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Article
Publication date: 23 April 2020

Ashraf M. Zenkour

The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized…

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Abstract

Purpose

The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized thermoelasticity theory have been proposed.

Design/methodology/approach

Some models with and without energy dissipation have been presented as well as the simple forms of GreenNaghdi (G–N) theories. These novel multi- and single-/dual-phase-lag models are presented to investigate the thermo-diffusion of the solid cylinder. The closed-form solution of thermo-diffusion governing equations of solid cylinder has been obtained to deduce all field variables.

Findings

A comparison study between the simple G–N II and III models and their improved models has been presented. The validations of outcomes are acceptable and so benchmarks are reported to help other investigators in their future comparisons.

Originality/value

The modified Green and Naghdi theories of types II and III are presented to get novel and accurate models of single- and dual-phase-lag of multiterms. The heat of mass diffusion equation as well as the constitutive equations for the stresses and chemical potential of a solid cylinder is added to the present formulation. The system of three differential coupled equations is solved, and all field variables are obtained for the thermal diffusion of the solid cylinder. Some validation examples and applications are presented to compare the simple and modified Green and Naghdi theories of types II and III. Sample plots are illustrated along the radial direction of the solid cylinder. Some results are tabulated to serve as benchmark results for future comparisons with other investigators. The reported and illustrated results show that the simple G–N II and III models yield the largest values of all field quantities. The single-phase-lag models give the smallest values. However, the dual-phase-lag model yields results that are intermediate between those of the simple and single-phase-lag G–N models.

Details

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

Keywords

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) are used…

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

Keywords

Article
Publication date: 2 May 2020

Leena Rani and Sushant Shekhar

The two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear…

Abstract

Purpose

The two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear temperature ramping function is used to more realistically model: thermal loading of the half-space surface. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The comparison for Lord-Shulman (L-S), Green and Lindsay (G–L), Green and Naghdi (G–N) and Chandrasekharaiah and Tzou (CTU) theories have been shown graphically to estimate the effect of ramping parameter of heating for an insulated and temperature gradient boundaries.

Design/methodology/approach

The design of the study is eigenvalue approach

Findings

Homogeneous, thermally conducting monoclinic material has been taken under consideration to study the effect of linear temperature ramping parameter on temperature and normal displacement field. It is observed that magnitude of field quantities is large near the point of application of source for the non-dimensional values of time in all the four models. The numerical values for the field quantities are computed graphically for a wide range of values of finite pulse rise-time in the two situations t0 < t, t0 > t for generalized thermoelasticity theories.

Originality/value

(1) Governing equations for homogeneous, t0 thermally conducting, monoclinic material are described and solved. (2) Eigen value approach is used to solve the problem. (3) The effect of ramping parameter of heating has been studied for various models of the thermoelasticity to show the comparision between them.

Details

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

Keywords

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) (Choudhuri…

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

Keywords

Article
Publication date: 8 November 2022

Mohamed I.A. Othman, Sarhan Y. Atwa, Ebtesam E.M. Eraki and Mohamed F. Ismail

In this work, the thermoelastic response in a micro-stretch thermoelastic half-space submerged in an unlimited non-viscous fluid under gravity, the medium is studied using the…

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Abstract

Purpose

In this work, the thermoelastic response in a micro-stretch thermoelastic half-space submerged in an unlimited non-viscous fluid under gravity, the medium is studied using the three-phase-lag model (3PHL) and Green-Naghdi theory (G-N III).

Design/methodology/approach

The normal mode analysis was the analytic technique used to obtain the exact formula of the physical quantities.

Findings

The magnesium crystal element is used as an application to compare the predictions induced by gravity on microstretch thermoelastic immersed in an infinite fluid of the three-phase-lag model with those for GreenNaghdi. Gravity has been noticed to have a major effect on all physical quantities. Comparisons were also made for three values of wave number and three values of the real part frequency.

Originality/value

This work is concerned with the thermoelastic micro-stretch solid immersed in an infinite and inviscid fluid and subjected to a gravitational field. The governing equations are formulated in the context of the 3PHL model and G-N theory. An analytical solution to the problem is obtained by employing normal mode analysis. Comparisons of the physical quantities are shown in figures to study the effects of gravity, wave number and the real part of the frequency.

