Wave Propagation in a Magneto-Micropolar Thermoelastic Medium with Two Temperatures for Three-Phase-Lag Model

The present paper is concerned with the wave propagation in a micropolar thermoelastic solid with distinct two temperatures under the effect of the magnetic field in the presence of the gravity field and an internal heat source. The formulation of the problem is applied in the context of the three-phase-lag model and Green-Naghdi theory without dissipation. The medium is a homogeneous isotropic thermoelastic in the half-space. The exact expressions of the considered variables are obtained by using normal mode analysis. Comparisons are made with the results in the two theories in the absence and presence of the magnetic field as well as the two-temperature parameter. A comparison is also made in the two theories for different values of an internal heat source.     

Magneto-rotation-fibre-reinforced thermoelastic with gravity and energy dissipation

In this article, two theories of the generalized thermoelasticity Green-Naghdi theory (of type II and III) are applied, as well as the coupled theory to study the effect of magnetic field and rotation under influence of gravity on 2D problem of a fibre-reinforced thermoelastic. The normal mode analysis is used to obtain the expressions for the temperature, displacement components and the thermal stresses distributions. The resulting formulation is applied for two different concrete problems. The first concerns the case of a punch moving across the surface of semi-infinite thermoelastic half-space subjected to appropriate boundary conditions. The second deals with a thick plate subjected to a time-dependent heat source on each face. Numerical results are illustrated graphically for each problem considered. A comparison is made with the results predicted obtained by the two theories in the presence and absence of magnetic field, rotation and gravity field.     

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space with Energy Dissipation

The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Green and Naghdi theory under the effect of magnetic field is discussed. The problem has been solved analytically using normal mode analysis to obtain the exact solution of the temperature, the displacement components, and the thermal stress. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by types II and III in the presence and in the absence of the effect of a magnetic field and fiber reinforcement. It is found that the reinforcement and magnetic field have great effects on the distribution of the field quantities.     

Effect of rotation on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

This paper deals with the theoretical investigation of the effect of rotation on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linear stability analysis theory and normal mode analysis method. For the case of stationary convection, the effect of various parameters like medium permeability, rotation, non-buoyancy magnetization, coupling parameter, spin diffusion parameter and micropolar heat conduction has been analyzed. The critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of magnetic parameter M₁ and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and rotation. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia and rotation, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.     

Generalized magneto-thermoviscoelastic plane waves under the effect of rotation without energy dissipation

A new model of the equations of generalized thermoviscoelasticity for a thermally, isotropic and electrically conducting half-space solid whose surface is subjected to a thermal shock is given. The formulation is applied to the generalized thermoelasticity based on the Green and Naghdi (GN) theory under the effect of rotation, where there is an initial magnetic field parallel to the plane boundary of the half-space. The medium is deformed because of thermal shock and due to the application of the magnetic field, it results in induced magnetic and electric fields in the medium. The normal mode analysis is used to obtain the expressions for the variables considered. The distributions of temperature, displacement, stress, induced magnetic and electric fields are represented graphically. Comparisons are made with the results predicted by the types II and III in the presence and absence of rotation.     

Effect of Rotation in a Generalized Thermoelastic Medium with Hydrostatic Initial Stress Subjected to Ramp-Type Heating and Loading

The present problem is concerned with the study of deformation of a rotating generalized thermoelastic medium with a hydrostatic initial stress. A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The components of displacement, force stress, and temperature distribution are obtained in the Laplace and Fourier domains by applying integral transforms. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. These components are then obtained in the physical domain by applying a numerical inversion method. Some particular cases are also discussed in the context of the problem. The results are also presented graphically to show the effect of rotation and hydrostatic initial stress.     

The Effect of Gravity on Plane Waves in a Rotating Thermo-Microstretch Elastic Solid for a Mode-I Crack with Energy Dissipation

The present article is aimed at studying the effect of gravity on the general model of the equations of generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid rotating about the fixed axis of rotation and whose surface is subjected to a Mode-I crack problem considered. The problem is in the context of the Green and Naghdi theory (GN). The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses, and microstress distribution. The variations of the considered variables perpendicular to the axis of rotation are illustrated graphically. Comparisons are made with the results in the presence and absence of gravity and rotational frequency of a particular case for the generalized micropolar thermoelasticity elastic medium (without microstretch constants) between the two types (II, III).     

