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Introduction to Plasmas and Plasma Dynamics by Haibin Tang, Thomas M. York

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Single Fluid Equations of Magnetofluid Mechanics

We will consider basic single fluid theory with the following variables: v,p,ρ,T,H,E,J,ρeimage, a total of 16 unknowns. This set can be solved using the following equations with appropriate boundary conditions (Pai, 1962).
State:

p=ρRT=nkT.

image

Continuity:

ρt+·(ρv)=0.

image

Momentum:

ρ[vt+(v·)v]=p+·τ+ρeE+J×B,where:τij=μ(uixj+ujxi)23μ(·v)δij.

Energy:

ρDe¯mDt=·(pv)+·(v·τ)+·Q+J·E.

But note ...

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