A Two-Dimensional Problem for a Rotating Magneto-Thermoelastic Half-Space with Voids and Gravity in a Two-Temperature Generalized Thermoelasticity Theory

2015 ◽  
Vol 31 (6) ◽  
pp. 639-651 ◽  
Author(s):  
S. Deswal ◽  
N. Hooda
Keyword(s):  
Half Space ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Hyperbolic Heat Conduction ◽  
Conduction Model ◽  
Conductive Temperature ◽  
Two Temperature

ABSTRACTThe present paper is concerned with an in-depth study of the effects of rotation, two-temperature parameter and voids on the magneto-thermoelastic interactions in a homogeneous, isotropic, generalized half-space with gravity field. The formulation is applied within the frame-work of two-temperature generalized thermoelasticity based on the hyperbolic heat conduction model with one relaxation time. Using normal mode analysis technique for the physical variables appearing in the governing equations, we get the analytical expressions for displacement components, stress, thermodynamic temperature, conductive temperature and change in volume fraction field. The general solution obtained is then applied to a specific problem of an infinite half-space having isothermal boundary subjected to mechanical load. Variations of the considered variables through the vertical distance are illustrated graphically.

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.

Three-Dimensional Thermoelastic Problem Under Two-Temperature Theory

2017 ◽  
Vol 14 (03) ◽  
pp. 1750030 ◽  
Author(s):  
Abhik Sur ◽  
M. Kanoria
Keyword(s):  
Thermal Loading ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Thermodynamic Temperature ◽  
Mode Analysis ◽  
Phase Lag ◽  
Field Equations ◽  
Conductive Temperature ◽  
Lag Model ◽  
Two Temperature

The present paper deals with the problem of thermoelastic interactions in a homogeneous, isotropic three-dimensional medium whose surface suffers a time dependent thermal loading. The problem is treated on the basis of three-phase-lag model and dual-phase-lag model with two temperatures. The medium is assumed to be unstressed initially and has uniform temperature. Normal mode analysis technique is employed onto the non-dimensional field equations to derive the exact expressions for displacement component, conductive temperature, thermodynamic temperature, stress and strain. The problem is illustrated by computing the numerical values of the field variables for a copper material. Finally, all the physical fields are represented graphically to analyze the difference between the two models. The effect of the two temperature parameter is also discussed.

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.

The effect of magnetic field on generalized thermoelastic medium with two temperature under three phase lag model

2015 ◽  
Vol 11 (4) ◽  
pp. 544-557 ◽  
Author(s):  
Mohamed I. Othman ◽  
W. M. Hasona ◽  
Nehal T. Mansour
Keyword(s):  
Magnetic Field ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Phase Lag ◽  
Thermoelastic Medium ◽  
Content Type ◽  
Conductive Temperature ◽  
Three Phase ◽  
Generalized Thermoelastic ◽  
Two Temperature

Purpose – The purpose of this paper is to introduce the Lord-Shulman (L-S), Green-Naghdi of type III (G-N III) and three phase lag (3PHL) theories to study the effect of a magnetic field on generalized thermoelastic medium with two temperature. Design/methodology/approach – The problem has been solved numerically by using the normal mode analysis. Findings – The problem is used to obtain the analytical expressions of the displacement components, force stress, thermodynamic temperature and conductive temperature. The numerical results are given and presented graphically thermal force is applied. Comparisons are made with the results predicted by 3PHL, G-N III and L-S in the presence and absence of magnetic field as well as two temperature. Originality/value – Generalized thermoelastic medium.

scholarly journals Effect of rotation on a semiconducting medium with two-temperatures under L-S theory

2017 ◽  
Vol 38 (2) ◽  
pp. 101-122 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Ramadan S. Tantawi ◽  
Ebtesam E.M. Eraki
Keyword(s):  
Relaxation Time ◽  
Angular Velocity ◽  
Elastic Medium ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Temperature Parameter ◽  
Two Temperatures ◽  
Two Temperature

