Two-Dimensional Thermal Shock Problem of Generalized Magneto-Thermoelasticity with a Time-Fractional Heat Conduction Law

2016 ◽  
Vol 04 (02) ◽  
pp. 1650004
Author(s):  
M. Bachher ◽  
N. Sarkar
Keyword(s):  
Magnetic Field ◽  
Thermal Shock ◽  
Half Space ◽  
Thermal Stresses ◽  
Dimensional Space ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Plane Boundary ◽  
Two Dimensional ◽  
Field Equations

An electromagneto-thermoelastic coupled problem for a homogeneous, isotropic, thermally and electrically conducting half-space solid whose surface is subjected to a thermal shock is considered in two-dimensional space. The equations of the theory of generalized electromagneto-thermoelasticity with fractional derivative heat transfer allowing the second sound effects are considered. An initial magnetic field acts parallel to the plane boundary of the half-space. The normal mode analysis and the eigenvalue approach techniques are used to solve the resulting nondimensional coupled field equations for the three theories. Numerical results for the temperature, displacements and thermal stresses distributions are presented graphically and discussed. A comparison is made with the results obtained in the presence and absence of the magnetic field.

scholarly journals Effect of Rotation for Two-Temperature Generalized Thermoelasticity of Two-Dimensional under Thermal Shock Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Kh. Lotfy ◽  
Wafaa Hassan
Keyword(s):  
Thermal Shock ◽  
Half Space ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Field Equations ◽  
Conductive Temperature ◽  
Two Temperature

The theory of two-temperature generalized thermoelasticity based on the theory of Youssef is used to solve boundary value problems of two-dimensional half-space. The governing equations are solved using normal mode method under the purview of the Lord-Şhulman (LS) and the classical dynamical coupled theory (CD). The general solution obtained is applied to a specific problem of a half-space subjected to one type of heating, the thermal shock type. We study the influence of rotation on the total deformation of thermoelastic half-space and the interaction with each other under the influence of two temperature theory. The material is homogeneous isotropic elastic half-space. The methodology applied here is use of the normal mode analysis techniques that are used to solve the resulting nondimensional coupled field equations for the two theories. Numerical results for the displacement components, force stresses, and temperature distribution are presented graphically and discussed. The conductive temperature, the dynamical temperature, the stress, and the strain distributions are shown graphically with some comparisons.

Effect of Rotation to a Half-Sapce in Magneto-Thermoelasticity with Thermal Relaxations

2007 ◽  
Vol 353-358 ◽  
pp. 3018-3021
Author(s):  
Ying Pan ◽  
Zi Hou Zhang ◽  
Li Hou Liu
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Induced Magnetic Field ◽  
Coupled Problem ◽  
Analytical Expressions

Based on Green and Lindsay’s generalized thermoelasticity theory with two relaxation times, a two-dimensional coupled problem in electromagneto-thermoelasticity for a rotating half-space solid whose surface is subjected to a heat is studied in this paper. The normal mode analysis is used to obtain the analytical expressions for the considered variables. It can be found electromagneto-thermoelastic coupled effect in the medium, and it also can be found that rotation acts to significantly decrease the magnitude of the real part of displacement and stress and insignificantly affect the magnitude of temperature and induced magnetic field.

scholarly journals Two-Dimensional Deformation in a Thermoelastic Solid with Microtemperatures Subjected to an Internal Heat Source

2018 ◽  
Vol 23 (1) ◽  
pp. 5-21 ◽  
Author(s):  
P. Ailawalia ◽  
S. Budhiraja ◽  
J. Singh
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Thermoelastic Medium ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

AbstractThe purpose of this paper is to study the two dimensional deformation in a generalized thermoelastic medium with microtemperatures having an internal heat source subjected to a mechanical force. The force is acting along the interface of generalized thermoelastic half space and generalized thermoelastic half space with microtemperatures having an internal heat source. The normal mode analysis has been applied to obtain the exact expressions for the considered variables. The effect of internal heat source and microtemperatures on the above components has been depicted graphically.

scholarly journals Electromagnetic Field and Three-Phase-Lag in a Compressed Rotating Isotropic Homogeneous Micropolar Thermo-Viscoelastic Half-Space

2020 ◽  
Author(s):  
S.M. Abo-Dahab ◽  
A. Abd-Alla ◽  
araby kilany
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Initial Stress ◽  
Half Space ◽  
Viscoelastic Medium ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Phase Lag ◽  
Three Phase ◽  
The Impact

A unified mathematical model of three-phase-lag in a compressed rotating isotropic homogeneous micropolar thermo-viscoelastic medium based on a ramp type thermal shock is developed. An application of this model is carried out to resolve the problem of a perfectly conducting half-space subjected to certain boundary conditions in the presence of an electromagnetic field. Lame’s potentials and normal mode analysis techniques are employed to get the general analytical solutions. Specific attention is paid to explore the impact of the rotation, magnetic field, ramp time, as well as initial stress on the distributions of temperature, displacement, stress, and induced electric and magnetic distribution. The findings show that the impact of the rotation, magnetic field, viscous, ramp parameter, initial stress, and phase-lag on the micropolar thermo-viscoelastic medium is noticeable.

