Cross section transfer

Higbie (H4) has made use of the foregoing solution to obtain an expression for the liquid-phase mass transfer coefficient for short contact times for absorption in wetted-wall towers. From Eq. (161) one may calculate the total moles of A transferred per unit time per unit cross-sectional transfer area ... 

A unified description of j- j and j, m - j, m transitions was formulated in several papers for quasiresonant processes in Na -He collisions. In the semiclassical approximation with rectilinear trajectories all cross sections (transfer of population and orientation between 2P1/S and 2P3/2 states, relaxation of orientation in 2P1/2 and 2P3/2 states, and relaxation of alignment in 2P3/2 state) were calculated by Masnou and Roueff [134]. The quantal study of these processes was completed recently by Reid [135]. It has been noted [132, 136, 137] that because of quasiresonance, the semiclassical solution can also be obtained by reducing the problem to depolarization of a... 

An AMPX master cross-section, library is the most comprehensive processed library in the AMPX system. The library contains multigroup cross sections, transfer matrices, resonance parameters, weighting functions, etc., has provisions for neutron, photon-production, and photon-interaction data, has provisions for temperature dependence on thermal scattering kernels, etc. 

The total moles of A transferred per unit time per unit cross-sectional transfer area is... 

We start from a model in which collision cross sections or rate constants for energy transfer are compared with a reference quantity such as average Leimard-Jones collision cross sections or the usually cited Leimard-Jones collision frequencies [54]... 

The momentum-transfer or diflfiision cross section is and the viscosity cross section is... 

Here t. is the intrinsic lifetime of tire excitation residing on molecule (i.e. tire fluorescence lifetime one would observe for tire isolated molecule), is tire pairwise energy transfer rate and F. is tire rate of excitation of tire molecule by the external source (tire photon flux multiplied by tire absorjDtion cross section). The master equation system (C3.4.4) allows one to calculate tire complete dynamics of energy migration between all molecules in an ensemble, but tire computation can become quite complicated if tire number of molecules is large. Moreover, it is commonly tire case that tire ensemble contains molecules of two, tliree or more spectral types, and experimentally it is practically impossible to distinguish tire contributions of individual molecules from each spectral pool. 

Now encounters between molecules, or between a molecule and the wall are accompanied by momentuin transfer. Thus if the wall acts as a diffuse reflector, molecules colliding wlch it lose all their axial momentum on average, so such encounters directly change the axial momentum of each species. In an intermolecuLar collision there is a lateral transfer of momentum to a different location in the cross-section, but there is also a net change in total momentum for species r if the molecule encountered belongs to a different species. Furthermore, chough the total momentum of a particular species is conserved in collisions between pairs of molecules of this same species, the successive lateral transfers of momentum associated with a sequence of collisions may terminate in momentum transfer to the wall. Thus there are three mechanisms by which a given species may lose momentum in the axial direction ... 

Finally we require a case in which mechanism (lii) above dominates momentum transfer. In flow along a cylindrical tube, mechanism (i) is certainly insignificant compared with mechanism (iii) when the tube diameter is large compared with mean free path lengths, and mechanism (ii) can be eliminated completely by limiting attention to the flow of a pure substance. We then have the classical Poiseuille [13] problem, and for a tube of circular cross-section solution of the viscous flow equations gives 2... 

Another automated approach to kinetic analyses is the centrifugal analyzer, a partial cross section of which is shown in Figure 13.9. In this technique the sample and reagents are placed in separate wells oriented radially around a circular transfer disk attached to the rotor of a centrifuge. As the centrifuge spins, the... 

Since capillary tubing is involved in osmotic experiments, there are several points pertaining to this feature that should be noted. First, tubes that are carefully matched in diameter should be used so that no correction for surface tension effects need be considered. Next it should be appreciated that an equilibrium osmotic pressure can develop in a capillary tube with a minimum flow of solvent, and therefore the measured value of II applies to the solution as prepared. The pressure, of course, is independent of the cross-sectional area of the liquid column, but if too much solvent transfer were involved, then the effects of dilution would also have to be considered. Now let us examine the practical units that are used to express the concentration of solutions in these experiments. 

The pulsed-plate column is typically fitted with hori2ontal perforated plates or sieve plates which occupy the entire cross section of the column. The total free area of the plate is about 20—25%. The columns ate generally operated at frequencies of 1.5 to 4 H2 with ampHtudes 0.63 to 2.5 cm. The energy dissipated by the pulsations increases both the turbulence and the interfacial areas and greatly improves the mass-transfer efficiency compared to that of an unpulsed column. Pulsed-plate columns in diameters of up to 1.0 m or mote ate widely used in the nuclear industry (139,140). 

Traditionally, production of metallic glasses requites rapid heat removal from the material (Fig. 2) which normally involves a combination of a cooling process that has a high heat-transfer coefficient at the interface of the Hquid and quenching medium, and a thin cross section in at least one-dimension. Besides rapid cooling, a variety of techniques are available to produce metallic glasses. Processes not dependent on rapid solidification include plastic deformation (38), mechanical alloying (7,8), and diffusional transformations (10). 

The cross-sectional area of the wick is deterrnined by the required Hquid flow rate and the specific properties of capillary pressure and viscous drag. The mass flow rate is equal to the desired heat-transfer rate divided by the latent heat of vaporization of the fluid. Thus the transfer of 2260 W requires a Hquid (H2O) flow of 1 cm /s at 100°C. Because of porous character, wicks are relatively poor thermal conductors. Radial heat flow through the wick is often the dominant source of temperature loss in a heat pipe therefore, the wick thickness tends to be constrained and rarely exceeds 3 mm. 

Reactor Configuration. The horizontal cross-sectional area of a reactor is a critical parameter with respect to oxygen mass-transfer effects in LPO since it influences the degree of interaction of the two types of zones. Reactions with high intrinsic rates, such as aldehyde oxidations, are largely mass-transfer rate-limited under common operating conditions. Such reactions can be conducted effectively in reactors with small horizontal cross sections. Slower reactions, however, may require larger horizontal cross sections for stable operation. 

Referring back to equation 47, the other quantity necessary in calculating the gas conductivity is the coUision cross section, Gases contain at least four types of particles electrons, ionized seed atoms, neutral seed atoms, and neutral atoms of the carrier gas. Combustion gases, of course, have many more species. Each species has a different momentum transfer cross section for coUisions with electrons. To account for this, the product nQ in equation 47 is replaced by the summation where k denotes the different species present. This generalization also aUows the conductivity calculation to... 

Sodium is used as a heat-transfer medium in primary and secondary cooling loops of Hquid-metal fast-breeder power reactors (5,155—157). Low neutron cross section, short half-life of the radioisotopes produced, low corrosiveness, low density, low viscosity, low melting point, high boiling point, high thermal conductivity, and low pressure make sodium systems attractive for this appHcation (40). 

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