An analytical method for magnetothermoelastic analysis of functionally graded hollow cylinders

This paper considers magnetothermoelastic behavior of a functionally graded material (FGM) hollow cylinder, placed in a uniform magnetic field, subjected to thermal and mechanical loads. Exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow cylinders is determined by using the infinitesimal theory of magnetothermoelasticity. Numerical results indicate that the inhomogeneous constants presented in the present study are useful parameters from a design point of view in that it can be tailored for specific applications to control the stress and perturbation of magnetic field vector distributions. This research is helpful for the optimum design annular cylindrical FGM sensors/actuators.     

Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder

Analytical study for electromagnetothermoelastic behaviors of a hollow cylinder composed of functionally graded piezoelectric material (FGPM), placed in a uniform magnetic field, subjected to electric, thermal and mechanical loads are presented. For the case that the electric, magnetic, thermal and mechanical properties of the material obey an identical power law in the radial direction, exact solutions for electric displacement, stresses, electric potential and perturbation of magnetic field vector in the FGPM hollow cylinder are determined by using the infinitesimal theory of electromagnetothermoelasticity. Some useful discussions and numerical examples are presented to show the significant influence of material inhomogeneity, and adopting a certain value of the inhomogeneity parameter β and applying suitable electric, thermal and mechanical loads can optimize the FGPM hollow cylindrical structures. This will be of particular importance in modern engineering design.     

A numerical solution of magneto-thermoelastic problem in non-homogeneous isotropic cylinder by the finite-difference method

This paper presents the development of the magneto-thermoelastic problem in non-homogeneous isotropic cylinder in a primary magnetic field when the curved surface of the cylinder subject to certain boundary conditions. The governing coupled linear partial differential equations in the hyperbolic-type have been solved numerically using the finite-difference method. Graphical results for the temperature, displacement and components of stresses are illustrated and discussed for copper-like material. The results indicate that the effects of inhomogeneity and magnetic field are very pronounced. Some more interesting particular cases have also been discussed.     

An algorithm for computing the one-dimensional electromagnetic field in a conducting ferromagnetic cylinder based on the method of finite differences

We propose an algorithm for computing the electromagnetic field in a conducting ferromagnetic cylinder, characterized by the presence of only the axial component of the electric field intensity vector. The algebraization of the partial derivatives over the radius is carried out using a high-precision method of finite differences, and the numerical integration with respect to time is done on the basis of the implicit method. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 145–148.     

A new coupling of mixed finite element and boundary element methods for an exterior Helmholtz problem in the plane

This paper deals with the scattering of time harmonic electromagnetic waves by an infinitely long cylinder containing a non-homogeneous conducting medium. More precisely, we study the transverse magnetic field that solves an interface problem holding between the cross section of the cylinder and the exterior two-dimensional free space. We apply a dual-mixed variational formulation in the obstacle coupled with a boundary integral equation method in the unbounded homogeneous space. A Fredholm alternative is utilized to prove that this continuous formulation is well posed. We define the corresponding discrete scheme by using the lowest order rotated Raviart-Thomas finite elements for the magnetic field and spectral elements for the boundary unknown. Then, we show that the resulting Galerkin scheme is uniquely solvable and convergent, and prove optimal error estimates. Finally, we illustrate our analysis with some results from computational experiments. This research was partially supported by CONICYT-Chile through the FONDAP Program in Applied Mathematics, by the Dirección de Investigación of the Universidad de Concepción through the Advanced Research Groups Program, and by the Ministerio de Educación y Ciencia of Spain, through the project No. MTM2004-05417.     

Galvanic-approximation investigation of magnetoacoustic dissipation in a viscoelastic weakly conducting cylinder

The radial oscillations of a viscoelastic, weakly conducting, nonmagnetic cylinder are studied. The oscillations are excited by a contact-free induction method in the presence of a constant axial magnetic field. The Joule heating and viscous heating densities are calculated for two types of boundary conditions. The effect of electric conductivity on the dissipation of the energy of magnetoacoustic disturbances is compared with the effect of viscosity. The spectra of resonance oscillations of the cylinder are investigated.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 5, pp. 44–49, 1987.     

Helical flow of a Bingham fluid arising from axial Poiseuille flow between coaxial cylinders

The Bingham fluid model represents viscoplastic materials that display yielding, that is, behave as a solid body at low stresses, but flow as a Newtonian fluid at high stresses. In any Bingham flow, there may be regions of solid material separated from regions of Newtonian flow by so-called yield boundaries. Such materials arise in a range of industrial applications. Here, we consider the helical flow of a Bingham fluid between infinitely long coaxial cylinders, where the flow arises from the imposition of a steady rotation of the inner cylinder (annular Coutte flow) on a steady axial pressure driven flow (Poiseuille flow), where the ratio of the rotational flow compared to the axial flow is small. We apply a perturbation procedure to obtain approximate analytic expressions for the fluid velocity field and such related quantities as the stress and viscosity profiles in the flow. In particular, we examine the location of yield boundaries in the flow and how these vary with the rotation speed of the inner cylinder and other flow parameters. These analytic results are shown to agree very well with the results of numerical computations.     

