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Article
Publication date: 17 December 2019

Ahmed E. Abouelregal

In this work, a modified thermoelastic model of heat conduction, including higher order of time derivative, is constructed by extending the Roychoudhuri model (TPL…

Abstract

Purpose

In this work, a modified thermoelastic model of heat conduction, including higher order of time derivative, is constructed by extending the Roychoudhuri model (TPL) (Choudhuri, 2007). In this new model, Fourier’s law of heat conduction is replaced by using Taylor series expansions, including three different phase lags for the heat flux, the thermal displacement and the temperature gradient. The generalized thermoelasticity models of Lord–Shulman (Lord and Shulman, 1967), Green and Naghdi (1991), dual-phase lag (Tzou, 1996) and three-phase lag (TPL) (Choudhuri, 2007) are obtained as special cases. The paper aims to discuss these issues.

Design/methodology/approach

The aim of this work is to establish a new generalized mathematical model of thermoelasticity that includes TPL in the vector of heat flux, and in the thermal displacement and temperature gradients extending TPL model (Li et al., 2019e). In this model, Fourier law of heat conduction is replaced by using Taylor series expansions to a modification of the Fourier law with introducing three different phase lags for the heat flux vector, the temperature gradient, and the thermal displacement gradient and keeping terms up with suitable higher orders.

Findings

The established high-order three-phase-lag heat conduction model reduces to the previous models of thermoelasticity as special cases.

Originality/value

In this paper, a TPL thermoelastic model is developed by extending the Roychoudhuri (Sherief and Raslan, 2017) model (TPL) considering the Taylor series approximation of the equation of heat conduction. This model is an alternative construction to the TPL model. The new model includes high order of TPL in the vector of heat flux, and in the thermal displacement and temperature gradients.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 4
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 28 April 2020

Aatef Hobiny, Faris S. Alzahrani and Ibrahim Abbas

The purposes of this study, a generalized model for thermoelastic wave under three-phase lag (TPL) model is used to compute the increment of temperature, the components of…

Abstract

Purpose

The purposes of this study, a generalized model for thermoelastic wave under three-phase lag (TPL) model is used to compute the increment of temperature, the components of displacement, the changes in volume fraction field and the stress components in a two-dimension porous medium.

Design/methodology/approach

By using Laplace-Fourier transformations with the eigen values methodologies, the analytical solutions of all physical variables are obtained.

Findings

The derived methods are estimated with numerical outcomes which are applied to the porous media in simplified geometry.

Originality/value

Finally, the outcomes are represented graphically to display the difference among the models of the TPL and the Green and Naghdi (GNIII) with and without energy dissipations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 12
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 15 August 2019

Mohamed I.A. Othman, Samia Said and Marin Marin

In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III…

Abstract

Purpose

In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium.

Design/methodology/approach

The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis.

Findings

The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed.

Originality/value

To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 12
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 20 May 2020

Biswajit Singh, Smita Pal (Sarkar) and Krishnendu Barman

This study aims to attempt to construct a new mathematical model of the generalized thermoelasiticity theory based on the memory-dependent derivative (MDD) considering…

Abstract

Purpose

This study aims to attempt to construct a new mathematical model of the generalized thermoelasiticity theory based on the memory-dependent derivative (MDD) considering three-phase-lag effects. The governing equations of the problem associated with kernel function and time delay are illustrated in the form of vector matrix differential equations. Implementing Laplace and Fourier transform tools, the problem is sorted out analytically by an eigenvalue approach method. The inversion of Laplace and Fourier transforms are executed, incorporating series expansion procedures. Displacement component, temperature and stress distributions are obtained numerically and illustrated graphically and compared with the existing literature.

Design/methodology/approach

This study is to analyze the influence of MDD of three-phase-lag heat conduction interaction in an isotropic semi-infinite medium. The current model has been connected to generalize two-dimensional (2D) thermoelasticity problem. The governing equations are shown in vector matrix form of differential equation concerning Laplace-transformed domain and solved by using the eigenvalue technique. The combined Laplace Fourier transform is applied to find the analytical interpretations of temperature, stresses, displacement for silicon material in a non-dimensional form. Inverse Laplace transform has been found by applying Fourier series expansion techniques introduced by Honig and Hirdes (1984) after performing the inverse Fourier transform.

Findings

The main conclusion of this current study is to demonstrate an innovative generalized concept for heat conducting Fourier’s law associated with moderation of time parameter, time delay variable and kernel function by applying the MDDs. However, an important role is played by the time delay parameter to characterize the behavioral patterns of the physical field variables. Further, a new categorization for materials may be created rendering to this new idea along MDD for the time delay variables to develop a new measure of its potential to regulate heat in the medium.

Originality/value

Generalized thermoelasticity is hastily undergoing modification day-by-day from basic thermoelasticity. It has been progressed to get over from the limitations of fundamental thermoelasticity, for instance, infinite velocity components of thermoelasticity interference, in the adequate thermoelastic response of a solid to short laser pulses and deprived illustrations of thermoelastic performance at low temperature. In the past few decades, the fractional calculus is used to change numerous existing models of physical procedure, and its applications are used in various fields of physics, continuum mechanics, fluid mechanics, biology, viscoelasticity, biophysics, signal and image processing, control theory, engineering fields, etc.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 6
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 7 November 2017

Rajneesh Kumar, Priyanka Kaushal and Rajni Sharma

The purpose of this paper is to investigate a two dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.

Abstract

Purpose

The purpose of this paper is to investigate a two dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.

Design/methodology/approach

Three phase lag theory of thermoelasticity has been used to formulate the problem. A numerical inversion technique is applied to obtain the result in the physical domain. The numerical values of the resulting quantities are presented graphically to show the effect of porosity and dual phase lag model. Some particular cases are also presented.