Thermo-mechanical Deformation in Magneto-micropolar Elastic Medium

The present investigation is concerned with a two-dimensional problem in electromagnetic micropolar elasticity for a half-space whose surface is subjected to distributed (concentrated or continuous) thermo-mechanical sources in the presence of a transverse magnetic field. As an application of the approach, the sources are taken as uniformly or linearly distributed. Laplace and Fourier transform techniques are used to solve the problem. The integral transforms have been inverted by using a numerical technique to obtain the components of normal strain, normal stress, tangential couple stress, and temperature distribution in the physical domain. Magnetic effects on the components of normal strain, normal stress, tangential couple stress, and temperature distribution have been depicted graphically for two different theories of generalized thermoelasticity, Lord and Shulman (L–S) theory and Green and Lindsay (G–L) theory. A particular case of interest is also deduced from the present investigation.     

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space

The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord–Shulman under the effect of a magnetic field is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of time. It is found that the reinforcement has a great effect on the distribution of field quantities.     

旋转半无限大体广义电磁热弹性耦合的二维问题

基于广义热弹性理论,研究了热和电可导的旋转半无限大体在其表面受随时间变化的热作用的广义电磁热弹性耦合的二维问题。半无限大体置于恒定的磁场中,受热作用产生膨胀变形,由于外加磁场的作用,介质中产生了感应的电场和感应的磁场。该文建立了电磁热弹性耦合的控制方程,利用正则模态法求解,得到了问题的解析解,并给出了各物理量的分布规律。可以看出,介质中呈现出电磁热弹耦合效应,由于旋转,位移和应力的幅值有很明显的降低,而旋转对温度和感应的磁场的影响不大。     

Numerical solution of free convection MHD micropolar fluid flow between two parallel porous vertical plates

The fully developed electrically conducting micropolar fluid flow between two vertical porous parallel plates is studied in the presence of temperature dependent heat sources including the effect of frictional heating and in the presence of a magnetic field. Profiles for velocity, microrotation and temperature are presented for a wide range of Hartmann numbers and the micropolar parameter. The skin friction, couple stress and Nusselt numbers at the plates are shown in the tables.     

Axi-symmetric problem in micropolar elastic half-space with stretch

The present investigation is concerned with axisymmetric problem in micropolar elastic half-space with stretch. The displacement, force stress, couple stress and vector first moment are obtained for a half-space subjected to an arbitrary normal load and a particular case of impulsive force is studied in detail. The graphs for various quantities have been drawn to illustrate the effect of stretch in each particular case.     

Plane Waves of a Fiber-Reinforcement Magneto-thermoelastic Comparison of Three Different Theories

In this article, the coupled theory, Lord–Shulman theory, and Green–Lindsay (GL) theory are used to study the influence of a magnetic field on a fiber-reinforced thermoelastic half-space. Normal mode analysis is used to solve a thermal shock problem. Numerical results for the temperature, displacement components, and stress components are given and illustrated graphically. A comparison is made between the coupled and GL theories in the absence and presence of a magnetic field and reinforcement.     

Thermal radiation effects on magnetohydrodynamic mixed convection flow of a micropolar fluid past a continuously moving semi-infinite plate for high temperature differences

Summary An analysis is presented to study the effect of radiation on magnetohydrodynamic mixed convective steady laminar boundary layer flow of an optically thick electrically conducting viscous micropolar fluid past a moving semi-infinite vertical plate for high temperature differences. A uniform magnetic field is applied perpendicular to the moving plate. The density of the micropolar fluid is assumed to reduce exponentially with temperature. The usual Boussinesq approximation is neglected because of the high temperature differences between the plate and the ambient fluid. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting governing equations are transformed using a similarity transformation and then solved numerically by applying an efficient technique. The effects of radiation parameter R, magnetic parameter M, couple parameter Δ and density/temperature parameter n on the velocity, angular velocity and temperature profiles as well as the local skin friction coefficient, wall couple stress and the local Nusselt number are presented graphically and in tabular form.     

