Two-temperature Parameter Research Articles

Reflection of Waves in a Two-Temperature Magneto-fiber-Reinforced Solid with Memory-Dependent Derivative Using Different Theories

Abstract Purpose The problem is concerned with the analysis of the reflection of the waves through a fiber-reinforced thermoelastic medium under the effect of the magnetic field, gravity, and the initial stress. The problem is discussed in the context of the three-phase-lag model and Green-Naghdi theory of type II and III with the memory-dependent derivative and variable thermal conductivity. Methods The harmonic representation of waves is used to find the solution to the problem. Based on the solution, it is concluded that after reflection three quasi-waves propagate through the medium. Results Numerical computations were performed using MATLAB software. The reflection coefficient ratio variations with the angle of the incident are shown graphically. Conclusion Comparisons are made with the results predicted for different values of the thermal conductivity parameter, two-temperature parameter, initial stress, gravity field, and different values of the magnetic field.

Response of photo-elasto-electric semiconductor porosity medium according to changing thermal conductivity with two-temperature

This study examines a new model for a solid semiconductor porosity medium with variable thermal conductivity under photo-thermoelastic conditions using two-temperature theory. A normal mode analysis is carried out to solve the equations in two dimensions analytically while taking into account the linear relationship between thermal conductivity and temperature. Physical fields, such as carrier density distribution, temperature, stress, and displacement, are then determined. The interaction between plasma and elastic waves is also considered. The simulation is conducted using silicon material, and the numerical calculations are illustrated graphically. This study investigates the effects of different porosity parameters (with and without porosity), thermal variable conductivity, and the two-temperature parameter on the physical field values.

Magneto-thermo-piezo-elastic wave in an initially stressed rotating monoclinic crystal in a two-temperature theory

This research problem is an investigation of wave propagation in a rotating initially stressed monoclinic piezoelectric thermo-elastic medium under with the effect of a magnetic field. A two-temperature generalized theory of thermo-elasticity in the context of Lord-Shulman’s theory is applied to study the waves under the magnetic field. The governing equations of a rotating initially stressed monoclinic piezoelectric thermo-elastic medium with a magnetic field are formulated. This research problem is solved analytically, for a two-dimensional model of the piezo-electric monoclinic solid, and concluded that there must be four piezo-thermoelastic waves, three coupled quasi waves (qP (quasi-P), qT (quasi-thermal), and qSV (quasi-SV)) and one piezoelectric potential (PE) wave propagating at different speeds. It is found that at least one of these waves is evanescent (an evanescent wave is a non-propagating wave that exists) and that there are therefore no more than three bulk waves. The speeds of different waves are calculated and the influence of the piezoelectric effect, two-temperature parameter, frequency, rotation, and magnetic field on phase velocity, attenuation coefficient, and specific loss is shown graphically. This model may be used in various fields, e.g. wireless communications, signal processing, and military defense equipment are all pertinent to this study.

Mathematical modelling of micropolar thermoelastic problem with nonlocal and hyperbolic two-temperature based on Moore–Gibson–Thompson heat equation

The aim of this article is to study a problem of thermomechanical deformation in a homogeneous, isotropic, micropolar thermoelastic half-space based on the Moore–Gibson–Thompson heat equation under the influence of nonlocal and hyperbolic two-temperature (HTT) parameters. The problem is formulated for the considered model by reducing the governing equations into 2D and then converting to dimensionless form. Laplace transform and Fourier transform techniques are employed to obtain the system of differential equations. In the transformed domain, the physical quantities like displacement components, stresses, thermodynamic temperature, and conductive temperature are calculated under the specific types of normal force and thermal source at the boundary surface. A numerical inversion technique is used to recuperate the equations in the physical domain to exhibit the influence of nonlocal and HTT in the form of graphs. Particular cases of interest are also discussed in the present problem. The present study finds applications in a wide range of problems in engineering and sciences, control theory, vibration mechanics, and continuum mechanics.

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.

