Longitudinal fluxes

In forced convection, the velocity of the liquid must be characterized by a suitable characteristic value Vih e.g. the mean velocity of the liquid flow through a tube or the velocity of the edge of a disk rotating in the liquid, etc. For natural convection, this characteristic velocity can be set equal to zero. The dimension of the system in which liquid flow occurs has a certain characteristic value /, e.g. the length of a tube or the longitudinal dimension of the plate along which the liquid flows or the radius of a disk rotating in the liquid, etc. Solution of the differential equations (2.7.5), (2.7.7) and (2.7.8) should yield the value of the material flux at the phase boundary of the liquid with another phase, where the concentration equals c. ... 

Effects of ribs or spacers. A spacer rib test was conducted by the Savannah River Laboratory (Mirshak and Towell, 1961). The results show that critical heat flux reduction due to contact of a longitudinal spacer rib can be as much as 32%. 

Whittaker [27,28] derived equations defining the electromagnetic field in the vacuum in terms of functions / and g with the units of magnetic flux directed longitudinally in the axis of propagation (Z)... 

Whittaker also argued [27,28] that longitudinal standing waves occur in the vacuum. These can be illustrated by the choice of flux... 

The gauge transform Aq A + does not modify the value of the magnetic flux F calculated on the basis of Stokes theorem, as dehned above. However, this gauge transform does not allow us to cancel the external vector potential. This statement is in sharp contrast with, and even contradicts, what is usually claimed in the available literature. Indeed, Helmholtz decomposition of the vector potential A = + Ax shows that only the longitudinal component An is modified in this process ... 

Time-like currents and flows do appear in the vacuum energy, if extended electrodynamic theory is utilized. For instance, in the received view, the Gupta-Bleuler method removes time-like photons and longitudinal photons. For disproof of the Gupta-Bleuler method, proof of the independent existence of such photons, and a short description of their characteristics, see Evans AIAS group papers on Whittaker s F and G fluxes and analysis of the EM entity in Ref. 24a to see how such entities produce ordinary EM fields and energy in vacuo, see Ref. 24b. 

Each little composite dipole also has a scalar potential between its ends. We may decompose that potential into a harmonic set of bidirectional EM longitudinal wave (LW) pairs [8], where each pair consists of an outgoing LW and an incoming LW. Now, however, the incoming (convergent) LWs are virtual i.e., comprised of organization and dynamics in the virtual flux of the vacuum [9(a)]. 

It is of firebrick. Fig. 558 shows the kiln in elevation, Above is a hot-floor, on which the charcoal is dried before it is strongly heated. The hot floor is seen also in tire longitudinal section, whore it is shown to be heated by the flux. which comes from the furnace on its way to the chimney. The kiln represented here contains twelve chambers for the charcoal, each two feet long and throe inches broad. 

It should be pointed out that for a low pressure gas the radial- and axial diffusion coefficients are about the same at low Reynolds numbers (Rediffusion effects may be important at velocities where the dispersion effects are controlled by molecular diffusion. For Re = 1 to 20, however, the axial diffusivity becomes about five times larger than the radial diffusivity [31]. Therefore, the radial diffusion flux could be neglected relative to the longitudinal flux. If these phenomena were also present in a high-pressure gas, it would be true that radial diffusion could be neglected. In dense- gas extraction, packed beds are operated at Re > 10, so it will be supposed that the Peclet number for axial dispersion only is important (Peax Per). 

The surface distribution of M stars is studied by differentiating them according to whether they show a circumstellar dust shell (CS) or not. Analysis shows that galactic latitudinal and longitudinal distributions are not determined by spectral subclasses alone. The study also indicates that the M type stars with CS have higher intrinsic luminosities in the K band than those without CS. The M stars used in the study are obtained from the Two Micron Sky Survey catalogue (IRC) which is an unbiased sample with respect to the interstellar extinction. The CS feature is identified by the ratio of flux densities at 12 and 25 m in the IRAS point source catalog. 

By heat losses capable of stopping propagation we mean those processes which lower the combustion temperature. These include (1) heat transfer from the heated explosive mixture to the tube walls, (2) evacuation of heat from the reaction zone itself to the walls of the container and (3) evacuation of heat from the reaction zone to the combustion products which depends on the cooling of the reaction products—cooling of the products creates a drop in temperature as one moves away from the reaction zone and a corresponding longitudinal (in the direction opposite the direction of propagation) heat flux. 

The vector potential A(3) and the longitudinal flux density B(y> are both phaseless, so Eq. (A. 17) with i = 3 is the invariant equation needed for a description of the Aharonov-Bohm effect... 

From general relativity, it may therefore be inferred that the B<3> field must exist, and that it is a physically meaningful magnetic flux density in the vacuum. The phaseless B<3> component is one of an infinite set of longitudinal, and in general oscillatory, components of the field tensor (B.4). This result has been tested experimentally to the precision of the Lamb shift. 

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