The Effect of Magnetic Field on 2-D Problem for a Mode-I Crack of a Fiber-Reinforced in Generalized Thermoelasticity

In the present paper, the coupled theory, Lord–?hulman theory, and Green–Lindsay theory are introduced to study the influence of a magnetic field on the 2-D problem of a fiber-reinforced thermoelastic. These theories are also applied to study the influence of reinforcement on the total deformation of an infinite space weakened by a finite linear opening Mode-I crack. The material is homogeneous and an isotropic elastic half-space. The crack is subjected to a prescribed temperature and stress distribution. Normal mode analysis is used to solve the problem of a Mode-I crack. Numerical results for the temperature, the displacement, and thermal stress components are given and illustrated graphically in the absence and the presence of the magnetic field. A comparison between the three theories is also made for different depths.     

The Effect of Rotation on a Fiber-Reinforced Medium under Generalized Magneto-Thermoelasticity with Internal Heat Source

In the present article, we discussed the transient waves caused by a line heat source with a uniform velocity inside a rotating half-space fiber-reinforced thermoelastic media permeated into a uniform magnetic field. The formulation of the problem is applied under the coupled theory (CD), Green-Lindsay (G-L) theory, and Lord-Shulman (L-S) theory. The normal mode analysis is used to obtain expressions for the temperature, displacement components, and thermal stresses. Numerical results are given and illustrated graphically. A comparison is made with the results predicted by three theories in the presence and absence of magnetic field and rotation as well as fiber-reinforced.     

Disturbance due to mechanical and thermal sources in a generalized thermo-microstretch elastic half space

Disturbances caused by impulsive concentrated mechanical and thermal sources in a homogeneous, isotropic generalized thermo-microstretch elastic medium are studied by the use of Laplace—Hankel transform techniques. The integral transforms are inverted using a numerical technique. Analytical expressions for displacement components, stress, couple stress, microstress and temperature field are derived for different models of generalized thermoelasticity and illustrated graphically. These results for stresses and displacements can be used in estimating the effects of a surface pressure wave. Stretch and micropolar effects on various expressions obtained analytically are also depicted graphically.     

Mechanical/Thermal Sources in a Micropolar Thermoelastic Medium Possessing Cubic Symmetry without Energy Dissipation

The present problem is concerned with the study of the deformation of a thermoelastic micropolar solid possessing cubic symmetry under the influence of various sources acting on the plane surface. The analytic expressions of displacement components, microrotation, force stress, couple stress, and temperature distribution are obtained in the physical domain for the Green and Nagdhi (G–N) theory of thermoelasticity by applying the integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically for a particular material.     

Fractional Order Thermoelasticity Theory for a Half-Space Subjected to an Axisymmetric Heat Distribution

The present work is concerned with a traction-free thermoelastic half-space subjected to a known axisymmetric temperature distribution. The thermoelastic interactions inside the medium are investigated by employing the fractional order theory of thermoelasticity. The problem is solved by using Laplace's and Hankel's transforms. The inverse transforms are computed numerically. The variations of temperature, displacements, and stresses inside the half-space are investigated. The field variables for a particular material are graphically presented. Comparisons are made within the theory in the presence and absence of fractional order parameter.     

Generalized electromagneto-thermoviscoelastic in case of 2-D thermal shock problem in a finite conducting medium with one relaxation time

Summary. This paper studies the problem of two-dimensional electromagneto-thermovisco-elasticity based on Lord-Shulman theory for a thermally and electrically conducting half-space solid whose surface is subjected to a thermal shock. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deforms because of thermal shock and due to the application of the magnetic field, it results in induced magnetic and electric fields in the medium. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the temperature, displacement, stress, induced magnetic and electric fields are represented graphically. Comparisons are made with the results predicted by both the coupled theory and with the theory of generalized thermo-viscoelasticity with one relaxation time.