Effect of magnetic field on a thermoviscoelastic body via a refined two-temperature Lord–Shulman model

This paper aims to modify the generalized thermoelasticity theory of Lord–Shulman. Higher-order time-derivative terms are incorporated to get accurate field variables. The refined theory is employed to examine the inclusion of a magnetic field, a two-temperature parameter, and the viscoelastic effects on a thermoelastic medium with two temperatures. The problem has been solved analytically and numerical data have been obtained by utilizing the normal mode technique. The analytic expressions of the displacements, stresses, dilatation, thermodynamic and conductive temperatures are outlined and investigated. The outcomes are reported for future comparison, and some are presented graphically in 2D and 3D plots. Comparisons with the existing literature due to the classical coupled and simple Lord–Shulman thermoviscoelasticity theories are made. The effects of many parameters are discussed.

Generalized Thermoelastic Infinite Annular Cylinder under the Hyperbolic Two-Temperature Fractional-Order Strain Theory

This work introduces a new thermoelastic model of an isotropic and homogeneous annular cylinder. The cylinder’s bounding inner surface is shocked thermally, and the bounding outer surface has no temperature increment and volumetric strain. The governing equations in the context of the hyperbolic two-temperature generalized thermoelasticity with fractional-order strain theory have been derived. The numerical solutions of the conductive temperature, dynamic temperature, displacement, strain, and stress are illustrated in figures that use various values of fractional-order and two-temperature parameters to stand on their effects on the thermal and mechanical waves. The fractional-order parameter has significant impacts on the displacement, strain, and stress distributions. However, it does not affect dynamic or conductive temperatures. The hyperbolic two-temperature model is a successful model for making thermal and mechanical waves propagate at limited speeds.

A Stochastic Thermo-Mechanical Waves with Two-Temperature Theory for Electro-Magneto Semiconductor Medium

This paper investigates an uncommon technique by using the influence of the random function (Weiner process function), on a two-temperature problem, at the free surface of the semiconducting medium, by using the photo-thermoelasticity theory. Using the Silicon material as an example of a semiconducting medium under the influence of a magnetic field, the novel model can be formulated. To make the problem more logical, the randomness of the Weiner process function is aged to the governing stochastic equation. A combining stochastic process with the boundary of the variables is studied. In this case, the stochastic and deterministic solutions were obtained for all physical quantities. The additional noise is regarded as white noise. The problem is investigated according to a two-dimensional (2D) deformation. The normal mode method can be used mathematically to obtain numerically the deterministic, stochastic, and variance solutions of all physical quantities. Three sample paths are obtained by making a comparison between the stochastic and deterministic distributions of the field variables. The impacts of adding randomization to the boundary conditions are highlighted. The numerical results are shown graphically and discussed in consideration of the two-temperature parameter effect.

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.

Thermo-Elastodifusive Waves in Semiconductor Excitation Medium with Laser Pulses under Two Temperature Photo-Thermoelasticity Theory

The current work aims to investigate elasto-thermodiffusive wave propagation in a homogeneous, isotropic, and thermally conducting excited semiconductor medium. The two-temperature theory is utilized in the context of the linear photo-thermoelasticity (PTE) theory of semiconductors. Thermal and elastic memories found in the equations for heat, motion, and charge carrier field are taken into account. The governing equations are applied according to the mass-diffusion transport processes in one dimension (1D), under the influence of optoelectronics with a non-Gaussian laser pulse. Laplace transforms for dimensionless quantities are utilized to obtain the analytical linear solutions for the main quantities during thermoelastic (TD) and electronic (ED) deformation. The numerical approximations solutions of the primary relevant relations are done in the Laplace inverse time domain to observe the exact expressions of the main physical quantities according to some boundary surface conditions. The physical parameters of silicon (Si) semiconductor material are used to obtain the numerical computational results. According to the difference of the thermal memories and two-temperature parameters, the wave propagation of the physical fields is obtained graphically and the results are discussed and analyzed theoretically.

