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Journal ArticleDOI

Effects of Hall Current and Rotation on Magneto-Micropolar Generalized Thermoelasticity Due to Ramp-Type Heating

31 Aug 2012-Vol. 2, Iss: 3, pp 24-32

AbstractIn this work, a two dimensional problem in magnetic micropolar generalized thermoelastic medium, in the presence of a transverse magnetic field -taking into consideration the effect of Hall current- subjected to ramp-type heating, is investigated. The entire elastic medium is rotating with a uniform angular velocity. Laplace-Fourier transform technique is used to solve the problem. The transformed components of normal strain, normal stress, tangential couple stress, temperature distribution, and the current density components are obtained. The integral transforms have been inverted by using a numerical technique. Hall current effects and effect of rotation have been depicted graphically on the resulting quantities.

Topics: Thermal Hall effect (59%), Thermoelastic damping (56%), Angular velocity (52%), Rotation (51%), Integral transform (50%)

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Journal Article
Abstract: The present paper is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field due to thermomechanical sources. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi Theories of Type-II and Type-III. Laplace and Fourier transform technique is applied to solve the problem. As an application, the bounding surface is subjected to concentrated and distributed sources (mechanical and thermal sources). The analytical expressions of displacement, stress components, temperature change and current density components are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show a comparison of effect of Hall current on the two theories GN-II and GN-III on resulting quantities. Some special cases are also deduced from the present investigation.

13 citations


Journal ArticleDOI
Abstract: Purpose – The purpose of this paper is to introduce the coupled theory, Lord-Shulman theory with one relaxation time and Green-Lindsay theory with two relaxation times to study the influence of rotation on generalized micropolar thermoelasticity subject to thermal loading due to laser pulse. The bounding plane surface is heated by a non-Gaussian laser beam with pulse duration of 8 ps. Design/methodology/approach – The problem has been solved numerically by using the normal mode analysis. Findings – The thermal shock problem is studied to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and micro-rotation. The distributions of the considered variables are illustrated graphically. Comparisons are made with the results predicted by three theories in the presence and absence of laser pulse and for different values of time. Originality/value – Generalized micropolar thermoelastic solid.

12 citations


Journal ArticleDOI
Abstract: The present article is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi theories of type-II and type-III. Laplace and Fourier transform techniques are applied to solve the problem. The analytical expressions of displacements, stress components, temperature change, and current density components are obtained in the transformed domain. A numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of Hall current and two temperatures on resulting quantities. Some special cases are also deduced from the present investigation.

12 citations


Cites background from "Effects of Hall Current and Rotatio..."

  • ...Particular cases (i) If we consider the medium to be isotropic, i.e., c11 = λ + 2μ = c33, c12 = c13 = λ, c44 = μ, β1 = β3= β , α1 = α3 = α, K1 = K3 = K, without two temperatures, i.e., a1 = a3 = 0, and consider the generalized heat conduction equation, then results are similar as derived by Zakaria [33]....

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  • ...[33] M. Zakaria, Effect of Hall current on generalized magnetothermoelasticity micropolar solid subjected to ramp-type heating, Int....

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  • ...Authors, such as Zakaria [32, 33], Salem [34], Kumar andDevi [35], and Sarkar and Lahiri [36], have considered the effect of Hall current for 2D problems in micropolar thermoelasticity....

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  • ...[32] M. Zakaria, Effects of Hall current and rotation on magnetomicropolar generalized thermoelasticity due to ramp-type heating, Int....

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Journal ArticleDOI
Abstract: The model of generalized micropolar magneto-thermoelasticity for a thermally and perfectly conducting half-space is studied. The initial magnetic field is parallel to the boundary of the half-space. The formulation is applied to the generalized thermo-elasticity theories of Lord and Shulman, Green and Lindsay, as well as to the coupled dynamic theory. The normal mode analysis is used to obtain expressions for the temperature increment, the displacement, and the stress components of the model at the interface. By using potential functions, the governing equations are reduced to two fourth-order differential equations. By numerical calculation, the variation of the considered variables is given and illustrated graphically for a magnesium crystal micropolar elastic material. Comparisons are performed with the results predicted by the three theories in the presence of a magnetic field.

