Search

Induction heating is a process of heat generation which uses metal conductors and the Joule effect. The induction heating process has many applications in industry, such as metal melting, preheating for forging operations, hardening, and welding. A model of induction heating is given by a coupled system of partial differential equations relating temperature field and magnetic potential. Precisely, a coupled system of Maxwell and heat equations is given in the workpiece, while in the exterior domain the Laplace equation for the magnetic potential is formulated. Finally, nonlinear boundary condition for the heat equation, transmission conditions and asymptotic condition for the magnetic potential are given. Solution of such coupled multifield problems requires advanced coupled numerical methods. Therefore, in this paper we present a coupled numerical approach connecting Finite Difference Method and discrete potential theory. The use of discrete potential theory is motivated by the fact that asymptotic conditions are satisfied exactly on the discrete level. Thus, a general scheme for the coupled numerical method is presented in this paper.Induction heating is a process of heat generation which uses metal conductors and the Joule effect. The induction heating process has many applications in industry, such as metal melting, preheating for forging operations, hardening, and welding. A model of induction heating is given by a coupled system of partial differential equations relating temperature field and magnetic potential. Precisely, a coupled system of Maxwell and heat equations is given in the workpiece, while in the exterior domain the Laplace equation for the magnetic potential is formulated. Finally, nonlinear boundary condition for the heat equation, transmission conditions and asymptotic condition for the magnetic potential are given. Solution of such coupled multifield problems requires advanced coupled numerical methods. Therefore, in this paper we present a coupled numerical approach connecting Finite Difference Method and discrete potential theory. The use of discrete potential theory is motivated by the fact that asymptotic condi...

To control thinning is a challenge in traditional flaring process of thin-walled tubes. Electromagnetic forming provides a new way to expand the tubes end with uniform wall thickness, as it can produce a uniform distribution of magnetic force on tubes and easily form by one step based on adjusting the discharge parameters. In this paper, a 3D asymmetric finite element model of electromagnetic flaring of thin-walled copper tubes based on the magnetic vector potential is developed for calculating magnetic field and magnetic forces, and Newmark integration method is used to calculate the dynamic plastic deformation of tubes in the mechanical model. A sequential-coupled simulation approach is developed to analyze the deformation behaviors and the influences of different discharge parameters on deformation behaviors for electromagnetic tube flaring. The deformation height and thinning rate of thin-walled copper tubes show a positive correlation with the charge voltage and capacitance, and deformation zone main...

Scattering problems in cracked magnetoelectroelastic plane subjected to timeharmonic SH wave are studied. The solution is based on integral representation of the scattered field in the frequency domain. The relationship between the jumps of the displacement, electric and magnetic potential and the generalized stress intensity factors (SIF) near the crack tip is presented. The stationary phase method is used to derive the asymptotic of the derivative of the fundamental solution in the far field. Generalized SIF near the crack edge are determined uniquely by far field data.

An analytical model of an axisymmetric eddy current probe with a cylindrical ferrite core above a layered conductive half-space is developed. Initially we consider the magnetic vector potential of a circular filament coaxial with a ferrite core over a layered conducting half-space. The principle of superposition is then used to derive close-form expressions for both the electromagnetic field and the impedance of a coil from the filament field. Rather than locating the probe in infinite space, it is confined coaxially within a circularly cylindrical boundary on which the vector potential field is zero. The radius of this artificial boundary is large in order to ensure that does not interfere substantially with the field near the probe. By using a truncated region in this way, the vector potential in the probe region can be expanded as a series rather than an integral form. Thus the solution of the problem amounts to finding the expansion coeefficients in the series. The numerical predictions of probe impedance have been compared with experimental data showing good agreement.

The confinement of pure electron plasmas in the Columbia Non‐neutral Torus (CNT) stellarator is limited by the presence of unconfined orbits. The existence of a very large electric field across magnetic surfaces should preclude such unconfined orbits. However variations in the electric potential on magnetic surfaces, inherent to the CNT equilibrium, add to the complexity of the trajectories and lead to bad orbits. We have written a code using magnetic coordinates to integrate the electron drift trajectories in the electric and magnetic fields expected in CNT equilibria. Results of such calculations are presented showing that there exists unconfined orbits in CNT if the potential is not constant on surfaces.

Current sheets are magnetic structures which are important for activity processes in the coronae of the Sun and of other stars. To lowest order current sheets can be described as one‐dimensional equilibria of a collisionless plasma described by the Vlasov‐Maxwell equations. In the present paper, a general mathematical framework for one‐dimensional equilibrium solutions of the Vlasov‐Maxwell equations is presented. The equilibrium equations for the magnetic vector potential are equivalent to the motion of a particle in a two‐dimensional potential. The theory is applied to some examples for one‐dimensional current sheets.

Brownian‐dynamics simulations without the hydrodynamic interactions between particles are performed to investigate two‐dimensional dilute suspensions of magnetic colloidal particles under a static magnetic field. From the detailed analyses of the numerical results, we obtain the phase diagram for the magnitude of magnetic potential J and the area fraction σ. The results also suggests that the phase transition line is determined only by the value of the parameter Γ(= Jσ32), where Γ ≃ 68 at the melting point.

Conservative, multidimensional, Lagrangian, staggered-grid hydrodynamics algorithms are well known[l]. Here, these principles are extended to include magnetic fields in the discretized momentum and energy equations. A magnetic vector potential, A, formulation is centered on edges so that the divergence law, ▽ · B = 0 is maintained to round-off error. The magnetic field is cell-centered. Magnetic forces from Maxwell's stress tensor are expressed in terms of the field and geometric quantities. This assures momentum and energy conservation. The method is expressed in 3D, but is generalizable to 1 or 2D. Resistive diffusion of the madoes not serve to straighten the azimuthal magnetic field lines [2]. gnetic field is handled by implicit time differencing and is solved by preconditioned, conjugate gradient methods. Multi-material, Z-pinch, test-problems are shown.

Magneto-optic imaging (MOI) is a relatively new sensor application of an extension of bubble memory technology to NDT and produce easy-to-interpret, real time analog images. MOI systems use a magneto-optic (MO) sensor to produce analog images of magnetic flux leakage from surface and subsurface defects. The instrument’s capability in detecting the relatively weak magnetic fields associated with subsurface defects depends on the sensitivity of the magneto-optic sensor. The availability of a theoretical model that can simulate the MOI system performance is extremely important for optimization of the MOI sensor and hardware system. A nodal finite element model based on magnetic vector potential formulation has been developed for simulating MOI phenomenon. This model has been used for predicting the magnetic fields in simple test geometry with corrosion dome defects. In the case of test samples with multiple discontinuities, a more robust model using the magnetic vector potential Ā and electrical scalar poten...

In interaction of magnetic fields with cracks in ferromagnetic steels has been calculated to assess the capability of magnetic particle inspection (MPI) for crack detection. In MPI the surface of a steel component is coated with magnetic ink and, under the influence of an applied magnetic field, particles in the ink diffuse through the liquid until a steady state is reached. The particles accumulate mainly in regions where the field is greatest—especially where the crack meets the material surface. The field is greater there because of the large difference in the magnetic potential across the crack mouth. The calculation shows that the field at the mouth increases with crack depth but reaches a saturation value due to the flux leakage between the crack faces. If oxide is present, the flux passing across the crack increases. Consequently, the magnetic potential difference at the mouth is reduced and the crack is more difficult to detect. The calculation has been performed using an integral formulation, ass...