Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace

Bermúdez, Alfredo; Gómez, Dolores; Muòiz, M. C.; Salgado, Pilar; Vázquez, Rafael

doi:10.1016/j.apnum.2008.12.005

Cited by 38 publications

(13 citation statements)

References 22 publications

(54 reference statements)

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“…We recall that in our analysis the domain of the conducting medium remains fixed throughout the process. This is what happens, for instance in magnetohydrodynamic problems which involve a fluid in motion occupying a fixed domain [2]. In particular, we consider the simulation of a small induction furnace composed by a graphite crucible and containing silicon in motion inside.…”

Section: B Simulation Of An Induction Heating Furnace Including a Momentioning

confidence: 99%

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Numerical analysis of a transient eddy current axisymmetric problem involving velocity terms

Bermúdez

Reales

Rodrı́guez

et al. 2011

Numerical Methods Partial

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The aim of this article is to analyze a transient axisymmetric electromagnetic model involving velocity terms in the Ohm's law. To this end, we introduce a time-dependent weak formulation leading to a degenerate parabolic problem and establish its well posedness. We propose a finite-element method for space discretization and prove well posedness and error estimates. Then, we combine it with a backward Euler time discretization and prove stability and error estimates. Finally, numerical results assessing the performance of the method are reported.

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Section: B Simulation Of An Induction Heating Furnace Including a Momentioning

confidence: 99%

“…Let V 0 be the dual space of V 0 with respect to the pivot space L 2 r ( 0 ) with measure σ r dr dz (which according to (2) is topologically equivalent to L 2 r ( 0 ) with measure r dr dz). Let us define the space…”

Section: ∂A ∂Tmentioning

confidence: 99%

Numerical analysis of a transient eddy current axisymmetric problem involving velocity terms

Bermúdez

Reales

Rodrı́guez

et al. 2011

Numerical Methods Partial

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“…So far, many temperature and electromagnetic fields of conventional spiral coil induction heating have been investigated using finite element method [9][10][11][12][13][14][15][16]. However, analytical or numerical studies about rolls temperature in induction heating by unconventional coils have not been reported.…”

Section: Introductionmentioning

confidence: 99%

2D-FEM analysis of rolls temperature field in induction heating process

Cai¹,

Wang²,

Rui-bin³

et al. 2013

AIP Conference Proceedings

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Hot-roller warm rolling process is expected to achieve a breakthrough in solving the problem of high quality rolling for difficult deformed metals. In this paper roll surface induction heating was studied based on the finite element theory of electromagnetic-thermal coupling and experiment. The law of temperature field for a static roll in induction heating process was analyzed by FEM. The results show that roll surface temperature can achieve 721 at 48s under 20000Hz power frequency, 350×10 4 A/m 2 current density, due to the skin effect on roll surface. Using a special induction coil in the laboratory, an experiment of roll induction heating was carried out with the same process parameters. The calculated results of temperature on roll surface agree well with the measured value.

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“…For example, in [9] zone melting with the aim of cleaning semiconductor crystals was investigated. The authors introduced the averaged value of the electromagnetic force acting on the melt and worked with the mean temperature value.…”

mentioning

confidence: 99%

Mathematical Model of the Processes of Heat and Mass Transfer and Diffusion of the Magnetic Field in an Induction Furnace

Perminov

Nikulin

2016

J Eng Phys Thermophy

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We propose a mathematical model describing the motion of a metal melt in a variable inhomogeneous magnetic fi eld of a short solenoid. In formulating the problem, we made estimates and showed the possibility of splitting the complete magnetohydrodynamical problem into two subproblems: a magnetic fi eld diffusion problem where the distributions of the external and induced magnetic fi elds and currents are determined, and a heat and mass transfer problem with known distributions of volume sources of heat and forces. The dimensionless form of the heat and mass transfer equation was obtained with the use of averaging and multiscale methods, which permitted writing and solving separately the equations for averaged fl ows and temperature fi elds and their oscillations. For the heat and mass transfer problem, the boundary conditions for a real technological facility are discussed. The dimensionless form of the magnetic fi eld diffusion equation is presented, and the experimental computational procedure and results of the numerical simulation of the magnetic fi eld structure in the melt for various magnetic Reynolds numbers are described. The extreme dependence of heat release on the magnetic Reynolds number has been interpreted.Keywords: induction melting, superalloy, variable magnetic fi eld, magnetic fi eld diffusion, inductive current, heat and mass transfer, convection, multiscale method, averaging method.Introduction. Induction heating is widely used in various fi elds of metallurgy and in precision production of semiconductor dielectric elements: induction melting, zone melting, strengthening of the surface of metal products, crystal growing, and production of optical fi bers. The main idea of induction heating is the use of the Joule heat of currents induced in a conducting material by a variable external magnetic fi eld. The power released by the currents leads to local heating of the material and, consequently, to changes in the density and equilibrium concentration of elements. The description of the heat and mass transfer in such systems requires, as a rule, solving a system of electrodynamical, thermal energy transfer, and mass transfer equations.If the pulse rate of the fi eld is fairly high, then the resulting magnetic fi eld composed of the external fi eld of the inductor and the fi elds of inductive currents attenuates into the depth of the conductor and becomes practically zero at some distance ζ from its surface [1]. Within the limits of the boundary layer ζ, inductive currents (heat sources) and bulk electromagnetic forces acting on the moving melt are localized. Such an approach is convenient if the intensity near the conductor surface is known.For the case where the fi elds cannot be assumed to be homogeneous [2], a popular approach is describing the fi eld is terms of the vector potential A whose rotor is equal to the magnetic fi eld intensity H = 1

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Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace

Cited by 38 publications

References 22 publications

Numerical analysis of a transient eddy current axisymmetric problem involving velocity terms

Numerical analysis of a transient eddy current axisymmetric problem involving velocity terms

2D-FEM analysis of rolls temperature field in induction heating process

Mathematical Model of the Processes of Heat and Mass Transfer and Diffusion of the Magnetic Field in an Induction Furnace

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