Radial flux density

Aetive magnetie bearing load eapabilities, both radially and axially, are mueh lower than those of eonventional oil-lubrieated bearings. The radial load limitation is mostly due to the limited magnetie flux density... 

In this equation ut should be interpreted as the volumetric flux density (directional flow rate per unit total area). The indexes range from 1 to 3, and repetition of an index indicates summation over that index according to the conventional summation convention for Cartesian tensors. The term superficial velocity is often used, but it is in our opinion that it is misleading because n, is neither equal to the average velocity of the flow front nor to the local velocity in the pores. The permeability Kg is a positive definite tensor quantity and it can be determined both from unidirectional and radial flow experiments [20], Darcy s law has to be supplemented by a continuity equation to form a complete set of equations. In terms of the flux density this becomes ... 

The dependence of Ych on the deuterium flux density has not yet been clarified sufficiently well. A summary of various published data of the CD4 yield is displayed in Fig. 1.5a as a function of the flux density of the back ground plasma (deuterium) [6,26]. The flux variations have been obtained either by density scans or for the limiter cases (TEXTOR) by a radial movement of the limiters. These published data suffer from some inconsistencies due to different experimental conditions (electron temperature, surface temperature). The photon efficiency from which particle fluxes are derived [27] depends on the electron temperature. The chemical reactivity [6] depends... 

For spherical symmetry, can vary only in the radial direction and not with any angle. The heat flux density at a sphere s surface for heat conduction across the air boundary layer followed by heat convection in the surrounding turbulent air then is... 

Figure 9-12. Cylindrically symmetric flow of soil water toward a root (flow arrows indicated only for outermost cylinder). The volume flux density, Jv, at the surface of each concentric cylinder times the cylinder surface area (2jrr x /) is constant in the steady state, so Jv then depends inversely on r, the radial distance from the root axis.

Parameters are assumed to vary only in the radial direction (not with time, angle, or position along a cylinder or around a sphere). The flux densities are at the surface of the cylinder or the sphere (r = radium Ar = radial distance away from the surface). See Footnote 2, Chapter 7, for a comment indicating that the geometrical part in both cases reduces to 1/Ar when Ar < r. 

For spherical symmetry we note that Jv4m2 is constant in the steady state, where Am2 is the area of a sphere. As concentric spherical shells of water thus move toward the sphere, the flux density increases inversely as r2. We thus obtain the following steady-state relation describing the volume flux density Jv at distance r from the center of a sphere when Jv varies only in the radial direction and LSDl1 is constant ... 

Equation 9.9 is similar to Equation 7.16 [J = (r -I- 5bl) au (rsutf — Tta)/(rSb1)] describing the heat flux density across an air boundary layer for spherical symmetry (ra =r + 8hl and t > = t). Also, Fick s first law for the flux density of species j at the surface of the sphere is then Jj=[(r + Ar)/(rAr)]Z) Acy, where Ar is the radial distance away from the surface across which Acy occurs (Table 9-2). 

The principle of the watt-balance experiment is the following A horizontal circular coil of wire is suspended in a radial magnetic flux density from one side of a pully and balanced by a counterweight on the other side as shown in Fig. 1. 

For larger reactors with hi bumup, however, out-in fueling leads to too great a depression in the flux and power density at the center of the reactor. This may be seen from the lower half of Fig. 3.9, which shows the power density calculated by Westinghouse [Dl ] for three-zone out-in fueling of a 1000-MWe PWR, with a core 6.5 ft in radius, operated at a burnup of 24,000 MWd/MT. At the begiiming of a cycle, the flux peaks heavily in the outside zone, and the peak-to-average radial power density ratio is 2.0. The reason for this poor... 

The radial increase of the average magnetic field comes partly from the effect of the hills and partly from the concentric current-carrying coils mounted on the upper and lower poles. The isochronous field B is defined as an average of the magnetic flux density over an orbit of radius r. It can be shown that... 

The experiments simulated the radial attack of a concrete wall with a relatively low heat flux density to the wall corresponding to a core melt accident in a German PWR 8 hours after start of basement erosion. The coolant fix)m the outside water is not sufficient to stabilize the melt in the concrete mainly because of the properties of the concrete. Because of the poor thermal conductivity of the concrete a thermodynami-gally stable concrete wall would have a thickness of some 10 mm only where the inner concrete surface is at the "melting temperature of1600 K and the outer surface has the temperature of the boiling water. This layer is mechanically unstable and penetration of melt into the water and vice versa can occur. This was observed in the two BETA tests and is to be expected for the simulated accident. 

Radial density gradients in FCC and other large-diameter pneumatic transfer risers reflect gas—soHd maldistributions and reduce product yields. Cold-flow units are used to measure the transverse catalyst profiles as functions of gas velocity, catalyst flux, and inlet design. Impacts of measured flow distributions have been evaluated using a simple four lump kinetic model and assuming dispersed catalyst clusters where all the reactions are assumed to occur coupled with a continuous gas phase. A 3 wt % conversion advantage is determined for injection feed around the riser circumference as compared with an axial injection design (28). 

The border between two three-dimensional atomic basins is a two-dimensional surface. Points on such dividing surfaces have the property that the gradient of the electron density is perpendicular to the normal vector of the surface, i.e. the radial part of the derivative of the electron density (the electronic flux ) is zero. 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

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