Flux - calculation/general

Single-stage simulations reveal that intermolecular friction forces do not lead to reverse diffusion effects, and thus the molar fluxes calculated with the effective diffusion approach differ only slightly from those obtained via the Maxwell-Stefan equations without the consideration of generalized driving forces. This result is as expected for dilute solutions and allows one to reduce model complexity for the process studied (143). 

In many modern top-fired reformers the heat flux calculated for the inner tube wall surface is around 60 000 W/m2, although in some designs it cam be as high as 75 000 W/m2. The maximum heat flux may be 1.4 to 2 times higher. In side-fired and terraced-wall furnaces, where the mean fluxes are generally in the range of 60 000-85 000 W/m2, the difference between mean and maximum flux is much smaller, as shown in Figure 37 [444],... 

In the mass-balance approach an attempt is made to determine field weathering rates from element flux calculations, usually focusing on the plant-nutrient important base cations (Ca- Mg ", K, and Na+) or on silica (cf. Velbel 1985). In some studies balances are also computed for Al (Swoboda-Colberg and Drever 1992) and/or the the major anions and nitrogen species (Likens et al. 1977 Mast et al. 1990). A general mass-balance equation for the base cations (BC) might be... 

The computation of the fluxes from either of Eqs. 8.3.24 necessarily involves an iterative procedure (except for the special cases discussed above), partly because the themselves are needed for the evaluation of the matrix of correction factors and also because an explicit relation for the matrix [0] cannot be derived as a generalization of Eq. 8.2.16 for binary mass transfer there is no requirement in matrix algebra for the matrices [FFq] be equal to each other even though the fluxes calculated from both parts of these equations must be equal. Indeed, these two matrices will be equal only in the case of vanishingly small mole fraction differences (yg Tg) and vanishingly small mass transfer rates. In almost all cases of interest these two matrices are quite different. An explicit solution was possible for binary systems only because all matrices reduce to scalar quantities. 

It is important to be able to quantitatively predict the water profiles in the multilayer structure as a function of time. Failure to make this calculation results in incorrect oxygen flux calculations. Since there is very little detailed understanding of water transport in polymers over the range of temperatures and pressures of interest, a good quantitative model for water transport cannot be made for a general case at present. 

I. These points differ somewhat from those used by Aller (1977), and the resulting Mn fluxes are generally lower than those reported previously. In the earlier work, points taken a long time (24-48 hr) after collection often resulted in calculation of higher fluxes than if only initial points were used. In some cases decreases in flux rate were also observed (e.g., DEEP). It is assumed here that the initial rates are the best approximations to in situ rates, particularly because cores were not continuously aerated. Fe fluxes are higher than reported in Aller (1977) due to correction for precipitation loss by use of Eq. (5.6). Curves illustrating types of time-concentration changes in Mn and Fe observed in the flux cores are shown in Fig. 12. 

Here a° is the vacuum vaporization coefficient, which accounts for the reduction in the observed vaporization fiux relative to the maximum flux calculated for equilibrium conditions, pi. In the general case where the condensed phase vaporizes in an unsaturated vapor phase, where pa is less than pi, the flux is given by ... 

Since the above-core calculations represented an infinite array of fuel channels, they did not include those parts of the pressure vessel in the vicinity of the hot gas duct penetration and therefore no account was taken in the above-core calculation of the neutrons wMch scatter around the top comer of the graphite stack and enter the hot gas duct penetration area. The neutron fluxes in the vicinity of the hot duct entrances were therefore takai to be equal to the fluxes calculated for the side shield model with a contribution added to account for the top-core leakage component. This component was scaled fi om the sub-core results and is considered to probably result in pessimistically high flux values for the hot gas duct pen ration since the neutron flux levels below the core are generally higher than those above. 

Until now the simulation of a thermal cracking coil has generally been uncoupled from that of the fire box by imposing either a tube wall temperature profile or a heat flux profile. It is then checked a posteriori whether or not the fire box permits such profiles to be attained. The fire box calculations generally proceed along the Lobo Evans approach (J ), although more recently zone methods have been applied, thus permitting a temperature distribution in the fire box to be calculated (2, 3, 4, 5). 

The calculation of the variation of the reactivity over the life of the core is a very complicated exercise. Allowance has to be made for (i) decrease in the overall fuel concentration, (ii) net buildup of fresh fissile material from conversion, and (iii) changes in the spatial distribution of fuel and fission products as bum-up proceeds. For example, the flux will generally be highest at the core center, and consequently the fuel will burn up and fission products accumulate more rapidly there, causing in turn a change in the flux distribution in the reactor. 

Unfortunately, satisfactory analytical methods for practical prediction of forced convection heat transfer at supercritical pressures have not yet been developed due to the difficulty in dealing with steep property variations, especially in turbulent flows and at high heat fluxes. Therefore, generalized correlations based on experimental data are used for HTC calculations at supercritical pressures. 

Resuspension of bottom sediments into the water column of aquatic systems represents an important source of particles and particle-associated contaminants into the water column. Unlike deposition, the resuspension process is very sporadic and short-lived, but when it does occur, the flux is generally quite large. Sediment resuspension occurs when hydraulic shear stress at the sediment-water interface rises above a critical level, sufficient to dislodge particles. Shear stress (x, dyn/cm ) is calculated as a function of shear velocity ( , cm/s) and water density (p, g/cm ) ... 

Figure 9.2-2 shows a data input screen in which general characteristics are input by radio buttons and numerical data is typed. The program calculates distances to specified in.sic concentrations and other requested consequence levels automatically. Results are available in a variety of formats including cloud footprints, sideview, cross section, pool evaporation rate, concentration vs distance and heat flux contours. Figure 9.2-3 shows the calculated results as a toxic plume. superimposed on the map with and without oligomerization. 

The evaporite source is characterized by covariation of sulfate (from gypsum) and chloride (from halite). That elements can be recycled from the ocean to land by movement of saltbearing aerosols (so-called "cyclic salts") has confused the interpretation of river flux data somewhat. While this cycling generally follows the ratio of salts in the sea, the S/Cl ratio is an exception. Taking the S/Cl ratio of the cyclic component to be 2 (based on compositional data for marine rains) and assuming that all chloride in rivers is cyclic, an upper limit for the cyclic influence can be calculated. 

The general criteria for an experimental investigation of the kinetics of reactions at liquid-liquid interfaces may be summarized as follows known interfacial area and well-defined interfacial contact are essential controlled, variable, and calculable mass transport rates are required to allow the transport and interfacial kinetic contributions to the overall rate to be quantified direct interfacial contact is preferred, since the use of a membrane to support the interface adds further resistances to the overall rate of the reaction [14,15] a renewable interface is useful, as the accumulation of products at the interface is possible. Finally, direct measurements of reactive fluxes at the interface of interest are desirable. 

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