathematical model of generalized thermoelasticity which investigates the transient phenomena in a two‐dimensional problem for a transversely isotropic thick plate having a heat source. The upper surface of the plate is stress‐free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the three‐phase‐lag thermoelastic model. The governing equations for displacement and temperature fields are obtained in the Laplace‐Fourier transform domain by applying the Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of the Laplace transform is done by using a method based on the Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the memory‐dependent derivative on the solutions has been studied. [ABSTRACT FROM AUTHOR]

The main concern of this article is to deal with the thermoelastic interaction in a thick plate subjected to a moving heat source and being enlightened by memory-dependent derivative (MDD). Due to the shortcomings of power law distributions in Taylor's series, some other forms of derivatives with few other kernel functions have been proposed. The present literature deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a thermoelastic thick plate in which, the memory-dependent heat transport equation involves the Dual-phase (DP) lag model of generalized thermoelasticity. Employing the Laplace transform and Fourier transforms, the analytical results for the distributions of the thermophysical quantities have been derived. The numerical inversions of the respective transforms have been carried out using a suitable numerical scheme based on the Fourier series expansion technique. Numerical computations for stress, displacement and temperature within the plate have been carried out and have been demonstrated graphically. The results also demonstrate how the heat source moves with time and influences the thermophysical quantities according to its respective position by that time. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field, memory effect and time-delay also. [ABSTRACT FROM AUTHOR]

The present study is concerned with the reflection and propagation of thermoelastic plane waves from the stress‐free and thermally insulated surface of a homogeneous, isotropic thermally conducting elastic half‐space in the frame of modified Green–Lindsay theory of generalized thermoelasticity with two‐temperature (2TMGL). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear‐type (SV‐type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV‐type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the two‐temperature Green–Lindsay (2TGL) and two‐temperature Lord–Shulman (2TLS) models. [ABSTRACT FROM AUTHOR]

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 dual-phase lag (DPL) 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 temperature, displacement and stress within the rod is carried out and displayed graphically. The effect of moving heat source speed, time instance, memory-dependent derivative, magnetic-field and nonlocality on temperature, displacement and stress are studied. [ABSTRACT FROM AUTHOR]

This article constructs a new model of nonlocal thermoelasticity which resolves a dynamical problem of a homogeneous, isotropic infinite space weakened by a finite linear mode I crack. The boundary of the crack is being subjected to a prescribed temperature distribution and stress. In the context of three-phase lag model of generalized thermoelasticity, the governing equations have been solved employing the Laplace and the Fourier transforms, which reduces to four dual integral equations, the solution of which is equivalent to solving the Fredholm's integral equation of the first kind. These integral equations have been solved employing the Maple software package, while the numerical inversion of the Laplace transform is carried out with the help of Bellman method. Numerical computations for a copper material are performed and demonstrated graphically. The results provide a motivation to further investigate the problem and draw concluding remarks due to the influence of nonlocality also. [ABSTRACT FROM AUTHOR]

The present study is concerned with the reflection of magneto-thermoelastic plane waves from stress free and thermally insulated surface in a homogeneous isotropic thermally conducting elastic half-space medium. The modified Green–Lindsay (MGL) theory of generalized thermoelasticity has employed with two temperatures (2 T). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. There exist also due to the thermoelastic coupling one independent vertically shear (SV-wave) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the reflection coefficients and their respective energy ratios for reflected thermoelastic waves have been determined when the coupled longitudinal wave incident on the free surface. A numerical result on the reflection coefficients and their respective energy ratios for the specific parameter has been calculated. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those in the classical GL model. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo fractional derivative, the present 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 three-phase lag (TPL) theory of thermoelasticity. 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 effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added. [ABSTRACT FROM AUTHOR]

