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Article
Publication date: 4 November 2014

Rajneesh Kumar and Vandana Gupta

The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material…

Abstract

Purpose

The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material symmetry. A generalized form of mass diffusion equation is introduced instead of classical Fick's diffusion theory by using two diffusion phase-lags, one phase-lag of diffusing mass flux vector, represents the delayed time required for the diffusion of the mass flux and the other phase-lag of chemical potential, represents the delayed time required for the establishment of the potential gradient. The basic equations for the anisotropic thermoelastic diffusion medium in the context of dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models are presented. The governing equations for transversely isotropic and isotropic case are also reduced. The different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically. Numerically computed results are depicted graphically for anisotropic, transversely isotropic and isotropic medium. The effect of diffusion and thermal phase-lags are shown on the different characteristic of waves. Some particular cases of result are also deduced from the present investigation.

Design/methodology/approach

The governing equations of thermoelastic diffusion are presented using DPLT model and a new model of DPLD. Effect of phase-lags of thermal and diffusion is presented on different characteristic of waves.

Findings

The effect of diffusion and thermal phase-lags on the different characteristic of waves is appreciable. Also 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

Introduction of a new model of DPLD in the equation of mass diffusion.

Details

Multidiscipline Modeling in Materials and Structures, vol. 10 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 6 April 2020

Sunita Deswal, Devender Sheoran and Kapil Kumar Kalkal

The purpose of this paper is to establish a model of two-dimensional half-space problem of linear, isotropic, homogeneous, initially stressed, rotating thermoelastic medium with…

Abstract

Purpose

The purpose of this paper is to establish a model of two-dimensional half-space problem of linear, isotropic, homogeneous, initially stressed, rotating thermoelastic medium with microtemperatures. The expressions for different physical variables such as displacement distribution, stress distribution, temperature field and microtemperatures are obtained in the physical domain.

Design/methodology/approach

Normal mode analysis technique is adopted to procure the exact solution of the problem.

Findings

Numerical computations have been carried out with the help of MATLAB programming, and the results are illustrated graphically. Comparisons are made to show the effects of rotation, time and microtemperatures on the resulting quantities. The graphical results indicate that the effects of rotation, microtemperatures and time are very pronounced on the field variables.

Originality/value

In the present work, we have investigated the effects of rotation, time and microtemperature in an initially stressed thermoelastic medium. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form, i.e. the disturbances in a thermoelastic medium in the presence of angular velocity, initial stress and microtemperature have not been studied till now. The present work is useful and valuable for analysis of problems involving coupled thermal shock, rotation parameter, microtemperatures and elastic deformation.

Details

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

Keywords

Article
Publication date: 15 December 2017

Jitesh Tripathi, Shrikant Warbhe, K.C. Deshmukh and Jyoti Verma

The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which…

Abstract

Purpose

The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues.

Design/methodology/approach

Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates.

Findings

This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter.

Research limitations/implications

Constructed purely on theoretical mathematical model by considering different parameters and the functions.

Practical implications

The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations.

Originality/value

In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 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

Article
Publication date: 9 August 2013

Rajneesh Kumar and Rajeev Kumar

The purpose of this research is to study the reflection and transmission of elastic waves at the interface of an elastic half‐space and initially stressed thermoelastic diffusion…

Abstract

Purpose

The purpose of this research is to study the reflection and transmission of elastic waves at the interface of an elastic half‐space and initially stressed thermoelastic diffusion with voids half‐space.

Design/methodology/approach

Two‐dimensional model has been considered of an isotropic elastic half‐space (Medium I) lying over a homogeneous isotropic generalized initially stressed thermoelastic diffusion with voids half‐space (Medium II). There exist two waves, P‐wave and SV‐wave, in isotropic elastic half‐space and four quasi‐longitudinal waves, namely, quasi‐longitudinal wave (QP‐mode), quasi‐longitudinal mass diffusive wave (QMD‐mode), quasi‐longitudinal thermal wave (QPT‐mode) and quasi‐longitudinal volume fractional wave (QPV‐mode), and one quasi‐transverse wave (QSV‐mode) exists in initially stressed thermoelastic diffusion with voids half‐space.

Findings

The energy ratios of these waves are computed along various directions of incident wave, and it is found that the sum of all energy ratios is exactly unity at each value of incident angle. The amplitude ratios of various waves have been obtained numerically.

Originality/value

Reflection and transmission of an elastic medium is of great practical importance. Since valuable organic and inorganic deposits beneath the earth surface are difficult to detect by drilling randomly, wave propagation is the simplest and most economic technique for these and does not require any drilling through the earth. Almost all the oil companies rely on seismic interpretation for selecting the sites for exploratory oil wells because seismic wave methods have higher accuracy, have higher resolution and are more economical, as compared to drilling which is expansive and time consuming.

