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1 – 10 of 334Rajneesh 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.
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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.
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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.
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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.
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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.
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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.
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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.
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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).
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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.
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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.
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