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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: 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 the…

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

Article
Publication date: 14 August 2017

Rajneesh Kumar, Aseem Miglani and Rekha Rani

The purpose of this paper is to study the axisymmetric problem in a micropolar porous thermoelastic circular plate with dual phase lag model by employing eigenvalue approach…

Abstract

Purpose

The purpose of this paper is to study the axisymmetric problem in a micropolar porous thermoelastic circular plate with dual phase lag model by employing eigenvalue approach subjected to thermomechanical sources.

Design/methodology/approach

The Laplace and Hankel transforms are employed to obtain the expressions for displacements, microrotation, volume fraction field, temperature distribution and stresses in the transformed domain. A numerical inversion technique has been carried out to obtain the resulting quantities in the physical domain. Effect of porosity and phase lag on the resulting quantities has been presented graphically. The results obtained for Lord Shulman theory (L-S, 1967) and coupled theory of thermoelasticity are presented as the particular cases.

Findings

The variation of temperature distribution is similar for micropolar thermoelastic with dual (MTD) phase lag model and coupled theory of thermoelasticity. The variation is also similar for tangential couple stress for MTD and L-S theory but opposite to couple theory. The behavior of volume fraction field and tangential couple stress for L-S theory and coupled theory are observed opposite. The values of all the resulting quantities are close to each other away from the sources. The variation in tangential stress, tangential couple stress and temperature distribution is more uniform.

Originality/value

The results are original and new because the authors presented an eigenvalue approach for two dimensional problem of micropolar porous thermoelastic circular plate with dual phase lag model. A comparison of porosity, L-S theory and coupled theory of micropolar thermoelasticity is made. Such problem has applications in material science, industries and earthquake problems.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 2
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

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: 10 October 2016

Rajneesh Kumar, Shaloo Devi and Veena Sharma

The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the…

Abstract

Purpose

The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model.

Design/methodology/approach

The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique.

Findings

The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter.

Originality/value

Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

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

Keywords

Article
Publication date: 10 August 2015

Rajneesh Kumar, Sanjeev Ahuja and S.K. Garg

The purpose of this paper is to study of propagation of plane wave and the fundamental solution of the system of differential equations in the theory of a microstretch…

Abstract

Purpose

The purpose of this paper is to study of propagation of plane wave and the fundamental solution of the system of differential equations in the theory of a microstretch thermoelastic diffusion medium in phase-lag models for the case of steady oscillations in terms of elementary functions.

Design/methodology/approach

Wave propagation technique along with the numerical methods for computation using MATLAB software has been applied to investigate the problem.

Findings

Characteristics of waves like phase velocity and attenuation coefficient are computed numerically and depicted graphically. It is found that due to the presence of diffusion effect, these characteristics get influenced significantly. However, due to decoupling of CD-I and CD-II waves from rest of other, no effect on these characteristics can be perceived.

Originality/value

Basic properties of the fundamental solution are established by introducing the dual-phase-lag diffusion (DPLD) and dual-phase-lag heat transfer (DPLT) models.

Details

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

Keywords

Article
Publication date: 3 June 2019

Ewa Majchrzak and Bohdan Mochnacki

The purpose of this paper is the application of the finite difference method (FDM) for numerical modeling of the microscale heat transfer processes occurring in the domain of thin…

Abstract

Purpose

The purpose of this paper is the application of the finite difference method (FDM) for numerical modeling of the microscale heat transfer processes occurring in the domain of thin metal film subjected to a laser pulse. The problem discussed is described by the different variants of the second-order dual-phase-lag equation (DPLE). The laser action is taken into account by the introduction of internal volumetric heat source to the governing equation. The capacity of the source is dependent on the geometrical co-ordinates and duration of the laser beam. The modified forms of DPLE presented in the paper, resulting from the certain substitutions introduced to the basic equation.

Design/methodology/approach

At the stage of numerical computations, the different variants of the FDM are applied. Both the explicit and implicit FDM schemes are used. The formula determining the capacity of the internal heat source suggests the formulation of the task discussed using the cylindrical co-ordinate system. The in-house programs realizing the numerical computations concern the axially-symmetrical tasks. In this paper, the metal films made of the nickel and gold are considered.

Findings

The algorithms presented make possible to analyze the heating/cooling processes occurring in the domain of metal film having a thickness Z for the different laser parameters (laser intensity, characteristic time of laser pulse and laser beam radius) and the different materials (optical penetration depth, reflectivity of irradiated surface, lag times, thermal conductivity and volumetric specific heat).

Research limitations/implications

Not for all metals, one can find information on lag times. In the literature, analytical formulas can be found to calculate these values, but they are strongly approximated. It should be pointed out that there are some limitations concerning the delay times of material considered, which assure the physical correctness of the second-order DPLE.

Originality/value

The FDM algorithm concerns the three-dimensional cylindrical domain while a large majority of the second-order DPLE numerical solutions have been obtained for the one-dimensional tasks. Both the implicit and explicit numerical schemes are proposed and the testing computations confirm the correctness and effectiveness of the algorithms presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 9 November 2015

Rajneesh Kumar and Vandana Gupta

– The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion.

Abstract

Purpose

The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion.

Design/methodology/approach

The field equations for the linear theory of homogeneous isotropic thermoelastic diffusion medium are taken into consideration by using dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. This equation is converted into a polynomial form of higher degree.

Findings

From the polynomial equation, Rayleigh wave root is found. The secular equation is resolved into a polynomial form to find the roots and therefore to find the existence and propagation of Rayleigh wave. The existence of Rayleigh wave in the assumed model depends on the values of various parameters involved in the secular equation. These roots are resolved for phase velocity and attenuation of the inhomogeneous propagation of Rayleigh wave. Behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. Particular cases of the interest are also deduced from the present investigation.

Originality/value

Governing equations corresponding to DPLT and DPLD models of thermoelastic diffusion are formulated to study the wave propagation and their dependence on various material parameters. In this paper effects of thermal and diffusion phase lags on the phase velocity, attenuation and on particle paths are observed and depicted graphically.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

1 – 10 of 83