ANSYS FLUENT 12.0 Magnetohydrodynamics Module Manual - 2.2.1 Case 1: Generated in Non-conducting Media

2.2.1 Case 1: $\vec{B_0}$ Generated in Non-conducting Media

In this case the imposed field $\vec{B_0}$ satisfies the following conditions:

$\nabla \times \vec{B_0} = 0$

(2.2-6)

$\nabla^2\vec{B_0} = 0$

(2.2-7)

With $\vec{B} = \vec{B_0} + \vec{b}$ , the induction equation (Equation 2.2-3) can be written as:

$\frac{\partial \vec{b}}{\partial t} + (\vec{U} \cdot \nabla)... ... \cdot \nabla)\vec{B_0} - \frac{\partial\vec{B_0}}{\partial t}$

(2.2-8)

The current density is given by:

$\vec{\jmath} = \frac{1}{\mu} \nabla \times \vec{b}$

(2.2-9)

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