Two-temperature Thermoelasticity Research Articles

Wave propagation in 2D between two elastic media in contact in theory of generalized two-temperature thermoelasticity with gravity effect

Wave propagation in 2D between two elastic media in contact in theory of generalized two-temperature thermoelasticity with gravity effect

Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory

In this work, a novel mathematical model of thermoelastic, homogenous, isotropic, and infinite medium with a spherical cavity has been constructed. Under the hyperbolic two-temperature Green-Naghdi theory of thermoelasticity type-I and type-III with fractional-order strain, the governing equations have been established. The bounding surface of the cavity has been thermally loaded by a ramp-type heat and is connected to a rigid foundation which prevents volumetric strain. Different values of the fractional-order and two-temperature parameters have shown numerical results for the dynamical and conductive temperature increment, strain, displacement, and average of principal stresses, which are graphically applicable to all the functions studied. The fractional-order parameter has significant effects on stress and strain distributions, while it has a limited effect on the dynamical and conductive temperatures increment. The hyperbolic two-temperature parameter has significant effects on all studied functions based on Green-Naghdi models of type-1 and type-II. Moreover, the ramp-time heat parameter has a significant impact on all the studied functions under all the studied models of thermoelasticity.

Two-Temperature Semiconductor Model Photomechanical and Thermal Wave Responses with Moisture Diffusivity Process

In the context of the two-temperature thermoelasticity theory, a novel mathematical–physical model is introduced that describes the influence of moisture diffusivity in the semiconductor material. The two-dimensional (2D) Cartesian coordinate is used to study the coupling between the thermo-elastic plasma waves and moisture diffusivity. Dimensionless quantities are taken for the main physical fields with some initial conditions in the Laplace transform domain. The linear solutions are obtained analytically along with unknown variables when some conditions are loaded at the surface of the homogenous medium according to the two-temperature theory. The Laplace transform technique in inversion form is utilized with some numerical algebraic approximations in the time domain to observe the exact expressions. Due to the effects of the two-temperature parameter and moisture diffusivity, the numerical results of silicon material have been introduced. The impacts of thermoelectric, thermoelastic, and reference moisture parameters are discussed graphically with some physical explanations.

The variationally principle of two-temperature thermoelasticity in the absence of the energy dissipation theorem

Youssef introduced two-temperature thermoelasticity without energy dissipation theorem. This theorem depends upon two distinct temperatures: the conductive temperature and the thermo-dynamical temperature. Through this work, the variational principle theorem will be obtained for an isotropic, homogeneous, and thermoelastic body in the context of two-temperature thermoelasticity without energy dissipation theorem.

Response of two-temperature semiconductor model photomechanical and thermal waves during electrons-holes interaction processes

A novel mathematical-physical model is introduced in the context of the two-temperature thermoelasticity theory which describes the interaction between electrons and holes in semiconductors material. The response of the elasto-thermo- mechanical continuous waves is investigated during thermo-mass-diffusion transport processes. The photothermal (PT) technique is applied for the exciting medium. The one-dimensional (1D) Cartesian coordinate is used to describe the governing equations. Dimensionless quantity is used in the Laplace transform domain. To obtain the unknown variables, some conditions are applied at the free surface of the medium to get the main quantities analytically. The conversion of the Laplace transform technique has been employed with some numerical approximations to obtain the exact expressions of the main physical fields. The computational results have been introduced of silicon material to illustrate the impacts of the two temperature parameter and thermal memories on the wave propagation of the physical fields according to photo-thermoelasticity theory.

Hyperbolic two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to the non-Gaussian laser beam

The present work is devoted to a study of the induced temperature and stress fields in an elastic infinite medium with a cylindrical cavity under the purview of hyperbolic two-temperature thermoelasticity. The medium is an isotropic homogeneous thermoelastic material. The bounding plane surface of the cavity is loaded thermally by a non-Gaussian laser beam with a pulse duration of two ps. An exact solution to the problem is obtained in the Laplace transform space and the inversions of the Laplace transform have been carried out numerically. The derived expressions are computed numerically for copper and the results are presented in graphical form. The two-temperature parameter has significant effects on all the studied functions and plays a vital role in the speed propagation of the thermomechanical waves.