Conservation theorems for magnetic field and vorticity in two-dimensional conducting fluid flows

The classical conservation theorems for magnetic force lines, magnetic flux through a fluid surface, and intensity of magnetic vector tubes are generalized to plane flows of a finitely conducting fluid in an orthogonal magnetic field. The Helmholtz and Kelvin vorticity conservation theorems are generalized for plane motion of a viscous conducting fluid in an orthogonal magnetic field and the Bernoulli integral is derived. The Bernoulli integral is also generalized for plane motion of viscous ideally conducting fluid in a longitudinal magnetic field. Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 46–49, 1994.     

Effects of an induced magnetic field on the peristaltic flow of a third‐order fluid

In this article, we carry out the effect of an induced magnetic field on the peristaltic transport of an incompressible conducting third order fluid in a symmetric channel. The flow analysis has been developed for low Reynolds number and long wave length approximation. Analytical solutions have been established for the axial velocity, stream function, magnetic force function, and axial‐induced magnetic field. The effects of pertinent parameters on the pressure rise per wavelength are investigated by using numerical integration. Besides this, we study the effect of these parameters on the pressure gradient and axial induced magnetic field. The phenomena of trapping and pumping are also discussed. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

Lie group method is investigated for solving the problem of heat transfer in an unsteady, three-dimensional, laminar, boundary-layer flow of a viscous, incompressible and electrically conducting fluid over inclined permeable surface embedded in porous medium in the presence of a uniform magnetic field and heat generation/absorption effects. A uniform magnetic field is applied in the y-direction and a generalized flow model is presented to include the effects of the macroscopic viscous term and the microscopic permeability of porous medium. The infinitesimal generators accepted by the equations are calculated and the extension of the Lie algebra for the problem is also presented. The restrictions imposed by the boundary conditions on the generators are calculated. The investigation of the three-independent-variable partial differential equations is converted into a two-independent-variable system by using one subgroup of the general group. The resulting equations are solved numerically with the perturbation solution for various times. Velocity, temperature and pressure profiles, surface shear stresses, and wall-heat transfer rate are discussed for various values of Prandtl number, Hartmann number, Darcy number, heat generation/absorption coefficient, and surface mass-transfer coefficient.     

Exact solution of thermal stress problem of an inhomogeneous hygrothermal piezoelectric hollow cylinder

The closed-form exact solution for the hygrothermal response of inhomogeneous piezoelectric hollow cylinders is obtained. The interaction of electric potentials, electric displacement and elastic deformations is presented. The present cylinder is subjected to both a mechanical load and an electric potential. The material properties coefficients of the present cylinder are assumed to be changed in the radial direction by different distribution forms. The field quantities like displacement, stresses and electric potentials in the inhomogeneous piezoelectric cylinders are determined. The significant of influences of material inhomogeneity, initial temperature, final moisture, and the load and electric ratios in the field quantities are investigated. The concluding remarks and suitable discussions are made.     

Magneto hydrodynamic stability of self-gravitational fluid cylinder

The self-gravitating instability of a fluid cylinder pervaded by magnetic field and endowed with surface tension has been discussed. The dispersion relation is derived and some reported works are recovered as limiting cases from it. The capillary force is destabilizing only in the small axisymmetric domain and stabilizing otherwise. The magnetic field has a strong stabilizing effect in all modes of perturbation for all wavelengths. The self-gravitating force is destabilizing in the axisymmetric perturbation. However the magnetic field effect modified a lot the destabilizing character of the model and could overcome the capillary and self-gravitating instability of the model for all short and long wavelengths.     

Point force in a stratified fluid in a cylinder under a magnetic field

The flow induced by a body moving in an inviscid incompressible density stratified fluid in an infinite circular cylinder under the influence of a uniform axial magnetic field is studied using the method of replacing the body by an isolated point force. This method was adopted by Childress and others in discussing the body effects in a viscous fluid. The solution is obtained using the Fourier transformation and the Lighthill’s radiation condition. The cases of weak and strong magnetic fields are discussed.     

