Magnetohydrodynamics or MHD is a magnetized fluid approximation to the kinetic theory describing a gas composed of charged particles.
Background
MHD is an approximation in plasma physics where one treats a plasma as a magnetized fluid. The theory is applicable when the spatial scales, $L$, and time scales, $\tau$, are much larger than the ion thermal gyroradius, $\rho_{ci}$, and ion cyclotron perod, $\Omega_{ci}^{-1}$, respectivley. In other words, the MHD approximation often holds if: $$ \left( \frac{ \rho_{ci} }{ L } \right)^{2} \ll \left( \frac{ 1 }{ \tau \ \Omega_{ci} } \right)^{2} \ll 1 $$
When to use
magnetohydrodynamics is often associated with plasma-physics and fluid-dynamics, but it is a specialized version of both. It is also often invoked in astrophysics.
