scholarly journals Normal Mode Analysis of Generalized Magneto-Thermoelastic Medium with Initial Stress Under Green-Naghdi Theory

2020 ◽  
Vol 35 (4) ◽  
pp. 313-325
Author(s):  
Alzaerah Ramadhan Mohammed Aldeeb
Keyword(s):  
Magnetic Field ◽  
Initial Stress ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Energy Dispersion ◽  
Elasticity Equations ◽  
Physical Quantities ◽  
The Magnetic Field ◽  
Research Show

The normal mode analysis method was used to study the effect of both the initial stress and the magnetic field on a thermally elastic body. This method is used to obtain the exact expressions for the considered variables. Some particular cases are also discussed in the context of the problem. The generalized thermal elasticity equations were reviewed under the influence of the basic initial stress and the magnetic field using the theory (Green-Naghdi) of the second and third types (the second type with no energy dispersion and the third type with energy dispersion). The different physical quantities were illustrated in the presence and absence of both the initial stress and the magnetic field. The results of this research show the extent of difference between the second and third types of Green and Naghdi's theory. All results and figures were obtained using (MATLAB R2013a) program

Effect of Magnetic Field on Generalized Thermo-Viscoelastic Diffusion Medium with Voids

2016 ◽  
Vol 16 (07) ◽  
pp. 1550033 ◽  
Author(s):  
Mohamed I. A. Othman ◽  
Montaser Fekry
Keyword(s):  
Magnetic Field ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Physical Domain ◽  
Specific Material ◽  
Analytical Expressions ◽  
And Diffusion ◽  
Physical Quantities ◽  
The Magnetic Field

The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic, generalized thermo-viscoelastic diffusion material with voids under the influence of magnetic field. The formulation is applied to the generalized thermoelasticity theory under the Lord–Shulman and the classical dynamical coupled theories. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a specific material and explained graphically. Comparisons are made with the results predicted by the Lord–Shulman and the coupled theories in the presence and absence of the magnetic field and diffusion.

Kelvin-Helmholtz and Rayleigh-Taylor Instability of Two Superimposed Magnetized Fluids with Suspended Dust Particles

2009 ◽  
Vol 64 (7-8) ◽  
pp. 455-466 ◽  
Author(s):  
Ramprasad Prajapati ◽  
Raj Kamal Sanghvi ◽  
Rajendra Kumar Chhajlani ◽  
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Particle Density ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Mode Analysis ◽  
Dust Particles ◽  
Suspended Dust ◽  
The Magnetic Field

AbstractThe effect of a magnetic field and suspended dust particles on both the Kelvin-Helmholtz (K-H) and the Rayleigh-Taylor (R-T) instability of two superimposed streaming magnetized plasmas is investigated. The magnetized fluids are assumed to be incompressible and flowing on top of each other. The usual magnetohydrodynamic (MHD) equations are considered with suspended dust particles. The basic equations of the problem are linearized and the dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The general dispersion relation is found to be modified due to the presence of the suspended dust particles and of the magnetic field. The effect of the magnetic field appears in the dispersion relation if three-dimensional perturbations of the system are considered. The general conditions of the K-H instability as well as the R-T instability are derived for the considered medium. The stability of the system for both cases is discussed by applying the Routh-Hurwitz criterion. Numerical analysis is performed to show the effect of various parameters on the growth rates of the K-H and R-T instabilities. Three different cases of the present configurations are considered and the conditions of instability are obtained. It is found that the conditions for the K-H and R-T instabilities depend on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. The magnetic field and particle density have stabilizing influence, while the density difference between the fluids has a destabilizing influence on the growth rate of the K-H and R-T configurations.

Effect of initial stress and rotation on magneto-thermoelastic material with voids and energy dissipation

2017 ◽  
Vol 13 (2) ◽  
pp. 331-346 ◽  
Author(s):  
Mohamed Ibrahim A. Othman ◽  
Mohamed Ibrahim M. Hilal
Keyword(s):  
Laser Pulse ◽  
Initial Stress ◽  
Pulse Heating ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Content Type ◽  
Thermoelastic Material ◽  
Analysis Technique ◽  
Laser Pulse Heating ◽  
Physical Quantities

Purpose The purpose of this paper is to study the effect of rotation and initial stress on magneto-thermoelastic material with voids heated by a laser pulse heating. Design/methodology/approach The analytical method used was the normal mode analysis technique. Findings Numerical results for the physical quantities were presented graphically and analyzed. The graphical results indicate that the effect of rotation, initial stress and magnetic fields are observable physical effects on the thermoelastic material with voids heated by a laser pulse. Comparisons are made with the results in the absence and the presence of the physical operators, also at various times. Originality/value In the present work, the authors shall investigate the effect of the rotation, initial stress, magnetic field and laser pulse on thermoelastic material with voids subjected to a laser pulse heating acting as a thermal shock. A comparison is also made between the two types (types II and III) of Green-Naghdi theory in the absence and the presence of the physical operators. Such problems are very important in many dynamical systems.

