Magnetohydrodynamics (MHD) is the study of how conducting fluids, such as liquid metals or plasmas, behave in the presence of electric and magnetic fields. It is a macroscopic form of electrodynamics, deriving from fluid dynamics such as magnetic pressure and magnetic viscosity. Its equations often defy exact solution. The most important applications are in magnetohydrodynamic generators and controlled nuclear fusion process. The extremely hot plasma produced by the fusion is contained by strong circulating magnetic fields; various designs are possible, the stability of each being the paramount consideration.


In MHD, both the magnetic field and the fluid motion are treated as coupled dynamical variables, and the equations governing their behavior are derived from the laws of electromagnetism and fluid mechanics.


One of the main applications of MHD is in the field of fusion energy research. In order to achieve fusion reactions, a high-temperature plasma must be confined by a magnetic field. MHD plays a crucial role in the design and optimization of fusion devices, such as tokamaks and stellarators, by providing insights into the behavior of the plasma and the magnetic field. For example, MHD simulations can predict the stability of the plasma and identify potential instabilities that could lead to disruptions.


Magnetohydrodynamics also forms an important part of astrophysics since plasma is one of the commonest forms of matter in the universe, occurring in stars, planetary magnetospheres, and interplanetary and interstellar space. MHD is used to model the behavior of plasmas in the Sun, Earth's magnetosphere, and other astrophysical environments. For example, MHD simulations can explain the formation of sunspots, the dynamics of coronal mass ejections, and the generation of magnetic fields in stars.


MHD is also used in industrial processes that involve the flow of electrically conducting fluids. For example, liquid metal MHD generators are used to convert the kinetic energy of a moving conductive fluid into electrical energy. This technology has been used in the past to generate power in nuclear reactors and is currently being explored as a potential source of renewable energy. In order to understand the behavior of fluids in the presence of a magnetic field, it is necessary to derive the equations that govern their behavior. The equations of MHD are derived from the equations of fluid mechanics and electromagnetism, which describe the behavior of fluids and magnetic fields, respectively. These equations are then combined to yield the MHD equations, which describe the behavior of electrically conducting fluids in the presence of a magnetic field.


The MHD equations are a set of partial differential equations that describe the behavior of the fluid velocity, magnetic field, and pressure. These equations can be solved numerically using computer simulations, which allow researchers to study the behavior of MHD systems in great detail. The solutions to the MHD equations can also be used to predict the behavior of real-world systems, such as fusion devices and astrophysical environments.