Thermoelastic interactions on temperature-rate-dependent two-temperature thermoelasticity in an infinite medium subjected to a line heat source

Thermoelastic interactions on temperature-rate-dependent two-temperature thermoelasticity in an infinite medium subjected to a line heat source

Thermomechanical interactions due to mode-I crack under modified temperature-rate dependent two-temperature thermoelasticity theory

Temperature-rate dependent two-temperature (TRDTT) thermoelasticity is reformulated by Shivay and Mukhopadhyay [On the temperature-rate dependent two-temperature thermoelasticity theory. J Heat Transfer. 2020;142(2):022102.] and it is suggested that the effect of the temperature-rate term should not be neglected in the two-temperature relation. As a result, an improved two-temperature theory has been proposed that generalize the TRDTT theory suggested by Youssef [Theory of two-temperature-generalized thermoelasticity. IMA J Appl Math 2006;71(3):383–390.]. The present work aims to investigate thermo-mechanical interactions due to the presence of crack under this modified TRDTT theory. We consider a homogeneous and isotropic 2D infinite medium weakened by mode-I crack of finite length. The boundary of the crack is subjected to time-dependent thermal and stress distributions. Laplace and Fourier transformations are used to solve the present problem in the transformed domain. Two different sets of dual integral equations are derived, which are solved by reducing them to the Fredholm integral equation of the first kind. The regularization method, along with a numerical integration technique, is used to solve this integral equation. Present results are validated with the results derived under GL (temperature-rate dependent) theory. Some interesting points highlighting the effects of a crack in the present context are concluded.

Thermoelastic Plane Waves in Materials with a Microstructure Based on Micropolar Thermoelasticity with Two Temperature and Higher Order Time Derivatives

The study of the effect of the microstructure is important and is most evident in elastic vibrations of high frequency and short-wave duration. In addition to deformation caused by temperature and acting forces, the theory of micropolar thermoelasticity is applied to investigate the microstructure of materials when the vibration of their atoms or molecules is increased. This paper addresses a two-dimensional problem involving a thermoelastic micro-polar half-space with a traction-free surface and a known conductive temperature at the medium surface. The problem is treated in the framework of the concept of two-temperature thermoelasticity with a higher-order time derivative and phase delays, which takes into consideration the impact of microscopic structures in non-simple materials. The normal mode technique was applied to find the analytical formulas for thermal stresses, displacements, micro-rotation, temperature changes, and coupled stress. The numerical results are graphed, and the effect of the discrepancy indicator and higher-order temporal derivatives is examined. There are also some exceptional cases that are covered.

Effect of viscosity and rotation on a generalized two-temperature thermoelasticity under five theories

In the current paper, an equational model for generalized thermo-visco-elasticity is set up for such an elastic medium that indicates isotropicity along with two temperatures. The angular velocity for rotating this medium is maintained uniformly. Several generalized thermoelasticity theories have been employed to fulfill the detailing purposes which include; Lord-Shulman (L-S) and Green-Lindsay (G-L) theories with one and two relaxation times respectively, coupled theory, Tzou theory consisting of dual-phase lags (DPL), and lastly Green-Naghdi (G-N II) theory in the absence of energy dissipation. The application of Normal mode examination leads to the attainment of specific articulations for the thought about factors. Some specific cases are additionally talked about with regards to the complexity. Also, Numerical as well as the graphical representation of the factors under consideration has been presented. Examinations are carried out by keeping outcome predictions in mind as anticipated by various theories (L-S, G-N II, G-L, and DPL), rotation, viscosity, and two temperatures.