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.

scholarly journals Hall Effect on Thermal Instability of Viscoelastic Dusty Fluid in Porous Medium

2013 ◽  
Vol 18 (3) ◽  
pp. 871-886
Author(s):  
M. Singh ◽  
R.K. Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Rayleigh Numbers ◽  
The Magnetic Field

Abstract The effect of Hall currents and suspended dusty particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico viscous fluid in a porous medium is considered. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of the magnetic field. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers are depicted graphically. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the systems, which did not exist in the absence of these parameters

scholarly journals Hydromagnetic thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles in porous medium

2013 ◽  
Vol 35 (4) ◽  
pp. 75-88
Author(s):  
G.C. Rana ◽  
H.S. Jamwal
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Analysis Method ◽  
Rotating Fluid ◽  
Medium Permeability ◽  
The Magnetic Field

Abstract In this paper, the thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles (fine dust) in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B′) elastico-viscous fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has stabilizing effect, suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions

Magneto Thermal Convection in a Compressible Couple-Stress Fluid

2010 ◽  
Vol 65 (3) ◽  
pp. 215-220 ◽  
Author(s):  
Mahinder Singh ◽  
Pardeep Kumar
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Linearized Stability ◽  
The Stability ◽  
The Magnetic Field

The problem of thermal instability of compressible, electrically conducting couple-stress fluids in the presence of a uniform magnetic field is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, couple-stress, and magnetic field postpone the onset of convection. Graphs have been plotted by giving numerical values of the parameters to depict the stability characteristics. The principle of exchange of stabilities is found to be satisfied. The magnetic field introduces oscillatory modes in the system that were non-existent in its absence. The case of overstability is also studied wherein a sufficient condition for the non-existence of overstability is obtained.

Magnetogravitational instability of a rotating anisotropic plasma with finite-ion-Larmor-radius corrections and generalized polytropic laws

1998 ◽  
Vol 60 (4) ◽  
pp. 673-694 ◽  
Author(s):  
G. D. SONI ◽  
R. K. CHHAJLANI
Keyword(s):  
Magnetic Field ◽  
Electrical Resistivity ◽  
Dispersion Relation ◽  
Normal Mode Analysis ◽  
Transverse Mode ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Axis Of Rotation ◽  
The Magnetic Field

The gravitational instability of an infinite homogeneous, finitely conducting, rotating, collisionless, anisotropic-pressure plasma in the presence of a uniform magnetic field with finite-ion-Larmor-radius (FLR) corrections and generalized polytropic laws is investigated. The polytropic laws are considered for the pressure components in directions parallel and perpendicular to the magnetic field. The method of normal-mode analysis is applied to derive the dispersion relation. Wave propagation is considered for both parallel and perpendicular axes of rotation. Longitudinal and transverse modes of propagation are discussed separately. The effects of rotation, finite electrical resistivity, FLR corrections and polytropic indices on the gravitational, firehose and mirror instabilities are discussed. The stability of the system is discussed by applying the Routh–Hurwitz criterion. Extensive numerical treatment of the dispersion relation leads to several interesting results. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, it is observed that rotation stabilizes the system by decreasing the critical Jeans wavenumber. It is also seen that the region of instability and the value of the critical Jeans wavenumber are larger for the Chew–Goldberger–Low (CGL) set of equations in comparison with the magnetohydrodynamic (MHD) set of equations. It is found that the effect of FLR corrections is significant only in the low-wavelength range, and produces a stabilizing influence. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, the finite electrical resistivity removes the polytropic index [nu] from the condition for instability. The inclusion of rotation alone or FLR corrections alone or both together does not affect the condition for mirror instability. The growth rate of the mirror instability is modified owing to uniform rotation or FLR corrections or both together. We note that the condition of mirror instability depends upon the polytropic indices. We also note that neither the mirror instability nor the firehose instability can be observed for the isotropic MHD set of equations.

Thermodynamical interactions in a two-temperature dual-phase-lag micropolar thermoelasticity with gravity

2018 ◽  
Vol 14 (1) ◽  
pp. 102-124 ◽  
Author(s):  
Sunita Deswal ◽  
Baljit Singh Punia ◽  
Kapil Kumar Kalkal
Keyword(s):  
Normal Mode ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Phase Lag ◽  
Dual Phase ◽  
Transient Wave ◽  
Content Type ◽  
Temperature Parameter ◽  
Physical Quantities ◽  
Two Temperature

Purpose The dual-phase-lag (DPL) model is applied to study the effect of the gravity field and micropolarity on the wave propagation in a two-temperature generalized thermoelastic problem for a medium. 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 to show the effect of angle of inclination. Comparisons of the physical quantities are also shown in figure to study the effect of gravity and two-temperature parameter. Originality/value This paper is concerned with the analysis of transient wave phenomena in a micropolar thermoelastic half-space subjected to inclined load. The governing equations are formulated in the context of two-temperature generalized thermoelasticity theory with DPLs. A medium is assumed to be initially quiescent and under the effect of gravity. An analytical solution of the problem is obtained by employing normal mode analysis. Numerical estimates of displacement, stresses and temperatures are computed for magnesium crystal-like material and are illustrated graphically. Comparisons of the physical quantities are shown in figures to study the effects of gravity, two-temperature parameter and angle of inclination. Some particular cases of interest have also been inferred from the present problem.

scholarly journals On Thermal Convection of a Plasma in Porous Medium

2021 ◽  
Vol 16 ◽  
pp. 110-119
Author(s):  
Pardeep Kumar ◽  
Sumit Gupta
Keyword(s):  
Magnetic Field ◽  
Thermal Convection ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
The Magnetic Field

The effect of finite Larmor radius of the ions on thermal convection of a plasma is investigated. The case with vertical magnetic field is discussed. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of finite Larmor radius and magnetic field introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, finite Larmor radius is found to have a stabilizing effect. Medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain conditions in the presence of finite Larmor radius effect whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively. The sufficient conditions for the non-existence of overstability are also obtained.

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