Zur theorie rotierender und schwingender schaufelkränze in einer unterschallstromung durch einen ringkanal

In this paper the three-dimensional perturbation flow induced by a rotating and oscillating blade row which operates in a subsonic flow in axial direction of an annular channel is studied. The velocity potential is reduced to the infinite Hilbert space vector of Fourier coefficients of an eigen-function expansion with respect to vanishing normal derivatives on both cylinder walls. These coefficients satisfy an infinite set of ordinary differential equations of second order after an application of a one-dimensional Fourier transform in axial direction. Several canonical two-part mixed boundary value problems are then investigated by reduction to “infinite two-by-two-Wiener-Hopf functional systems”. In case of strong factorizability of certain matrix-operator-valued functions on the line these systems may be solved explicitely. Criteria for the factorization are not given here.     

The scattering of electromagnetic wave at oblique incidence in a homogeneous chiral medium

We consider the scattering of a time-harmonic electromagnetic wave by a perfectly and imperfectly conducting infinite cylinder at oblique incidence respectively. We assume that the cylinder is embedded in a homogeneous chiral medium and the cylinder is parallel to the z axis. Since the x components and y components of electric field and magnetic field can be expressed in terms of their z components, we can derive from Maxwell's equations and corresponding boundary conditions that the scattering problem is modeled as a boundary value problem for the z components of electric field and magnetic field. By using Rellich's lemma and variational approach, the uniqueness and the existence of solutions are justified.     

Perturbation analysis of a magnetohydrodynamic boundary layer flow

This paper presents a perturbation analysis study of the flow of an electrically conducting power-law fluid in the presence of a uniform transverse magnetic field over a stretching sheet. The perturbation solutions for small and large values of the mixed convection parameter are explored. The asymptotic behavior of the solutions was examined for different values of the power-law index and the magnetic parameter.     

Hydromagnetic instability of a power-law liquid film flowing down a vertical cylinder using numerical approximation approach techniques

The long-wave perturbation method is employed to investigate the hydromagnetic stability of a thin electrically-conductive power-law liquid film flowing down the external surface of a vertical cylinder in a magnetic field. The validity of the numerical results is improved through the introduction of the flow index and the magnetic force into the governing equation. In contrast to most previous studies presented in the literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The normal mode approach is used to analyze the stability of the film flow. The modeling results reveal that the stability of the film flow system is weakened as the radius of the cylinder is reduced. However, the flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index, respectively. In general, the optimum conditions can be found through the use of a system to alter stability of the film flow by controlling the applied magnetic field.     

Stability of a cylindrical plasma in the presence of a monotonic field—II

The stability of an incompressible inviscid, perfectly conducting cylindrical plasma against azimuthal disturbances in the presence of a monotonic decreasing magnetic field having a constant pitch is discussed by using energy principle. The results obtained by this principle are compared form = 1 mode (which is a dangerous mode in which there is a lateral shift of the entire column) with that obtained by normal mode analysis. It is found thatm = 1 mode is always unstable. Further, an axial line current, external axial field and the surface tension tend to stabilisem ≠ modes.     

Study of magnetohydrodynamic pulsatile flow in a constricted channel

The present work reports the study of steady and pulsatile flows of an electrically conducting fluid in a differently shaped locally constricted channel in presence of an external transverse uniform magnetic field. The governing nonlinear magnetohydrodynamic equations simplified for low conducting fluids are solved numerically by finite difference method using stream function-vorticity formulation. The analysis reveals that the flow separation region is diminished with increasing values of magnetic parameter. It is noticed that the increase in the magnetic field strength results in the progressive flattening of axial velocity. The variations of wall shear stress with increasing values of the magnetic parameter are shown for both steady and pulsatile flow conditions. The streamline and vorticity distributions in magnetohydrodynamic flow are also shown graphically and discussed.     

Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors

Realistic applications in metal detection involve multiple inhomogeneous‐conducting permeable objects, and the aim of this paper is to characterise such objects by polarizability tensors. We show that, for the eddy current model, the leading order terms for the perturbation in the magnetic field, due to the presence of N small conducting permeable homogeneous inclusions, comprises of a sum of N terms with each containing a complex symmetric rank 2 polarizability tensor. Each tensor contains information about the shape and material properties of one of the objects and is independent of its position. The asymptotic expansion we obtain extends a previously known result for a single isolated object and applies in situations where the object sizes are small and the objects are sufficiently well separated. We also obtain a second expansion that describes the perturbed magnetic field for inhomogeneous and closely spaced objects, which again characterises the objects by a complex symmetric rank 2 tensor. The tensor's coefficients can be computed by solving a vector valued transmission problem, and we include numerical examples to illustrate the agreement between the asymptotic formula describing the perturbed fields and the numerical prediction. We also include algorithms for the localisation and identification of multiple inhomogeneous objects.