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.

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.

scholarly journals The effect of two-temperature on thermoelastic medium with diffusion due to three phase-lag model

2017 ◽  
Vol 2 (1) ◽  
pp. 259-270 ◽  
Author(s):  
Sarhan Y. Atwa ◽  
M. K. Ammar ◽  
Eman Ibrahim
Keyword(s):  
Elastic Medium ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Phase Lag ◽  
Thermoelastic Medium ◽  
Three Phase ◽  
Lag Model ◽  
Isotropic Elastic Medium ◽  
Two Temperature ◽  
Made In

AbstractThis paper is concerned on the distribution of a homogeneous isotropic elastic medium with diffusion under the effect of Three-phase-lag model. Normal mode analysis is used to express the exact expressions for temperature, displacements and stresses functions. Comparisons are made in the absence and presence of diffusion with some theories like Three-phase-lag and GNIII.

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.

Effect of Magnetic Field on Thermoelastic Micro-Elongated Solid with Diffusion Under Dual-Phase-Lag Model

2021 ◽  
pp. 2150189
Author(s):  
Amnah M. Alharbi ◽  
Mohamed I. A. Othman ◽  
Elsayed M. Abd-Elaziz
Keyword(s):  
Magnetic Field ◽  
Laser Pulse ◽  
Thermal Loading ◽  
Normal Mode Analysis ◽  
Concentration Field ◽  
Mode Analysis ◽  
Phase Lag ◽  
Dual Phase ◽  
Lag Model ◽  
Non Gaussian

This study considers a thermoelastic micro-elongated solid which is being heated by a laser pulse in order to investigate the corresponding impact of thermal loading and magnetic field. A laser beam that is non-Gaussian in nature is used to heat the surface of the bounded plane with a pulse duration [Formula: see text][Formula: see text]ps. The dual-phase-lag (DPL) model is considered to develop a better understanding of the problem. Also, the problems are solved using normal mode analysis as well as it helps in attaining the appropriate expressions for micro-rotation, components of displacement, the force stress, couple stress, concentration field, the temperature distribution the scalar micro-elongated function, and the micro-stress. The results obtained from the thermal variations are validated by comparing them to Coupled Theory (CT) of thermo-elasticity, Lord and Shulman (L–S) theory, and the DPL model. The graphical illustration of these comparisons has been presented as it helps in exploring the impacts of the laser pulse at two different times and the magnetic field parameter. The investigation also helped deduce some specific cases of interest.

Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dual-phase lag model

2014 ◽  
Vol 92 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
W.M. Hasona ◽  
Elsayed M. Abd-Elaziz
Keyword(s):  
Numerical Solutions ◽  
Generalized Thermoelasticity ◽  
Thermodynamic Temperature ◽  
Phase Lag ◽  
Dual Phase ◽  
Conductive Temperature ◽  
Mode Method ◽  
Lag Model ◽  
Two Temperatures ◽  
Physical Quantities

In the present paper, we introduce the dual-phase lag theory to study the effect of the rotation on a two-dimensional problem of micropolar thermoelastic isotropic medium with two temperatures. A normal mode method is proposed to analyze the problem and obtain numerical solutions for the displacement, the conductive temperature, the thermodynamic temperature, the microrotation, and the stresses. The results of the physical quantities have been obtained numerically and illustrated graphically. The results show the effect of phase lag of the heat flux τq, a phase lag of temperature gradient τθ and two-temperature parameter on all the physical quantities.

Effect of gravity on generalized thermoelastic diffusion due to laser pulse using dual-phase-lag model

2018 ◽  
Vol 14 (3) ◽  
pp. 457-481 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Ebtesam E.M. Eraki
Keyword(s):  
Plane Surface ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Graphical Form ◽  
Phase Lag ◽  
Dual Phase ◽  
Field Equations ◽  
Gaussian Laser Beam ◽  
Content Type ◽  
Non Gaussian

Purpose The purpose of this paper is to obtain a general solution to the field equations of generalized thermo-diffusion in an infinite thermoelastic body under the effect of gravity in the context of the dual-phase-lag (DPL) model. The half space is considered made of an isotropic homogeneous thermoelastic material. The boundary plane surface is heated by a non-Gaussian laser beam. Design/methodology/approach An exact solution to the problem is obtained using the normal mode analysis. Findings The derived expressions are computed numerically for copper and the results are presented in graphical form. Originality/value Comparisons are made with the results predicted by Lord-Shulman theory and DPL model for different values of time and in the presence and absence of gravity as well as diffusion.

