## Single Fluid Equations of Magnetofluid Mechanics

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

$p=ρRT=nkT.$

Continuity:

$∂ρ∂t+∇·(ρv→)=0.$

Momentum:

$ρ[∂v→∂t+(v→·∇)v→]=−∇p+∇·τ↔+ρeE→+J→×B→,where:τij=μ(∂ui∂xj+∂uj∂xi)−23μ(∇·v→)δij.$

Energy:

$ρDe¯mDt=−∇·(pv→)+∇·(v→·τ↔)+∇·Q→+J→·E→.$

But note ...

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