Effect of magnetic field and a mode-I crack problem in micropolar thermoelastic medium possessing under three theories

2014 ◽  
Vol 5 (2) ◽  
pp. 86-106 ◽  
Author(s):  
Khaled Lotfy ◽  
N. Yahia ◽  
W. Hassan
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Crack Problem ◽  
Mode Analysis ◽  
Plane Boundary ◽  
Mode I ◽  
Horizontal Distance ◽  
Mode I Crack ◽  
Thermoelastic Medium ◽  
Content Type

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.

A Generalized Magneto-Thermoelastic Coupled Problem

2007 ◽  
Vol 353-358 ◽  
pp. 1153-1156
Author(s):  
Tian Hu He ◽  
You He Zhou
Keyword(s):  
Half Space ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Plane Boundary ◽  
Dimensional Problem ◽  
Wave Effect ◽  
Electrically Conducting ◽  
Coupled Problem ◽  
Lord And Shulman Theory ◽  
Initial Magnetic Field

two-dimensional problem in electromagneto-thermoelasticity for a thermally and electrically conducting half-space solid whose surface is subjected to a time-dependent heat is studied in the context of Lord and Shulman theory. The solid is placed in an initial magnetic field parallel to the plane boundary of the half-space. The normal mode analysis is used to obtain the exact expressions for the considered variables. The results of the considered variables are represented graphically. From the distributions it can be found the coupled effect and thermal wave effect.

A two-dimensional half-space problem in an initially stressed rotating medium with microtemperatures

2020 ◽  
Vol 16 (6) ◽  
pp. 1313-1335 ◽  
Author(s):  
Sunita Deswal ◽  
Devender Sheoran ◽  
Kapil Kumar Kalkal
Keyword(s):  
Half Space ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Thermoelastic Medium ◽  
Space Problem ◽  
Content Type ◽  
Rotation Time ◽  
Effects Of Rotation ◽  
Matlab Programming

PurposeThe 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/approachNormal mode analysis technique is adopted to procure the exact solution of the problem.FindingsNumerical 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/valueIn 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.

scholarly journals Propagation of Surface Waves in a Rotating Coated Viscoelastic Half-Space under the Influence of Magnetic Field and Gravitational Forces

2021 ◽  
Vol 5 (4) ◽  
pp. 250
Author(s):  
Ali Mubaraki ◽  
Saad Althobaiti ◽  
Rahmatullah Ibrahim Nuruddeen
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Frequency Equation ◽  
Mode Analysis ◽  
Gravitational Forces ◽  
External Forces ◽  
High Level ◽  
The Magnetic Field

The present manuscript focuses on the study of surface wave propagation in a rotating coated viscoelastic half-space and its response to external forces comprised of the magnetic field and gravitational forces. A celebrated normal mode analysis procedure is adopted as the methodology of interest for its high level of efficiency in the literature. The analytically obtained frequency equation is analyzed for certain scenarios of curiosity, in addition to the determination of the resulting displacements and stresses. Moreover, certain physical data of relevance with the viscoelasticity index of unity are considered for the numerical simulations. As for the findings, the presented graphical illustrations showed that both the magnetic field and rotation positively accelerated the dispersion of surface waves in the coated half-space, while the obtained approximate fields in the half-space are found to be oscillatory as they steadily move towards the limiting point.

scholarly journals A two dimensional fibre reinforced micropolar thermoelastic problem for a half-space subjected to mechanical force

2015 ◽  
Vol 42 (1) ◽  
pp. 11-25
Author(s):  
Praveen Ailawalia ◽  
Sunil Sachdeva ◽  
Devinder Pathania
Keyword(s):  
Temperature Distribution ◽  
Half Space ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Displacement Component ◽  
Mechanical Force ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Thermoelastic Medium ◽  
Component Force

The purpose of this paper is to study the two dimensional deformation of fibre reinforced micropolar thermoelastic medium in the context of Green-Lindsay theory of thermoelasticity. A mechanical force is applied along the interface of fluid half space and fibre reinforced micropolar thermoelastic half space. The normal mode analysis has been applied to obtain the exact expressions for displacement component, force stress, temperature distribution and tangential couple stress. The effect of anisotropy and micropolarity on the displacement component, force stress, temperature distribution and tangential couple stress has been depicted graphically.

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