AbstractThe model of the equations of generalized thermoelasticity in a semi-conducting medium with two-temperature is established. The entire elastic medium is rotated with a uniform angular velocity. The formulation is applied under Lord-Schulman theory with one relaxation time. The normal mode analysis is used to obtain the expressions for the considered variables. Also some particular cases are discussed in the context of the problem. Numerical results for the considered variables are obtained and illustrated graphically. Comparisons are also made with the results predicted in the absence and presence of rotation as well as two-temperature parameter.

scholarly journals Two-Temperature Generalized Thermoviscoelasticity with Fractional Order Strain Subjected to Moving Heat Source: State Space Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Renu Yadav ◽  
Kapil Kumar Kalkal ◽  
Sunita Deswal
Keyword(s):  
Heat Source ◽  
State Space ◽  
Fractional Order ◽  
Mechanical Load ◽  
Generalized Thermoelasticity ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Conductive Temperature ◽  
Special Cases ◽  
Two Temperature

The theory of generalized thermoelasticity with fractional order strain is employed to study the problem of one-dimensional disturbances in a viscoelastic solid in the presence of a moving internal heat source and subjected to a mechanical load. The problem is in the context of Green-Naghdi theory of thermoelasticity with energy dissipation. Laplace transform and state space techniques are used to obtain the general solution for a set of boundary conditions. To tackle the expression of heat source, Fourier transform is also employed. The expressions for different field parameters such as displacement, stress, thermodynamical temperature, and conductive temperature in the physical domain are derived by the application of numerical inversion technique. The effects of fractional order strain, two-temperature parameter, viscosity, and velocity of internal heat source on the field variables are depicted graphically for copper material. Some special cases of interest have also been presented.

Thermo-mechanical disturbances in a nonlocal rotating elastic material with temperature dependent properties

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Devender Sheoran ◽  
Rajesh Kumar ◽  
Seema Thakran ◽  
Kapil Kumar Kalkal
Keyword(s):  
Rotational Speed ◽  
Mechanical Load ◽  
Normal Mode Analysis ◽  
Nonlocal Parameter ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Temperature Dependent ◽  
Content Type ◽  
Temperature Dependent Properties ◽  
Physical Quantities

Purpose The purpose of this paper is to study two-dimensional deformations in a nonlocal, homogeneous, isotropic, rotating thermoelastic medium with temperature-dependent properties under the purview of the Green-Naghdi model II of generalized thermoelasticity. The formulation is subjected to a mechanical load. Design/methodology/approach The normal mode analysis technique is adopted to procure the exact solution of the problem. Findings For isothermal and insulated boundaries, discussions have been made to highlight the influences of rotational speed, nonlocality, temperature-dependent properties and time on the physical quantities. Originality/value The exact expressions for the displacement components, stresses and temperature field are obtained in the physical domain. These are also calculated numerically for a magnesium crystal-like material and depicted through graphs to observe the variations of the considered physical quantities. The present study is useful and valuable for the analysis of problems involving mechanical shock, rotational speed, nonlocal parameter, temperature-dependent properties and elastic deformation.

Thermodynamic behaviour of microstretch viscoelastic solids with internal heat source

2014 ◽  
Vol 92 (5) ◽  
pp. 425-434 ◽  
Author(s):  
Sunita Deswal ◽  
Renu Yadav
Keyword(s):  
Heat Source ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Moving Heat Source ◽  
Line Heat Source ◽  
Epoxy Material ◽  
Mech Phys Solid

The dynamical interactions caused by a line heat source moving inside a homogeneous isotropic thermo-microstretch viscoelastic half space, whose surface is subjected to a thermal load, are investigated. The formulation is in the context of generalized thermoelasticity theories proposed by Lord and Shulman (J. Mech. Phys. Solid, 15, 299 (1967)) and Green and Lindsay (Thermoelasticity, J. Elasticity, 2, 1 (1972)). The surface is assumed to be traction free. The solutions in terms of displacement components, mechanical stresses, temperature, couple stress, and microstress distribution are procured by employing the normal mode analysis. The numerical estimates of the considered variables are obtained for an aluminium–epoxy material. The results obtained are demonstrated graphically to show the effect of moving heat source and viscosity on the displacement, stresses, and temperature distribution.

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