What is the most general form of the momentum equation in MHD?
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The momentum equation for an electrically neutral, conducting, nonpermeable fluid has the form (Jackson, 1962):
ρdvdt=−∇p+J×B+Fv+ρgρdvdt=−∇p+J×B+Fv+ρg
where FvFv is the viscous force, which in the Navier-Stokes momentum equation is usually written in terms of the stress deviator tensor ττ:
Fv=∇⋅τFv=∇⋅τ
What is the corresponding form for an electrically non-neutral, permeable fluid?
I am particularly interested in the case of a permeable material. I expect that in this case the magnetic field HH should appear in the equation instead of the magnetic induction BB.
References from book/articles are much appreciated.
ρdvdt=−∇p+J×B+Fv+ρgρdvdt=−∇p+J×B+Fv+ρg
where FvFv is the viscous force, which in the Navier-Stokes momentum equation is usually written in terms of the stress deviator tensor ττ:
Fv=∇⋅τFv=∇⋅τ
What is the corresponding form for an electrically non-neutral, permeable fluid?
I am particularly interested in the case of a permeable material. I expect that in this case the magnetic field HH should appear in the equation instead of the magnetic induction BB.
References from book/articles are much appreciated.
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Magnetohydrodynamics is the study of the magnetic properties and behaviour of ... The ideal MHD equations consist of the continuity equation, the Cauchy momentum equation, ...
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