Variational and reciprocal principles on the temperature-rate dependent two-temperature thermoelasticity theory

The motive of the present work is to establish some theorems under a recent theory of thermoelasticity proposed by Shivay and Mukhopadhyay (2019). The governing equations for the temperature-rate dependent two-temperature (TRDTT) thermoelasticity theory were stated by Youssef (2006). Shivay and Mukhopadhyay (2019) employed generalized thermodynamics laws and presented a modified TRDTT thermoelasticity theory. The generalized two-temperature relation obtained in view of this modified TRDTT thermoelasticity theory for an anisotropic material reduces to the two-temperature relation provided by Youssef in a specific situation. They further discussed the uniqueness of solution under this theory. In the present work, we consider the basic equations of this new model for the homogeneous and anisotropic material. Later, we present an alternative formulation of a mixed boundary-initial value problem incorporating initial data into the field equations. The variational principle of the convolution type by using this formulation is derived. Lastly, we derive a reciprocal principle for this theory.

On the Temperature-Rate Dependent Two-Temperature Thermoelasticity Theory

Abstract This work aims to formulate the temperature-rate dependent two-temperature (TRDTT) theory of thermoelasticity. The two-temperature thermoelasticity theory and the temperature-rate dependent thermoelasticity theory are two well-established thermoelasticity theories, which are developed from the generalized thermodynamic principles independently. Although the constitutive equations for TRDTT theory have been introduced, the formulation for the theory from the thermodynamical principles is not yet derived. Therefore, this work is an attempt to establish the theory from the generalized laws of thermodynamics and derive all the governing equations and constitutive relations for the theory. We derive a new and more general two-temperature relation that involves the temperature-rate terms of conductive and thermodynamic temperatures. We observe that this relation is different from the two-temperature relation reported in the literature. Further, we prove the uniqueness of solution for a general mixed initial boundary value problem in the context of linear modified TRDTT thermoelasticity theory for anisotropic medium. To investigate the effect of the present modified TRDTT theory, we solve a one-dimensional half-space problem and highlight the significance of the present theory.

Two-Temperature Thermoelastic Damping of a Gold Nano-Beam Resonator with Variable Young's Modulus

This paper deals with the thermoelastic damping (Q-factor) of a gold nano-beam resonator and is based on twotemperature thermoelasticity models. An explicit formula of the Q-factor has been derived when Young’s modulus is variable as a function of the room temperature. The length of the beam and Young’s modulus has been studied with comparison being made between the Biot model and the Lord-Shulman model (L-S). The numerical results show that the values of beam length, the relaxation time parameter, and the two-temperature parameter have a strong influence on the thermoelastic damping quality factor.

Magnetothermoelastic interactions in non-simple medium with a spherical cavity due to time-harmonic varying heat

PurposeThe purpose of this paper is to investigate the dynamic response for a thermoelastic infinite medium with a spherical cavity in the context of the theory of two-temperature thermoelasticity without energy dissipation.Design/methodology/approachThe cavity is fixed and subjected to a subjected to harmonically varying temperature.FindingsThe exact expressions for displacement, temperature and thermal stresses are computed and represented graphically. These distributions are calculated for a copper material and results are analyzed.Originality/valueEffects of non-simple heat conduction, frequency of thermal vibrations and magnetic field are depicted graphically on the field variables.

A 2D problem of time-fractional heat order for two-temperature thermoelasticity under hydrostatic initial stress

ABSTRACTThe present study solves the problem of thermoelastic interactions in a half-space medium under hydrostatic initial stress in the context of a fractional order heat conduction model with two-temperature theory. The analytical solutions of the field variables are obtained by using the normal mode analysis. The obtained solutions are then applied to a specific problem for a thermally insulated surface which is acted upon by a load. The distributions of the two temperatures, displacements, and the stress components inside the half-space are studied. The graphical results depict that the fractional parameter has significant effects on all the studied field variables. Comparisons are made within the theory in the presence and absence of the hydrostatic initial stress. Thus, we can conclude that the fractional order generalized thermoelasticity model may be an improvement on studying elastic materials.

