NUMERICAL MODELING OF INDUCTION HEATING FOR TWO-DIMENSIONAL GEOMETRIES

1993 ◽  
Vol 03 (06) ◽  
pp. 805-822 ◽  
Author(s):  
S. CLAIN ◽  
J. RAPPAZ ◽  
M. SWIERKOSZ ◽  
R. TOUZANI
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Numerical Method ◽  
Induction Heating ◽  
Two Dimensional ◽  
Time Periodicity ◽  
Model Equations ◽  
Thermal Phenomena ◽  
The Magnetic Field ◽  
Different Time Scales

We present both a mathematical model and a numerical method for simulating induction heating processes. The geometry of the conductors is cylindrical and the magnetic field is assumed to be parallel to the invariance axis. The model equations have current tension as prescribed data rather than current intensity. In particular, the formulation of the electromagnetic problem uses the magnetic field as the unknown function. The numerical method takes into account the time periodicity of the prescribed tension and deals with the two different time scales of electromagnetic and thermal phenomena.

A QUASI-STATIC TWO-DIMENSIONAL INDUCTION HEATING PROBLEM I: MODELLING AND ANALYSIS

1998 ◽  
Vol 08 (06) ◽  
pp. 1003-1021 ◽  
Author(s):  
C. PARIETTI ◽  
J. RAPPAZ
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Induction Heating ◽  
System Modelling ◽  
Two Dimensional ◽  
Joule Effect ◽  
Nonlinear Elliptic ◽  
Uniqueness Of The Solution ◽  
The Magnetic Field ◽  
Temperature Equation

We consider a nonlinear elliptic–parabolic system modelling induction heating processes when a sinusoidal electromagnetic field is applied at the boundary of the inductor. The magnetic field satisfies an elliptic equation whereas the temperature equation is parabolic. These equations are coupled together due to the conductivities and the Joule effect. We show the existence of a weak solution to the corresponding problem and under additional assumptions, we study the uniqueness of the solution.

A QUASI-STATIC TWO-DIMENSIONAL INDUCTION HEATING PROBLEM II: NUMERICAL ANALYSIS

1999 ◽  
Vol 09 (09) ◽  
pp. 1333-1350 ◽  
Author(s):  
C. PARIETTI ◽  
J. RAPPAZ
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Numerical Analysis ◽  
Elliptic Equation ◽  
Induction Heating ◽  
Two Dimensional ◽  
Joule Effect ◽  
Nonlinear Elliptic ◽  
The Magnetic Field ◽  
Temperature Equation

We consider a nonlinear elliptic–parabolic system which stems from the modelling of heat induction processes in which a sinusoidal electromagnetic field is applied at the boundary of the inductor. The magnetic field satisfies an elliptic equation whereas the temperature equation is parabolic. These two equations are coupled due to the Joule effect and to the conductivity dependence on temperature. A Galerkin method for our problem is analyzed and shown to yield error estimates in L2 and H1.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

The Function of Magnetic Field in a Magnetic-Electrochemical Compound Polishing

2010 ◽  
Vol 97-101 ◽  
pp. 4141-4145 ◽  
Author(s):  
Li Min Shi ◽  
Er Liang Liu ◽  
Yong Jiang Niu ◽  
Yu Quan Chen
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Concentration Polarization ◽  
Electrochemical Reaction ◽  
Charged Particles ◽  
Polishing Process ◽  
Electrical Field ◽  
Movement Model ◽  
The Mathematical Model ◽  
The Magnetic Field

Traditionally, the magnetic field is always vertical to the electrical field in a magnetic-electrochemical compound polishing.The magnetic field is set to parallel the electrical field in this paper. The mathematical model of the charged particles movement in a magnetic field is established through the analysis of its movement process when using Coulomb laws and Lorentz force. Through constructing the velocity formulation and loci formulation, the function of the magnetic field is proved. Because of the magnetic field, the concentration polarization of electrochemical reaction can be reduced more and the electrochemical reaction can be accelerated easily than the traditional polishing in which the magnetic field is vertical to the electrical field. Finally, to verify the model, the magnetic-electrochemical compound polishing process has been tested and the results, compared with those obtained from the model, have shown the movement model is reasonable and the analysis to function of magnetic field is correct.

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

scholarly journals INCREASING THE EFFICIENCY OF MULTY-VARIANT CALCULATIONS OF ELECTROMAGNETIC FIELD DISTRIBUTION IN MATRIX OF A POLYGRADIENT SEPARATOR

2021 ◽  
Author(s):  
Jasim Mohmed Jasim Jasim ◽  
Iryna Shvedchykova ◽  
Igor Panasiuk ◽  
Julia Romanchenko ◽  
Inna Melkonova
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Three Dimensional ◽  
Magnetic Potential ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Air Gaps ◽  
Vector Magnetic Potential ◽  
Electromagnetic Separator ◽  
The Magnetic Field

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device

scholarly journals Numerical simulation of induction heating thick-walled tubes

2018 ◽  
Vol 168 ◽  
pp. 02004
Author(s):  
Richard Lenhard ◽  
Milan Malcho ◽  
Katarína Kaduchová
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Field Distribution ◽  
Induction Heating ◽  
Electromagnetic Induction ◽  
Magnetic Field Distribution ◽  
The Magnetic Field ◽  
Heated Material ◽  
Ansys Workbench

In the paper is shown the connection of two toolboxes in an Ansys Workbench solution for induction heating. In Ansys Workbench, Maxwell electromagnetism programs and Fluent have been linked. In Maxwell, a simulation of electromagnetic induction was performed, where data on the magnetic field distribution in the heated material was obtained and then transformed into the Fluent program in which the induction heating simulation was performed.

Методика практического восстановления параметров формы поверхностных двухмерных дефектов с учетом нелинейных свойств ферромагнетика

2021 ◽  
pp. 46-55
Author(s):  
А.В. Никитин ◽  
А.В. Михайлов ◽  
А.С. Петров ◽  
С.Э. Попов
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Numerical Experiments ◽  
Input Data ◽  
Metal Plate ◽  
Two Dimensional ◽  
Nonlinear Properties ◽  
Data Errors ◽  
The Magnetic Field

A technique for determining the depth and opening of a surface two-dimensional defect in a ferromagnet is presented, that is resistant to input data errors. Defects and magnetic transducers are located on opposite sides of the metal plate. The nonlinear properties of the ferromagnet are taken into account. The components of the magnetic field in the metal were reconstructed from the measured components of the magnetic field above the defect-free surface of the metal. As a result of numerical experiments, the limits of applicability of the method were obtained. The results of the technique have been verified experimentally.

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