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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) (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: 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 (TPL…

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

Keywords

Article
Publication date: 24 July 2023

Rachaita Dutta, Soumik Das, Shishir Gupta, Aditi Singh and Harsh Chaudhary

The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids…

Abstract

Purpose

The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.

Design/methodology/approach

With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.

Findings

The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.

Originality/value

As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 November 2022

Sandeep Singh Sheoran, Shilpa Chaudhary and Kapil Kumar Kalkal

The purpose of this paper is to study the transient thermoelastic interactions in a nonlocal rotating magneto-thermoelastic medium with temperature-dependent properties…

Abstract

Purpose

The purpose of this paper is to study the transient thermoelastic interactions in a nonlocal rotating magneto-thermoelastic medium with temperature-dependent properties. Three-phase-lag (TPL) model of generalized thermoelasticity is employed to study the problem. An initial magnetic field with constant intensity acts parallel to the bounding plane. Therefore, Maxwell's theory of electrodynamics has been effectively introduced and the expression for Lorentz's force is obtained with the help of modified Ohm's law.

Design/methodology/approach

The normal mode technique has been adopted to solve the resulting non-dimensional coupled field equations to obtain the expressions of physical field variables.

Findings

For uniformly distributed thermal load, normal displacement, temperature distribution and stress components are calculated numerically with the help of MATLAB software for a copper material and the results are illustrated graphically. Some particular cases of interest are also deduced from the present study.

Originality/value

Influences of nonlocal parameter, rotation, temperature-dependent properties, magnetic field and time are carefully analyzed for mechanically stress free boundary and uniformly distributed thermal load. The present work is useful and valuable for analysis of problem involving thermal shock, nonlocal parameter, temperature-dependent elastic and thermal moduli.

Details

Multidiscipline Modeling in Materials and Structures, vol. 18 no. 6
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 2 October 2018

Gaurav Mittal and Vinayak Kulkarni

The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction…

Abstract

Purpose

The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction based upon Tzou model that includes temperature gradient, the thermal displacement and two different translations of heat flux vector and temperature gradient has been used to formulate the heat conduction model. The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration.

Design/methodology/approach

The work presented in this manuscript proposes a dual-phase-lag mathematical model of a thick circular plate in a finite cylindrical domain subjected to axis-symmetric heat flux. The model has been designed in the context of fractional thermoelasticity by considering two successive terms in Taylor’s series expansion of fractional Fourier law of heat conduction in the two different translations of heat flux vector and temperature gradient. The analytical results have been obtained in Laplace transform domain by transforming the original problem into eigenvalue problem using Hankel and Laplace transforms. The numerical inversions of Laplace transforms have been achieved using the Gaver−Stehfast algorithm, and convergence criterion has been discussed. For illustrative purpose, the dual-phase-lag model proposed in this manuscript has been applied to a periodically varying heat source. The numerical results have been depicted graphically and compared with classical, fractional and generalized thermoelasticity for various fractional orders under consideration.

Findings

The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. This model has been applied to study the thermal effects in a thick circular plate subjected to a periodically varying heat source.

Practical implications

A dual-phase-lag model can effectively be incorporated to study the transient heat conduction problems for an exponentially decaying pulse boundary heat flux and/or for a short-pulse boundary heat flux in long solid tubes and cylinders. This model is also applicable to study the various effects of the thermal lag ratio and the shift time. These dual-phase-lag models are also practically applicable in the problems of modeling of nanoscale heat transport problems of semiconductor devices and accordingly semiconductors can be classified as per their ability of heat conduction.

Originality/value

To the authors’ knowledge, no one has discussed fractional thermoelastic dual-phase-lag problem associated with relaxation time in a finite cylindrical domain for a thick circular plate subjected to an axis-symmetric heat source. This is the latest and novel contribution to the field of thermal mechanics.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 no. 5
Type: Research Article
ISSN: 1573-6105

Keywords

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…

77

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 Green–Naghdi (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: 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

Keywords

Article
Publication date: 14 August 2019

Siddhartha Biswas

The purpose of this paper is to deal with the three-dimensional analysis of free vibrations in a stress-free and rigidly fixed homogeneous transversely isotropic hollow cylinder…

Abstract

Purpose

The purpose of this paper is to deal with the three-dimensional analysis of free vibrations in a stress-free and rigidly fixed homogeneous transversely isotropic hollow cylinder in the context of three-phase-lag (TPL) model of hyperbolic thermoelasticity.

Design/methodology/approach

The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate.

Findings

The natural frequency, dissipation factor and inverse quality factor in the stress-free and rigidly fixed hollow cylinder get significantly affected due to thermal vibrations and thermo-mechanical coupling.

Originality/value

The modified Bessel functions and matrix Frobenius method have been directly used to study the vibration model of a homogeneous, transversely isotropic hollow cylinder in the context of TPL model based on three-dimensional thermoelasticity.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 6
Type: Research Article
ISSN: 1573-6105

Keywords

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 temperature-dependent…

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

Keywords

Article
Publication date: 18 September 2017

Rajneesh Kumar and Shaloo Devi

The purpose of this paper is to investigate the thermoelastic functionally graded beam in a modified couple stress theory subjected to a dual-phase-lag model.

Abstract

Purpose

The purpose of this paper is to investigate the thermoelastic functionally graded beam in a modified couple stress theory subjected to a dual-phase-lag model.

Design/methodology/approach

The governing equations are solved by using the Euler-Bernoulli beam assumption and the Laplace transform technique. The lateral deflection, temperature change, displacement component, axial stress and thermal moment of the beam are obtained by ramp type heating in the transformed domain. A general algorithm of the inverse Laplace transform is developed to recover the results in a physical domain.

Findings

The lateral deflection, temperature change, displacement component, axial stress and thermal moment of the beam are computed numerically and presented graphically to show the effect of ramp time parameter and phase lags of heating.

Originality/value

Comparisons are made in the absence and presence of coupled dual-phase-lag thermoelastic and coupled thermoelastic L-S theories and also different values of ramp type parameter.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

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