Two temperature theory of initially stressed electro-microstretch medium without energy dissipation

The present study is attempted to analyze the thermoelastic interactions in a homogeneous isotropic electro-microstretch semi-space caused by mechanical source acting on the initially stressed surface. The problem is treated on the basis of two-temperature thermoelasticity without energy dissipation proposed by Youssef. Normal mode analysis is applied to derive the exact expressions for displacement components, force stresses, couple stress, microstress, conductive temperature, thermodynamic temperature and electric field. Numerical computations have been performed for magnesium crystal material to depict the response of mechanical source in the medium for thermally insulated boundary. Some comparisons have been made in figures to estimate the effects of two-temperature parameter and initial stress.

Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature

In this work, a novel generalized model of photothermal theory with two-temperature thermoelasticity theory based on memory-dependent derivative (MDD) theory is performed. A one-dimensional problem for an elastic semiconductor material with isotropic and homogeneous properties has been considered. The problem is solved with a new model (MDD) under the influence of a mechanical force with a photothermal excitation. The Laplace transform technique is used to remove the time-dependent terms in the governing equations. Moreover, the general solutions of some physical fields are obtained. The surface taken into consideration is free of traction and subjected to a time-dependent thermal shock. The numerical Laplace inversion is used to obtain the numerical results of the physical quantities of the problem. Finally, the obtained results are presented and discussed graphically.

An in-depth investigation on plane harmonic waves under two-temperature thermoelasticity with two relaxation parameters

The present work is concerned with an in-depth analysis of plane harmonic waves in a thermoelastic medium under two-temperature thermoelasticity with two relaxation parameters. After the mathematical formulation of the present problem, we obtain the dispersion relation solution of harmonic plane waves propagating in the medium. The transverse wave is observed to be not affected by the thermal field and the longitudinal wave is coupled with the thermal field. Hence, special attention is paid on two different modes of longitudinal plane wave. One is predominantly elastic and the other is predominantly thermal in nature. The asymptotic expressions for the phase velocity, specific loss and many other important wave characteristics are derived in the cases of very high- and low-frequency regions for both the elastic and thermal mode longitudinal waves. Numerical results of these wave components are obtained for the intermediate values of frequency and the results are illustrated graphically in order to verify the analytical results. On the basis of analytical and numerical results a thorough analysis of the effects of the thermal relaxation parameters on various wave characteristics is presented. A detailed comparison of the results in the context of the present model with the corresponding results of three other models is also provided and several findings regarding the prediction of the present model as compared to other models are highlighted. The present investigation brought out the effects of the second relaxation parameter and the two-temperature parameter on the propagation of a plane harmonic wave through the medium.

Effects of two temperatures and thermal phase-lags in a thick circular plate with axisymmetric heat supply

AbstractThe present investigation is concerned with thermomechanical interactions for the dual-phase-lag in a homogeneous isotropic thick circular plate in the light of two-temperature thermoelasticity theory. The upper and lower surfaces of the thick plate are traction free and subjected to an axisymmetric heat supply. The solution is found by using Laplace and Hankel transform technique and a direct approach without the use of potential functions. The analytical expressions of displacement components, stresses, conductive temperature, temperature change and cubic dilatation are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effects of thermal phase-lags and two temperatures are shown on the various components. Some particular cases are also deduced from the present investigation.

Two-Temperature Generalized Thermoelastic Infinite Medium with Cylindrical Cavity Subjected To Time Exponentially Decaying Laser Pulse

The present work is devoted to a study of the induced temperature and stress fields in an elastic infinite medium with cylindrical cavity under the purview of two-temperature thermoelasticity. The medium is considered to be an isotropic homogeneous thermoelastic material. The bounding plane surface of the cavity is loaded thermally by time exponentially decaying laser pulse. An exact solution of the problem is obtained in Laplace transform space, and the inversion of Laplace transforms have been carried numerically. The derived expressions are computed numerically for copper, and the results are presented in graphical form.