Details

Multidiscipline Modeling in Materials and Structures, vol. 19 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 8 September 2022

Samia M. Said, Mohamed I.A. Othman and Mohamed G. Eldemerdash

In the present article, the three-phase-lag (3PHL) model and the Green-Naghdi theory of types II, III with memory-dependent derivative is used to study the effect of rotation on a…

Abstract

Purpose

In the present article, the three-phase-lag (3PHL) model and the Green-Naghdi theory of types II, III with memory-dependent derivative is used to study the effect of rotation on a nonlocal porous thermoelastic medium.

Design/methodology/approach

In this study normal mode analysis is used to obtain analytical expressions of the physical quantities. The numerical results are given and presented graphically when mechanical force is applied.

Findings

The model is illustrated in the context of the Green-Naghdi theory of types II, III and the three-phase lags model. Expressions for the physical quantities are solved by using the normal mode analysis and represented graphically.

Originality/value

Comparisons are made with the results predicted in the absence and presence of the rotation as well as a nonlocal parameter. Also, the comparisons are made with the results of the 3PHL model for different values of time delay.

Details

Multidiscipline Modeling in Materials and Structures, vol. 18 no. 5
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 8 August 2016

Mohamed Ibrahim A Othman and Mohamed I. M. Hilal

The purpose of this paper is to investigate the influence of the gravity and the magnetic fields on the plane waves in a homogenous, linear and isotropic thermoelastic medium…

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Abstract

Purpose

The purpose of this paper is to investigate the influence of the gravity and the magnetic fields on the plane waves in a homogenous, linear and isotropic thermoelastic medium subjected to the laser pulse heating.

Design/methodology/approach

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

Findings

Numerical results for the temperature, the displacement components, the stress components and the volume fraction were presented graphically and analyzed the results. The graphical results indicate that the effect of gravity and magnetic fields are observable physical effects on the porous thermoelastic material heated by a laser pulse. Comparisons are made with the results in the absence and presence of the gravity and the magnetic fields, also at various times.

Originality/value

In the present work, the authors shall formulate a 2-D problem for the propagation of plane waves on the porous thermoelastic material influenced by the gravity and the magnetic fields subjected to a laser pulse heating act as a thermal shock. A comparison is also made between the two types II and III of Green-Naghdi theory in the absence and the presence of the gravity and the magnetic fields. Such problems are very important in many dynamical systems.

Details

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

Keywords

Article
Publication date: 9 August 2013

Mohamed I.A. Othman, Sarhan Y. Atwa, A. Jahangir and A. Khan

The purpose of this paper is to study the effect of gravity on the general model of the equations of generalized magneto‐thermo‐microstretch for a homogeneous isotropic elastic…

Abstract

Purpose

The purpose of this paper is to study the effect of gravity on the general model of the equations of generalized magneto‐thermo‐microstretch for a homogeneous isotropic elastic half‐space solid whose surface is subjected to a mode‐I crack. The problem is in the context of the Green and Naghdi theory of both types (II and III).

Design/methodology/approach

The normal mode analysis is used to obtain the expressions for the displacement components, the force stresses, the temperature, the couple stress and the microstress distribution.

Findings

The variations in variables against distance components are given graphically in 2D and 3D.

Practical implications

The linear theory of elasticity is of paramount importance in the stress analysis of steel, which is the commonest engineering structural material. To a lesser extent, the linear elasticity describes the mechanical behavior of the other common solid materials, e.g. concrete, wood and coal. However, the theory does not apply to the behavior of many of the newly synthetic materials of the elastomer and polymer type, e.g. polymethyl‐methacrylate (Perspex), polyethylene and polyvinyl chloride.

Originality/value

Comparisons are made with the results in the presence and absence of gravity and initially applied magnetic field with two cases: the first for the generalized micropolar thermoelasticity elastic medium (without stretch constants) between both types (II, III); and the second for the generalized magneto‐thermoelastic medium with stretch (without micropolar constants) between both types (II, III).

Details

Multidiscipline Modeling in Materials and Structures, vol. 9 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

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

Keywords

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 heat…

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

Keywords

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