Reflection/transmission of plane waves at the interface of an ideal fluid and nonlocal piezothermoelastic medium

PurposeThis paper aims to study the variation of energy ratios of different reflected and transmitted waves by calculating the amplitude ratios.Design/methodology/approachThis investigation studied the reflection and transmission of plane waves on an interface of nonlocal orthotropic piezothermoelastic space (NOPHS) and fluid half-space (FHS) in reference to dual-phase-lag theory under three different temperature models, namely, without-two-temperature, classical-two-temperature, and hyperbolic-two-temperature with memory-dependent derivatives (MDDs).FindingsThe primary (P) plane waves propagate through FHS and strike at the interface x3 = 0. The results are one wave reflected in FHS and four waves transmitted in NOPHS. It is noticed that these ratios are observed under the impact of nonlocal, dual-phase-lag (DPL), two-temperature and memory-dependent parameters and are displayed graphically. Some particular cases are also deduced, and the law of conservation of energy across the interface is justified.Research limitations/implicationsAccording to the available literature, there is no substantial research on the considered model incorporating NOPHS and FHS with hyperbolic two-temperature, DPL and memory.Practical implicationsThe current model may be used in various fields, including earthquake engineering, nuclear reactors, high particle accelerators, aeronautics, soil dynamics and so on, where MDDs and conductive temperature play a significant role. Wave propagation in a fluid-piezothermoelastic media with different characteristics such as initial stress, magnetic field, porosity, temperature, etc., provides crucial information about the presence of new and modified waves, which is helpful in a variety of technical and geophysical situations. Experimental seismologists, new material designers and researchers may find this model valuable in revising earthquake estimates.Social implicationsThe researchers may classify the material using the two-temperature parameter and the time-delay operator, where the parameter is a new indication of its capacity to transmit heat in interaction with various materials.Originality/valueThe submitted manuscript is original work done by the team of said authors and each author contributed equally to preparing this manuscript.

A Novel Photo Elasto-Thermodiffusion Waves with Electron-Holes in Semiconductor Materials with Hyperbolic Two Temperature

In this paper, a novel mathematical—physical model of the generalized elasto-thermodiffusion (hole/electron interaction) waves in semiconductor materials is studied when the hyperbolic two-temperature theory in the two-dimensional (2D) deformation is taken into account. Shear (purely transverse) waves are dissociated from the remainder of the motion and remain unaffected by external fields. The coupled system of partial differential equations of the main interacting fields has been solved. Using the Laplace transform method, the governing equations of motion and heat conduction can be formulated in 2D. The hole charge carrier, displacement, thermal, and plasma boundary conditions are applied on the interface adjacent to the vacuum to obtain the basic physical quantities in the Laplace domain. The inversion of the Laplace transform with the numerical method is applied to obtain the complete solutions in the time domain for the main physical fields under investigation. The effects of thermoelastic, the phase-lag of the temperature gradient and the phase-lag of the heat flux, the hyperbolic two-temperature parameter, and comparing between silicon and germanium materials on the displacement component, carrier density, hole charge carrier, and temperature distribution have been discussed and obtained graphically.

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.

Influence of the Electromagnetic Energy Due to Cellular Devices in a Multi-Layer Human Head under Two-Temperature Heat Conduction Model

In this study, a mathematical model of a human head with three layers of skin, bone, and brain for both children and adults was created. The phase-lag time definition was used to evaluate the internal thermal reaction that is created via the human head as a result of chemical processes. In the framework of the two-temperature heat conduction model, the governing equations were developed. The inversions were numerically derived using an approximation approach after applying Laplace transforms. When the human head is exposed to cellular devices that emit an electromagnetic wave, the dynamic and conductive temperature increments distributions have been calculated and discussed with various values of the two-temperature parameter, time, relaxation time, power transmission frequency, and power density. Each layer of the human cranium is affected by all of the characteristics analysed. The impacts of electromagnetic waves emitted by cellular devices were more detrimental to the bones of children’s heads than they are to the bones of adults’ heads.

Thermal analysis of fractional hyperbolic two-temperature porous skin tissue subjected to fractional thermal diffusion by using diagonalization method

This work is dealing with a model of a layer of porous skin tissue exposed to fractional thermal diffusion based on one relaxation time consideration. The surface plane of the skin tissue is influenced by variable thermal and chemical potential shocks with time. Laplace transform has been used, and the general solution was carried out analytically in the Laplace transform domain by applying the diagonalization method. The inverse of the Laplace transforms has been calculated by using a numerical method based on the Tzou formula. The dynamical and conductive temperature increments and the concentration have been computed and represented graphically with different cases. The two-temperature parameter, fractional order parameter, and porosity parameter have significant effects on the dynamical and conductive temperature increment and concentration of the diffusive material. Applying hyperbolic two-temperature of heat conduction on porous skin tissue based on fractio of heat conduction and thermal diffusion is a novel mathematical model. Moreover, this work introduces the diagonalization method as a different new method for this type of mathematical model.