9 citations


Journal ArticleDOI
Abstract: Abstract The present investigation is concerned with one dimensional problem in a homogeneous, isotropic thermoelastic medium with double porosity structure in the presence of Hall currents subjected to thermomechanical sources. A state space approach has been applied to investigate the problem. As an application of the approach, normal force and thermal source have been taken to illustrate the utility of the approach. The expressions for the components of normal stress, equilibrated stress and the temperature change are obtained in the frequency domain and computed numerically. A numerical simulation is prepared for these quantities. The effect of the Hartmann number is depicted graphically on the resulting quantities for a specific model. Some particular cases of interest are also deduced from the present investigation.

8 citations


References
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Journal ArticleDOI
Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.

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"Effects of Hall Current and Rotatio..." refers background in this paper

  • ...The first is due to Lord and Shulman[7], who obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier’s law....

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  • ...In this work, we introduced a new model of the equations of the generalized magneto micropolar thermoelasticity in the presence of transverse magnetic field, taking into consideration the effects of Hall current and rotation, is applied to both generalizations, Lord–Shulman theory and Green–Lindsay theory, as well as to the coupled theory....

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Journal ArticleDOI
Abstract: A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.

1,929 citations


"Effects of Hall Current and Rotatio..." refers background in this paper

  • ...Biot[6] introduced the theory of coupled thermoelasticity to overcome the first shortcoming....

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Journal ArticleDOI
Abstract: The present work is concerned with the formulation of the basic field equations, boundary conditions and constitutive equations of what we call ‘simple micro-elastic’ solids. Such solids are affected by the ‘micro’ deformations and rotations not encountered in the theory of finite elasticity. The theory, in a natural fashion, gives rise to the concept of stress moments, inertial spin and other types of second order effects and their laws of motion. The mechanism of the surface tension is contained in the theory. In a forthcoming paper (Part II) explicit expressions of constitutive equations of several simple micro-elastic solids will be given and applied to some special problems.

1,228 citations


Journal ArticleDOI
Abstract: In this paper a numerical inversion method for Laplace transforms, based on a Fourier series expansion developed by Durbin [5], is presented. The disadvantage of the inversion methods of that type, the encountered dependence of discretization and truncation error on the free parameters, is removed by the simultaneous application of a procedure for the reduction of the discretization error, a method for accelerating the convergence of the Fourier series and a procedure that computes approximately the ‘best’ choice of the free parameters. Suitable for a given problem, the inversion method allows the adequate application of these procedures. Therefore, in a big range of applications a high accuracy can be achieved with only a few function evaluations of the Laplace transform. The inversion method is implemented as a FORTRAN subroutine.

915 citations


ReportDOI
01 Sep 1965
Abstract: : Equations of motion, constitutive equations and boundary conditions are presented for a special class of micro-elastic materials called Micropolar Solids. These solids respond to micro-rotational motions and spin inertia and can support couple stress and distributed body couples. The couple stress theory is shown to emanate as a spacial case of the present theory when the motion is constrained so that micro- and macro-rotations coincide. Several energy and uniqueness theorems are given.

845 citations


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  • ...C Eringen, Nonlinear theory of micro-elastic Solids II....

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  • ...Purdue University, (1965) [5] A. C. Eringen, Linear theory of micropolar elasticity, J. Mech....

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  • ...REFERENCES [1] A. C. Eringen, E. S. Suhubi, Non-linear theory of mi- cro-elastic Solids I. Int....

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  • ...J. Eng. Sci. 4(1966), 179–202 [4] A. C. Eringen, Linear theory of micropolar elasticity, ONR Technical Report No. 29, School of Aeronautics, Aeronautics and Engineering Science....

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