Electromagnetic body forces

The composite conductor is typically wound in the form of a cable, which can be cooled either internally by a forced belium flow or externally by immersion in a pool of belium. Large electromagnetic body forces, up to 500 t/m, are experienced by the conductor during operation. These are contained by a massive external stmcture, although designs have been proposed in which the conductor itself serves as its own force containment stmcture (126). 

As described above, instability of the interface between the electrolyte and molten metal is a significant problem that is one root cause of the energy inefficiency of Hall cells. Expressed simply, the interface is deformed by the electromagnetic body forces arising from the interaction between currents in the cell and the magnetic field. The currents are themselves affected by the interface position because it determines the distance between the top surface of the aluminum and the bottom of the anode. There is therefore the possibility that interface deformation leads to further interface deformation. Other mechanisms for generating waves at the interface may be significant, for example, the Kelvin-Helmholtz... 

In their studies of interface instability, most of the investigators listed above have employed a Fourier analysis of the coupling between the fluid motion and the electromagnetic body force. Davidson [81] and, in simpler form, Davidson and Lindsay [82] have pursued an alternative approach whereby a global energy balance... 

According to Hughes and Young [64], the most general form of the electromagnetic body forces (F ) in a control volume filled with a fluid that includes the effects of charge and current interactions can be determined by... 

Body forces gravity force, centrifugal force, Coriolis force electromagnetic force. 

Potential energy. Potential energy (P) is energy the system possesses because of the body force exerted on its mass by a gravitational or electromagnetic... 

In the case of gravitational force with kj = gj and fj = QQj, in general it holds that fj = gkj. Other body forces are centrifugal forces or forces created by electromagnetic helds. 

Density gradients are normally caused by temperature gradients, less often by concentration or pressure gradients. However in multicomponent mixtures the concentration differences can also create notable density gradients, so that under the preconditions named before, a free flow can also develop. The body force is frequently gravity, and less often centrifugal or electromagnetic forces. 

Forces that act on a fluid can be classified as either body forces or surface forces. Body forces are distributed throughout the material, e.g., gravitational, centrifugal, and electromagnetic forces. Surface forces are forces that act on the surface. 

As part of the specification of the physical models and boundary conditions, the user has to specify the body forces on the fluid. Body forces are those forces that act on the entire volume of fluid throughout the domain. These forces include gravity, electromagnetic forces (if relevant), and the Coriolis force for rotating domains. 

Finally, we note that the surface body force term constitutes the sum of the surface-excess body force and the bulk-phase body force vector densities. The surface-excess body force is the 2D analog of continuum body forces in 3D fluids (e.g., gravitational force, electromagnetic force, etc). This force is often neglected. The bulk-phase body force has no counterpart for 3D fluids, as it denotes the stresses applied intimately at the interface by the surrounding 3D bulk phases. The normal component of this force equals the pressure difference between the two bulk phases, a relationship often referred to as the Young-Laplace equation. 

Acceleration of the fluid elements is due to two types of forces, body forces (per unit of volume), F, acting within the whole fluid element volume (e.g. gravitational or electromagnetic forces) and forces acting on the surface of the small fluid element representing interaction with the rest of the fluid. The surface forces per unit of volume can be written as the divergence of a stress tensor [Pg.3]

Consider the isothermal incompressible smectic A liquid crystal in the absence of significant body forces due to electromagnetic or gravitational fields. The elastic strain for the liquid crystal can be descril d in terms of a single variable w (x, y, z ) that specifies the local displacement of the smectic layers. The theoretical pr iction [2,3 or 7] is that w (x, y, z ) satisfies the differential equation... 

The supply S is the contribution to the physical quantity G from forces acting from a far distance onto every point in Q(0- These forces are also called body forces and can be due to gravity, radiation or electromagnetic interactions. The supply term is given by... 

The total force vector F[n] consists of surface forces (pressure, normal and shear stresses) acting on the fluid element surface and body forces (gravity and electromagnetic force) acting on the volume of the same fluid element. By replacing the x component of the force vector, we get the following notation ... 

The rate of work C done on the moving fluid element due to body forces (gravity, electromagnetic force) and surface forces (pressure, normal stresses, shear stresses) is mathematically defined as... 

The coupling between the electromagnetism and hydrodynamics through the body force PeE leads to the modified N-S equation as... 

Similarly also, the effect of an electromagnetically coupled elastic inhornogeneity can be characterized by the raultipole fictitious body force, eq fictitious current — ... 

---