Publication

A quasi-static two-dimensional induction heating problem. I: Modelling and analysis

Jacques Rappaz, Catherine Parietti
1998
Journal Articles

Abstract

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.

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https://infoscience.epfl.ch/entities/publication/7afdcaba-ef44-4652-b1a1-425450d3af68

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Jacques Rappaz, Catherine Parietti
1998
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/7afdcaba-ef44-4652-b1a1-425450d3af68

About this result

Related concepts (16)

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.

Electromagnetic field

An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by moving electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified as light) and interacts with charges and currents.

Magnetic vector potential

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: . Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.

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A quasi-static two-dimensional induction heating problem. I: Modelling and analysis

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