Numerical modelling of magnetic shielding by a cylindrical ferrofluid layer

A coupled method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics. The problem describes an interaction of a uniform magnetic field with a cylindrical ferrofluid layer. Ferrofluid magnetisations, based on expansions over the Langevin law, are considered to model ferrofluids with a different concentration of ferroparticles. The shielding effectiveness factor of the cylindrical thick-walled ferrofluid layer is calculated depending on intensities of the uniform magnetic field and on thickness of the ferrofluid layer

Numerical Study of Diffusion of Interacting Particles in a Magnetic Fluid Layer

The paper is devoted to construction of mathematical model and computational algorithm for determining equilibrium shapes of a free surface of a magnetic fluid subject to diffusion of ferromagnetic particles in the fluid. The mathematical model consists of the Maxwell equations to determine the structure of magnetic field, the mass transfer equation for the particles, and the Young-Laplace equations for the fluid-air interface as well. Models of the uniform distribution of the particles, the nonuniform distribution without considering the particle interaction, and the nonuniform distribution subject to the particle interaction are considered. Numerical comparison of the models is carried out on the ferrohydrostatic problem of stability of a magnetic-fluid layer under a uniform magnetic fiel

Application of Collocation BEM for Axisymmetric Transmission Problems in Electro- and Magnetostatics

This paper considers the numerical solution of boundary integral equations for an exterior transmission problem in a three-dimensional axisymmetric domain. The resulting potential problem is formulated in a meridian plane as the second kind integral equation for a boundary potential and the first kind integral equation for a boundary flux. The numerical method is an axisymmetric collocation with equal order approximations of the boundary unknowns on a polygonal boundary. The complete elliptic integrals of the kernels are approximated by polynomials. An asymptotic kernels behavior is analyzed for accurate numerical evaluation of integrals. A piecewise-constant midpoint collocation and a piecewise-linear nodal collocation on a circular arc and on its polygonal interpolation are used for test computations on uniform meshes. We analyze empirically the influence of the polygonal boundary interpolation to the accuracy and the convergence of the presented method. We have found that the polygonal boundary interpolation does not change the convergence behavior on the smooth boundary for the piecewise-constant and the piecewise-linear collocation

Numerical study of the shielding properties of a ferrofluid taking into account magnitophoresis and particle interaction

Shielding properties of a cylindrical thick-walled ferrofluid layer that protects against externally applied uniform magnetic fields are numerically investigated. We take into account the diffusion of magnetic nanoparticles in the ferrofluid with magnetic dipole-dipole, steric and hydrodynamic interactions between particles. Permeability of the ferrofluid is considered to be dependent on the magnetic-field strength and the particle concentration. A combined method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics in the whole space, augmented by nonlinear algebraic equations based on the mass transfer equation for magnetic nanoparticles in ferrofluids. Numerical experiments revealed that the diffusion of particles has negligible influence on the shielding properties at weak and strong intensities of the applied magnetic field when comparing with the results of computations for a uniform particle distribution

Lamp in the South Head Lighthouse, Sydney, 31 October 1930, 1 [picture].

Title devised from accompanying information where available.; Part of the: Fairfax archive of glass plate negatives.; Fairfax number: 6718.; Also available online at: http://nla.gov.au/nla.pic-vn6296133; Acquired from Fairfax Media, 2012

genehmigt durch die Fakultät für Mathematik der Otto-von-Guericke-Universität Magdeburg Gutachter:

Numerical methods for axisymmetric equilibrium magnetic-fluid shapes Dissertatio