Three-Dimensional Analysis of a Thermo-Viscoelastic Half-Space due to Thermal Shock in Temperature-Rate-Dependent Thermoelasticity

2016 ◽  
Vol 32 (4) ◽  
pp. 401-411 ◽  
Author(s):  
S. Kumar ◽  
J. S. Sikka ◽  
S. Choudhary
Keyword(s):  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Displacement Component ◽  
Mode Analysis ◽  
Field Equations ◽  
Finite Speed Of Propagation ◽  
Rate Dependent ◽  
Coupled Field Equations ◽  
Temperature Rate ◽  
Thermoelastic Waves

AbstractThe present paper is aimed at studying the effects of viscosity and time on the propagation of thermoelastic waves in a homogeneous and isotropic three-dimensional medium whose surface is acted upon by a thermal load under the purview of temperature-rate-dependent thermoelasticity. The normal mode analysis technique has been employed to solve the resulting non-dimensional coupled field equations and hence the exact expressions for displacement component, stress, temperature field and strain are obtained. The problem is further illustrated by computing the numerical values of the field variables for a copper- like material and depicting them graphically. Numerical results predict finite speed of propagation for thermoelastic waves.

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.

Memory-dependent derivative effect on wave propagation of micropolar thermoelastic medium under pulsed laser heating with three theories

2019 ◽  
Vol 30 (3) ◽  
pp. 1025-1046 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Sudip Mondal
Keyword(s):  
Wave Propagation ◽  
Laser Pulse ◽  
Thermal Loading ◽  
Plane Surface ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Phase Lag ◽  
Gaussian Laser Beam ◽  
Content Type ◽  
Non Gaussian

Purpose The purpose of this paper is to introduce the phase-lag models (Lord-Shulman, dual-phase-lag and three-phase-lag) to study the effect of memory-dependent derivative and the influence of thermal loading due to laser pulse on the wave propagation of generalized micropolar thermoelasticity. The bounding plane surface is heated by a non-Gaussian laser beam with a pulse duration of 10 nanoseconds. Design/methodology/approach The normal mode analysis technique is used to obtain the exact expressions for the displacement components, the force stresses, the temperature, the couple stresses and the micro-rotation. Comparisons are made with the results predicted by three theories of the authors’ interest. Excellent predictive capability is demonstrated at a different time also. Findings The effect of memory-dependent derivative and the heat laser pulse on the displacement, the temperature distribution, the components of stress, the couple stress and the microrotation vector have been depicted graphically. Research limitations/implications Some particular cases are also deduced from the present investigation. Originality/value The numerical results are presented graphically and are compared with different three theories for both in the presence and absence of memory-dependent effect and with the results predicted under three theories for two different values of the time.

The effect of initial stress on generalized thermoelastic medium with three-phase-lag model under temperature-dependent properties

2014 ◽  
Vol 92 (5) ◽  
pp. 448-457 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
W.M. Hasona ◽  
Ebtesam E.M. Eraki
Keyword(s):  
Initial Stress ◽  
Modulus Of Elasticity ◽  
Thermal Stresses ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Phase Lag ◽  
Temperature Dependent ◽  
Three Phase ◽  
Lag Model ◽  
Temperature Dependent Properties

The present paper attempts to investigate the propagation of plane waves in an isotropic elastic medium under the effect of initial stress and temperature-dependent properties. The modulus of elasticity is taken as a linear function of reference temperature. The formulation is applied under the thermoelasticity theory with three-phase-lag, proposed by Choudhuri (J. Thermal Stresses, 30, 231 (2007)). Normal mode analysis is used to obtain the expressions for the displacement components, the temperature, the stress, and the strain components. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made with the results predicted by different theories (Lord–Shulman theory, the theory of thermoelasticity type III, and the three-phase-lag model) in the absence and presence of the initial stress as well as the case where the modulus of elasticity is independent of temperature.

Sign in / Sign up

Export Citation Format

Share Document