Findings

The Laplace and Hankel transforms are employed followed by the eigen value approach to obtain the components of displacements, microrotation, volume fraction field, temperature distribution and stresses in the transformed domain.

Originality/value

This paper fulfils the need to study the two-dimensional problem of micropolar porous thermoelastic circular plate subjected to ramp type heating.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 4
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 10 August 2015

Samia M Said

The purpose of this paper is to investigate the effect of rotation and a magnetic field on the wave propagation in a generalized thermoelastic problem for a medium with an…

Abstract

Purpose

The purpose of this paper is to investigate the effect of rotation and a magnetic field on the wave propagation in a generalized thermoelastic problem for a medium with an internal heat source that is moving with a constant speed.

Design/methodology/approach

The formulation is applied to a generalized thermoelastic problem based on the three-phase-lag model and Green-Naghdi theory without energy dissipation. The medium is a homogeneous isotropic thermoelastic in the half-space.

Findings

The exact expressions of the displacement components, temperature, and stress components are obtained by using normal mode analysis.

Originality/value

Comparisons are made with the results predicted by the two models in the absence and presence of a magnetic field as well as a rotation. A comparison also is made with the results predicted by the two models for two different values of an internal heat source.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 14 November 2016

Rajneesh Kumar and Shaloo Devi

The purpose of this paper is to deal with the study of plane waves and fundamental solution in a modified couple stress generalized thermoelastic solid with three-phase-lag

Abstract

Purpose

The purpose of this paper is to deal with the study of plane waves and fundamental solution in a modified couple stress generalized thermoelastic solid with three-phase-lag (TPL) model of thermoelasticity.

Design/methodology/approach

It is found that for two-dimensional model, there exists two longitudinal waves, namely, longitudinal wave (P-wave), thermal wave (T-wave), and a set of coupled transverse waves (SV1 and SV2 waves). In addition, the fundamental solution for the system of differential equations for steady oscillations in terms of elementary functions has been constructed. Some properties of fundamental solution are also established. Various particular cases of interest are also deduced from the present investigations and compared with the known results.

Findings

The phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically to see the effect of TPL model, dual-phase-lag (DPL) model and GN-III model in the presence of couple stress parameter.

Originality/value

The results are compared with couple stress TPL model, couple stress DPL model and GN-III model.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 4
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 12 June 2017

Samia M. Said

The purpose of this paper is to investigate the effect of a hydrostatic initial stress and the gravity field on a fiber-reinforced thermoelastic medium with an internal…

Abstract

Purpose

The purpose of this paper is to investigate the effect of a hydrostatic initial stress and the gravity field on a fiber-reinforced thermoelastic medium with an internal heat source that is moving with a constant speed.

Design/methodology/approach

A general model of the equations of the formulation in the context of the three-phase-lag model and Green-Naghdi theory without energy dissipation.

Findings

The exact expressions for the displacement components, force stresses, and the thermal temperature for the thermal shock problem obtained by using normal mode analysis.

Originality/value

A comparison made between the results of the two models for different values of a hydrostatic initial stress as well as an internal heat source. Comparisons also made with the results of the two models in the absence and presence of the gravity field as well as the reinforcement.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 12 June 2017

Mohamed I.A. Othman, Yassmin D. Elmaklizi and Nehal T. Mansoure

The purpose of this paper is to investigate the propagation of plane waves in an isotropic elastic medium under the effect of rotation, magnetic field and…

Abstract

Purpose

The purpose of this paper is to investigate the propagation of plane waves in an isotropic elastic medium under the effect of rotation, magnetic field and temperature-dependent properties with two‐temperatures.

Design/methodology/approach

The problem has been solved analytically by using the normal mode analysis.

Findings

The numerical results are given and presented graphically when mechanical and thermal force are applied. Comparisons are made with the results predicted by the three-phase-lag (3PHL) model and dual-phase-lag model in the presence and absence of cases where the modulus of elasticity is independent of temperature.

Originality/value

In this work, the authors study the influence of rotation and magnetic field with two‐temperature on thermoelastic isotropic medium when the modulus of elasticity is taken as a linear function of reference temperature in the context of the 3PHL model. The numerical results for the field quantities are obtained and represented graphically.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 8 August 2016

Rajneesh Kumar, Nidhi Sharma and Parveen Lata

The purpose of this paper is to depict the effect of time and thermal and diffusion phase-lags due to axisymmetric heat supply in a ring. The problem is discussed within…

Abstract

Purpose

The purpose of this paper is to depict the effect of time and thermal and diffusion phase-lags due to axisymmetric heat supply in a ring. The problem is discussed within the context of dual-phase-lag heat transfer and dual-phase-lag diffusion models. The upper and lower surfaces of the ring are traction free and subjected to an axisymmetric heat supply.

Design/methodology/approach

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 displacements, stresses and chemical potential, temperature and mass concentration 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 effect of time and diffusion and thermal phase-lags are shown on the various components. Some particular cases of result are also deduced from the present investigation.

Findings

It is observed that change in time changes the behaviour of deformations of the various components of stresses, displacements, chemical potential function, temperature change and mass concentration. The authors find that for t=0.2, trends are oscillatory in all the cases whereas for t=0.1, trends are quite different. A sound impact of diffusion and thermal phase-lags on the various quantities is observed. A lot of difference in the trends of single phase lag and dual phase lag is observed. The use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient.

Originality/value

This problem is totally new because dual phase lag is applied in heat conduction and diffusion equation while considering the problem of plate in axisymmetric heat supply.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

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