scholarly journals Mathematical Model on Gravitational Electro-Magneto-Thermoelasticity with Two Temperature and Initial Stress in the Context of Three Theories

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 735
Author(s):  
Sayed M. Abo-Dahab ◽  
Alaa A. El-Bary ◽  
Yas Al-Hadeethi ◽  
Mohamed Alkashif
Keyword(s):  
Magnetic Field ◽  
Initial Stress ◽  
Two Dimensions ◽  
Phase Lag ◽  
Space Problem ◽  
Type Iii ◽  
Three Phase ◽  
Stress Components ◽  
Fundamental Equations ◽  
Two Temperature

The main aim of this paper is to study two temperature thermoelasticity in a generalization form to solve the half-space problem of two dimensions under gravity, perturbed magnetic field, and initial stress. The fundamental equations are solved considering a new mathematical technique under Lord-Şhulman (LS), Green-Naghdi (GN type III) and three-phase-lag (3PHL) theories to investigate displacement, stress components, and temperature distribution. The results obtained by the three theories, i.e., (LS), (GN type III), and (3PHL), considering the absence and the presence of gravity, initial stress, and magnetic field have been compared. The results were numerically calculated and graphically displayed to exhibit the physical meaning of the phenomenon and the external parameters’ effect. A comparison has been presented between the results obtained in the absence and the presence of the external considered parameters and with the previously obtained results by other researchers.

scholarly journals Magnetic field on surface waves propagation in gravitational thermoelastic media with two temperature and initial stress in the context of three theories

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 285-299
Author(s):  
Jamel Bouslimi ◽  
Sayed Abo-Dahab ◽  
Khaled Lotfy ◽  
Sayed Abdel-Khalek ◽  
Eied Khalil ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Initial Stress ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Mathematical Methods ◽  
Numerical Work ◽  
Suitable Material ◽  
Two Temperature

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.

scholarly journals Magnetic field on surface waves propagation in gravitational thermoelastic media with two temperature and initial stress in the context of three theories

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 285-299
Author(s):  
Jamel Bouslimi ◽  
Sayed Abo-Dahab ◽  
Khaled Lotfy ◽  
Sayed Abdel-Khalek ◽  
Eied Khalil ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Initial Stress ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Mathematical Methods ◽  
Numerical Work ◽  
Suitable Material ◽  
Two Temperature

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.

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.

The effect of temperature-dependent properties on generalized magneto-thermo-elastic medium with two-temperature under three-phase-lag model

2017 ◽  
Vol 13 (1) ◽  
pp. 122-134 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Yassmin D. Elmaklizi ◽  
Nehal T. Mansoure
Keyword(s):  
Magnetic Field ◽  
Elastic Medium ◽  
Modulus Of Elasticity ◽  
Phase Lag ◽  
Temperature Dependent ◽  
Content Type ◽  
Three Phase ◽  
Lag Model ◽  
Temperature Dependent Properties ◽  
Two Temperature

Purpose The purpose of this paper is to investigate the propagation of plane waves in an isotropic elastic medium under the effect of rotation, magnetic field and temperature-dependent properties with two‐temperatures. Design/methodology/approach The problem has been solved analytically by using the normal mode analysis. Findings The numerical results are given and presented graphically when mechanical and thermal force are applied. Comparisons are made with the results predicted by the three-phase-lag (3PHL) model and dual-phase-lag model in the presence and absence of cases where the modulus of elasticity is independent of temperature. Originality/value In this work, the authors study the influence of rotation and magnetic field with two‐temperature on thermoelastic isotropic medium when the modulus of elasticity is taken as a linear function of reference temperature in the context of the 3PHL model. The numerical results for the field quantities are obtained and represented graphically.

Two-temperature generalized magneto-thermoelastic medium for dual-phase-lag model under the effect of gravity field and hydrostatic initial stress

2016 ◽  
Vol 12 (2) ◽  
pp. 362-383 ◽  
Author(s):  
Samia M Said
Keyword(s):  
Magnetic Field ◽  
Gravity Field ◽  
Initial Stress ◽  
Mode Analysis ◽  
Phase Lag ◽  
Temperature Dependent ◽  
Content Type ◽  
Temperature Dependent Properties ◽  
Hydrostatic Initial Stress ◽  
Two Temperature

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.

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 Rayleigh wave propagation in transversely isotropic magneto-thermoelastic medium with three-phase-lag heat transfer and diffusion

2019 ◽  
Vol 14 (1) ◽  
Author(s):  
Iqbal Kaur ◽  
Parveen Lata
Keyword(s):  
Heat Transfer ◽  
Rayleigh Wave ◽  
Homogeneous Medium ◽  
Transversely Isotropic ◽  
Phase Lag ◽  
Attenuation Coefficients ◽  
Three Phase ◽  
Stress Components ◽  
And Diffusion ◽  
Penetration Depths

Abstract The present research deals with the propagation of Rayleigh wave in transversely isotropic magneto-thermoelastic homogeneous medium in the presence of mass diffusion and three-phase-lag heat transfer. The wave characteristics such as phase velocity, attenuation coefficients, specific loss, and penetration depths are computed numerically and depicted graphically. The normal stress, tangential stress components, temperature change, and mass concentration are computed and drawn graphically. The effects of three-phase-lag heat transfer, GN type-III, and LS theory of heat transfer are depicted on the various quantities. Some particular cases are also deduced from the present investigation.

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