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Magnetohydrodynamics (MHD) is fluid dynamics that includes the effects of electrical conductivity of the fluids. (Note that the term MHD is definitely used for compressible fluids, even though the term "hydrodynamics" is sometimes used specifically to indicate fluid dynamics of non-compressible fluids.) MHD modeling was initiated by Hannes Alfvén, who coined the word in the 1940s. MHD specifically deals with the acceleration of the fluid due to electromagnetic (EM) forces, including those EM forces resulting from that acceleration, but often approximation-methods are used that presume some of the forces are negligible. In MHD's full form, it more-or-less consists of the combination of fluid dynamics' Navier-Stokes equations and electrodynamics' Maxwell's equations.
Applications in astrophysics include modeling plasma in the interplanetary medium and interstellar medium as well as star models, both the interior and the atmosphere. Such a system involving plasma is sometimes termed a magneto-plasma system. Other applications include geophysics (the fluid interior of the Earth), engineering and medicine.
In some astrophysical phenomena, the electrical resistance is minor and MHD modeling can be effectively simplified by ignoring it, i.e., assuming resistance is zero. The phrase resistive MHD indicates inclusion of electrical resistance. Among other variants are Hall MHD (HMHD), taking into account the Hall effect and general-relativistic MHD (GRMHD), taking into account general relativity (GR).