= Hartmann flow
{c}
Hartmann flow is a fully developed viscous conducting-fluid flow driven along a planar channel while a uniform <magnetic field> crosses the walls. Induction and the <Lorentz force density> couple its velocity and tangential induced field. For no-slip, normal-field walls separated by $2L$, the velocity is a <hyperbolic cosine> profile that approaches <plane Poiseuille flow> at zero imposed field and develops a uniform core with <Hartmann layers> at large <Hartmann number>.
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