The Fractional derivative is a widely accepted theory to describe physical phenomena and the processes with memory effects which is defined in the form of convolution having kernels as power functions. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of the magnetic field and moving heat source in a thermoelastic rod in the context of the Lord–Shulman (LS) theory of generalized thermo-visco-elasticity. Both ends of the rod are fixed and are thermally insulated. Employing the 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 on applying the numerical inversion of the Laplace transform, which has been carried out employing the Riemann sum approximation method. Numerical computations for stress, displacement, and temperature within the rod is carried out and have been demonstrated graphically. The results also demonstrate how the speed of the moving heat source influences the thermophysical quantities. It is observed that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. Also, significant differences in the thermophysical quantities are revealed due to the influence of the magnetic field and memory effect [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Following the link of work of He and Cao (2009, Math. Comput. Modell., 49(7-8), 1719-1720), we employ the theory of generalized thermoelasticity with dual-phase-lag (DPL) to study the transient phenomena in a thin slim strip due to a moving heat source. Both ends of the strip are assumed to be fixed and thermally insulated. Using 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 strip are carried out and presented graphically. The effect of moving heat source speed on temperature, stress, and displacement is studied. The temperature, displacement, and stress in the strip are found to be decreasing at large source speed. [ABSTRACT FROM AUTHOR]

This present work is devoted to the investigation of the transient phenomena for a fiber-reinforced medium with a cylindrical cavity in the context of the three-phase-lag model of generalized thermoelasticity with a new form of derivative of the Caputo–Fabrizio (CF) type in the heat transport equation, where the medium is under the action of an induced magnetic field. The Laplace transform is incorporated as a tool for the solution of the problem when the boundary of the cavity is exposed to harmonically varying heat with a constant angular frequency of thermal vibration. The numerical inversion of the Laplace transforms is computed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of reinforcement, the angular frequencies on thermal vibrations, CF fractional parameter and magnetic field. [ABSTRACT FROM AUTHOR]

The main idea of the present work is to extend Eringen's theory of nonlocal elasticity to generalized thermoelasticity with dual-phase-lag and voids. Then we study the propagation of time harmonic plane waves in an infinite nonlocal dual-phase-lag thermoelastic medium with voids. Three sets of coupled dilatational waves and an independent transverse wave may travel with distinct speeds through the medium. All these waves are found to be dispersive in nature. The coupled dilatational waves are damping, while the transverse wave is undamped in a certain range of the angular frequency. Coupled dilatational waves are found to be influenced by the presence of voids, thermal field and elastic nonlocal parameter, while the transverse wave is found to be influenced by the nonlocal parameter, but independent of void and thermal parameters. For a particular model, the effects of angular frequency, elastic nonlocality parameter, and some voids and thermal parameters on the wave speeds and damping coefficients of all the propagating waves have been studied numerically. Some comparisons are made between the results obtained for local and nonlocal cases. All the computed results have been depicted graphically and explained in details. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a piezoelastic half-space due to the influence of a magnetic field in the context of the dual-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The bounding plane of the medium is assumed to be stress free and subjected to a thermal shock. Employing the Laplace transform as a tool, the problem is transformed to the space domain, where the solution in the space–time domain is achieved by applying a suitable numerical technique based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are constructed. Excellent predictive capability is demonstrated due to the presence of electric field, memory-dependent derivative and magnetic field. [ABSTRACT FROM AUTHOR]

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter. [ABSTRACT FROM AUTHOR]

This work deals with the study of transient responses in a two‐temperature generalized thermoelastic infinite medium having a cylindrical cavity due to a time‐dependent moving heat source where the conventional Fourier's law of heat conduction is modified by introducing a new Taylor's series expansion using memory‐dependent derivative (MDD). The resulting non‐dimensional equations are applied to a specific problem. A direct approach is introduced to obtain the analytical expressions of the physical quantities in the Laplace transform domain. The inversion of the Laplace transforms are carried out using the methods based on the Fourier series expansion technique. Numerical results for the dynamical and conductive temperatures, stress, strain, and displacement are presented graphically. The effects of time‐delay and kernel function have been studied on the thermo‐physical quantities. [ABSTRACT FROM AUTHOR]