Fluid flow influenced by electric and magnetic fields has classically been divided into two separate fields of study: electro-hydrodynamics (EHD) studying flows under the influence of an electric field with free electric charges and no magnetic field, and magneto-hydrodynamics (MHD) studying flows under the influence of a magnetic field and no free electric charges or electric fields. This division was necessary to reduce the extreme complexity of the coupled system of Navier-Stokes, Maxwell's and constitutive equations describing combined electro-magneto-hydrodynamic (EMHD) flows. Recent advances in numerical techniques and computing power, as well as fully rigorous theoretical treatments, have made analysis of combined EMHD flows well within reach. The combined EMHD theory is compared with separate EHD and MHD models. This reveals the inconsistencies and shortcomings of classical formulations and allows discussion of the relative importance of terms describing the electro-magnetic force, electric current and heat transfer.