Details

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

Keywords

Article
Publication date: 1 March 2005

Mohamed I. A. Othman

A two‐dimensional coupled problem in electromagneto‐thermoelasticity for a thermally and electrically conducting half‐space solid whose surface is subjected to a thermal shock is…

Abstract

A two‐dimensional coupled problem in electromagneto‐thermoelasticity for a thermally and electrically conducting half‐space solid whose surface is subjected to a thermal shock is considered. The problem is in the context of the Lord and Shulman’s generalized thermoelasticity with one relaxation time. There acts an initial magnetic field parallel to the plane boundary of the half‐space. The medium deformed because of thermal shock and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the medium. The Maxwell’s equations are formulated and the electromagneto‐thermoelastic coupled governing equations are established. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier’s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium. Comparisons are made with the results predicted by the coupled theory for two values of time.

Details

Multidiscipline Modeling in Materials and Structures, vol. 1 no. 3
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: 29 March 2022

Samia M. Said

The present study discussed wave propagation in a nonlocal generalized thermoelastic half-space with moving an internal heat source under influence of rotation.

Abstract

Purpose

The present study discussed wave propagation in a nonlocal generalized thermoelastic half-space with moving an internal heat source under influence of rotation.

Design/methodology/approach

Normal mode analysis is introduced to obtain the analytical expressions of the physical quantities.

Findings

Numerical results are presented graphically to explore the effects of rotation, the nonlocal parameter, and the time-delay on the physical quantities. It is found that the physical quantities are affected by rotation, the nonlocal parameter, and the time-delay.

Originality/value

The problem is solved based on the classical-coupled theory, the Lord–Shulman theory, and the Green–Lindsay theory with memory-dependent derivative (MDD).

Details

Multidiscipline Modeling in Materials and Structures, vol. 18 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 13 May 2014

Khaled Lotfy, N. Yahia and W. Hassan

A model of the equations of two-dimensional problems in a half space, whose surface in free of micropolar thermoelastic medium possesses cubic symmetry as a result of a mode-I…

Abstract

Purpose

A model of the equations of two-dimensional problems in a half space, whose surface in free of micropolar thermoelastic medium possesses cubic symmetry as a result of a mode-I crack is studied. There acts an initial magnetic field parallel to the plane boundary of the half-space. The crack is subjected to prescribed temperature and stress distribution. The formulation in the context of the Lord-Shulman theory includes one relaxation time and Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory. The paper aims to discuss these issues.

Design/methodology/approach

The normal mode analysis is used to obtain the exact expressions for the displacement, microrotation, stresses and temperature distribution.

Findings

The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence of magnetic field.

Originality/value

A comparison is also made between the three theories for different depths in 3D plots.

Details

International Journal of Structural Integrity, vol. 5 no. 2
Type: Research Article
ISSN: 1757-9864

Keywords

Article
Publication date: 8 August 2016

Samia M Said

The dual-phase-lag (DPL) model and Lord-Shulman theory with one relaxation time are applied to study the effect of the gravity field, the magnetic field, and the hydrostatic…

Abstract

Purpose

The dual-phase-lag (DPL) model and Lord-Shulman theory with one relaxation time are applied to study the effect of the gravity field, the magnetic field, and the hydrostatic initial stress on the wave propagation in a two-temperature generalized thermoelastic problem for a medium with an internal heat source that is moving with a constant speed. The paper aims to discuss this issue.

Design/methodology/approach

The exact expressions of the considered variables are obtained by using normal mode analysis.

Findings

Numerical results for the field quantities are given in the physical domain and illustrated graphically in the absence and presence of the gravity field as well as the magnetic field. Comparisons are made between the results of the two different models with and without temperature dependent properties and for two different values of the hydrostatic initial stress. A comparison is also made between the results of the two different models for two different values of the time.

Originality/value

In the present work, the author shall formulate a two-temperature generalized magneto-thermoelastic problem for a medium with temperature dependent properties and with an internal heat source that is moving with a constant speed under the influence of a gravity field and a hydrostatic initial stress. Normal mode analysis is used to obtain the exact expressions for the displacement components, thermodynamic temperature, conductive temperature, and stress components. A comparison is carried out between the considered variables as calculated from the generalized thermoelasticity based on the DPL model and the L-S theory in the absence and presence of a magnetic field as well as a gravity field. Comparisons are also made between the results of the two theories with and without temperature dependent properties and for two different values of hydrostatic initial stress. A comparison is also made between the results of the two different models for two different values of the time.

Details

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

Keywords

1 – 10 of 334