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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: 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: 13 June 2016

Rajneesh Kumar, Kulwinder Singh and Devinder Pathania

The purpose of this paper is to investigate a two dimensional problem in magneto-micropolar thermoelastic half-space with fractional order derivative in the presence of combined…

Abstract

Purpose

The purpose of this paper is to investigate a two dimensional problem in magneto-micropolar thermoelastic half-space with fractional order derivative in the presence of combined effects of hall current and rotation subjected to ramp-type heating.

Design/methodology/approach

The fractional order theory of thermoelasticity with one relaxation time derived by Sherief et al. (2010) has been used to investigate the problem. Laplace and Fourier transform technique has been used to solve the resulting non-dimensional coupled field equations to obtain displacement, stress components and temperature distribution. A numerical inversion technique has been applied to obtain the solution in the physical domain.

Findings

Numerical computed results of all the considered variables have been shown graphically to depict the combined effect of hall current and rotation. Some particular cases of interest are also deduced from the present study.

Originality/value

Comparison are made in the presence and absence of hall current and rotation in a magneto-micropolar thermoelastic solid with fractional order derivative.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 1
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: 5 June 2017

Constantin Fetecau, Shahraz Akhtar, Ioan Pop and Corina Fetecau

The purpose of this note is to provide general solutions for radiative magnetohydrodynamic natural convection flow.

Abstract

Purpose

The purpose of this note is to provide general solutions for radiative magnetohydrodynamic natural convection flow.

Design/methodology/approach

To obtain exact solutions for such motions of Newtonian fluids, as seen in the existing literature, the Laplace transform technique is used.

Findings

General solutions are obtained for temperature, velocity and Nusselt number in the presence of heat source and shear stress on the boundary. They can generate exact solutions for any motion with technical relevance of this type. Fluid velocity is presented as the sum of mechanical and thermal components. Influence of physical parameters on temperature and velocity is graphically underlined for ramp-type heating plate that applies a constantly accelerating shear stress to the fluid. Thermal and mechanical effects are significant and must be taken into consideration.

Practical implications

For illustration, as well as for a check of results, three special cases with applications in engineering are considered and some known results are recovered.

Originality/value

Obtained solutions are presented in the simplest forms. In addition, the solutions corresponding to cosine oscillatory heating and oscillating shear are presented so that they can be immediately reduced to those corresponding to constant heating and uniform shear if the oscillations’ frequency becomes zero. Heat transfer characteristics with thermal radiation are graphically illustrated using one parameter only for such motions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 8 January 2020

Tareq Saeed and Ibrahim Abbas

The purposes of this study, a mathematical model of generalized thermoelastic theory subjected to thermal loading is presented to study the wave propagation in a two-dimensional…

Abstract

Purpose

The purposes of this study, a mathematical model of generalized thermoelastic theory subjected to thermal loading is presented to study the wave propagation in a two-dimensional porous medium.

Design/methodology/approach

By using Fourier–Laplace transforms with the eigenvalue approach, the physical quantities are analytically obtained.

Findings

The derived method is evaluated with numerical results, which are applied to the porous medium in simplified geometry.

Originality/value

Numerical outcomes for all the physical quantities considered are implemented and represented graphically. The variations of temperature, the changes in volume fraction field, the displacement components and the stress components have been depicted graphically.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 23 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

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: 21 February 2020

Aatef Hobiny and Ibrahim Abbas

The purpose of this study is to use the generalized model for thermoelastic wave under the dual phase lag (DPL) model to compute the increment of temperature, the components of…

Abstract

Purpose

The purpose of this study is to use the generalized model for thermoelastic wave under the dual phase lag (DPL) model to compute the increment of temperature, the components of displacement, the changes in volume fraction field and the stress components in a two-dimensional (2D) porous medium.

Design/methodology/approach

Using Fourier and Laplace transformations with the eigenvalue technique, the exact solutions of all physical quantities are obtained.

Findings

The derived method is evaluated with numerical results, which are applied to the porous medium in a simplified geometry.

Originality/value

Finally, the outcomes are graphically represented to show the difference among the models of classical dynamical coupled, the Lord and Shulman and DPL.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 August 2010

Praveen Ailawalia, Sunit Kumar and Devinder Pathania

The purpose of this paper is to study the deformation of a rotating generalized thermoelastic medium with two temperatures under hydrostatic initial stress subjected to different…

Abstract

Purpose

The purpose of this paper is to study the deformation of a rotating generalized thermoelastic medium with two temperatures under hydrostatic initial stress subjected to different types of sources.

Design/methodology/approach

The methodology applied here is the use of integral transforms to obtain the components of displacement, force stress, conductive temperature and temperature distribution in Laplace and Fourier domain. The general solution obtained is applied to a specific problem of a half‐space subjected to concentrated force, uniformly distributed force and a moving source. These components are then obtained in the physical domain by applying a numerical inversion method. Some particular cases are also discussed in the context of the problem. The results obtained are also presented graphically to show the effect of rotation and gravity.

Findings

The variations of all the quantities and for all the mediums are similar for concentrated force and distributed forces applied along the free surface of the solid. The values of these quantities are very close to each other for GTES and GTESWG. Deformation of a body depends on the nature of force applied as well as the type of boundary conditions. The variations of all the quantities are more uniform in nature when a force of constant magnitude moves along the surface of solid with some velocity.

Originality/value

Such types of problems in rotating media will find great applications in many dynamical systems and industries.

Details

Multidiscipline Modeling in Materials and Structures, vol. 6 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

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