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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]

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]

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]

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]

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]