= Hartmann number
{c}
{title2=$H=|B_0|L/\sqrt{\mu_0\rho\nu\eta}$}
{wiki}
The Hartmann number measures the strength of magnetic coupling relative to viscous and resistive effects in a channel:
$$
H=\frac{|B_0|L}{\sqrt{\mu_0\rho\nu\eta}}=|B_0|L\sqrt{\frac{\sigma_c}{\rho\nu}}.
$$
Here $L$ is the channel half-width, $\nu$ the <kinematic viscosity>, $\eta$ the <magnetic diffusivity> and $\sigma_c$ the <electrical conductivity>. In <Hartmann flow>, large $H$ produces thin magnetic-viscous wall layers and a flatter, slower core for fixed <pressure gradient>.
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