Induction Magnetic Equation

Numerical methods and mathematical models of Elmer
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Andrea_P
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Induction Magnetic Equation

Post by Andrea_P »

Hi,
I have a theoric question this time. By reading the Elmer models manual, I don't understand how the superposition between the induced magnetic field B^i and the external magnetic field B^e appears in the induced magnetic equation

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B=B^i+B^e
Indeed, according to Faraday’s law of induction, the relative movement of a conducting fluid and a magnetic field causes an electromotive force (EMF) (of order |U × B|) to arise. Electrical currents will flow in general, with a current density

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J = sigma_m(U × B^e)

While, according to Ampere’s rule, these induced currents must produce a second, induced magnetic field. This adds to the initial magnetic field, and the change is generally sufficient that the magnetic field lines appear to be dragged along with the fluid:

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 nabla × B^i = μJ
The total magnetic field (imposed and induced) interacts with the induced current density, J, to produce a Lorentz force of J × B per unit volume. This has an effect on the conductor and is usually addressed at it.
Thanks in advance for your help,
Regards,
Andrea
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raback
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Re: Induction Magnetic Equation

Post by raback »

Hi

I verified looking at the code. The external field results to a right-hand-side term: curl(v x B^e). This makes sense since in Eq. (23.1) in Elmer Models Manual the two leading terms vanish for the external field and hence only the 3rd term gives a contribution.

-Peter
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