A GL photo-thermal theory upon new hyperbolic two-temperatures in a semiconductor material

A novel GL model of a new hyperbolic two-temperatures theory is studied to investigate the propagation of the thermoelastic waves on semiconductor materials. The basic equations are studied during the photo-excitation processes in the context of the photo-thermo-elastic model. The outer surface of the semiconductor medium is illuminated by a laser pulse. By using Laplace transform with the eigenvalues scheme, the analytical solutions of all studying fields are presented. The carrier density variation, the variations of the thermodynamic and the conductive temperatures, the displacement and stress components in a semi-infinite semi-conductor material are estimated. The effects of the hyperbolic two-temperature parameter and the relaxation times on the distributions of wave propagation of physical fields for semiconductor silicon (Si) medium are shown graphically and discussed.

Hyperbolic two-temperature generalized thermoelasticity with fractional order strain of solid cylinder

A novel mathematical model of thermoelastic of a homogenous isotropic solid cylindrical infinite medium has been constructed in this paper. Thermally shocked is the bounding surface of the cylinder. In the sense of the hyperbolic two-temperature generalized thermoelasticity with fractional stress theory, the governing equations have been taken. 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 stress, which are graphically applicable to all the functions studied. The fractional-order parameter has significant effects on stress and displacement distributions, while it has little effect on the dynamical and conductive temperatures increment and significant effects on all studied functions as well as on the two-temperature parameter. The two-temperature hyperbolic model is precious and effective.

Diagonalization Method to Hyperbolic Two-Temperature Generalized Thermoelastic Solid Sphere under Mechanical Damage Effect

This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.

Effect of two-temperature parameter on thermoelastic vibration in micro and nano beam resonator

Thermoelastic vibration of micro and nano-beam resonators is described by the Euler-Bernoulli beam theory in context with two-temperature generalized thermoelasticity theory. The amplitude of deflection and thermal moment in the case of simply supported and the isothermal beam are obtained by the Laplace transform method along with the finite Fourier sine transform method and the vibration frequency is examined by the normal mode analysis when the beam-ends are clamped and isothermal. The effects of the two-temperature parameter and micro and nano-beam thickness on the amplitude of deflection, thermal moment, and thermoelastic vibration frequency of the micro and nano-beam resonator have been studied and shown with the numerical results. A comparison of the results with the corresponding results of the two-temperature generalized thermoelasticity (2TLS) and the Lord-Shulman (LS) theories is also presented. Besides, the size dependency nature of the micro and nano-beam is analyzed by analytical and numerical results.

State–space approach on two-temperature three-phase-lag thermoelastic medium with a spherical cavity due to memory-dependent derivative

In this article, thermoelastic interaction in a two-temperature generalized thermoelastic unbounded isotropic medium having spherical cavity has been studied in the context of memory-dependent derivative (MDD). The governing coupled equations for the problem associated with kernel function and time delays are considered in the perspective of two-temperature (2 T) three-phase-lag thermoelasticity theory. The bounding surface of the spherical cavity is subjected to mechanical and thermal loading. Using Laplace transform, the problem is transformed from the space–time domain and then solved by the state–space approach method. Suitable numerical technique is used to find the inversion of Laplace transforms. Comparisons are made graphically, between the 2 T three-phase-lag model and 2 T Lord Shulman model with MDD. Also, the effects of time-delay parameter and the kernel function on the distributions of the strain component, thermodynamic temperature, conductive temperature, displacement components, radial and hoop stresses are examined and illustrated graphically. The results show that due to the influence of the three-phase-lag-effect, memory effect, two-temperature parameter, the kernel function and time-delay, all the distributions are affected extensively.