Flux time

The leak rate through a porous seal volume can be computed as flux times area and converting from moles to volume with the ideal gas law. The seal void fraction and tortuosity have the same effect as in the hydrodynamic leakage calculations. 

Strategy. Remembering that sometimes things are actually as simple as they look, this problem should be nothing more than multiplying the flux times the area and then converting units into mass. 

Therefore for highly reversible systems, the net flux is proportional to the reverse flux times the thermodynamic driving force the Onsager coefficient is equal to J-/RT. 

Procedure. Specimen Fabrication. The reinforcements were mixed into the polystyrene melt on a Farrell two-roll mill at 320°F. It was necessary to dry the asbestos fibers for 24 hr at 250°F prior to mixing to ensure the breakup of bundle aggregates. The milling/fluxing time was held to 8 min for all samples. The sheets obtained in milling were cut, crossplied, and compression molded in an open frame on a Wabash press. After they reached the platen temperature the material was held at 330 °F and 2000 psi for 6 min. The frame was then transferred to a cold press, and the sample was cooled under the same pressure. The test specimens were cut from ys-inch thick plates prepared in the foregoing manner. 

If we assume for a moment that the linear dissolution rates (LDR) are constant as long as the particle survives and that the flux (F) from the surface may be described in terms of moles silica/cm sec, then this surface flux times the molar volume (MV) of the mineral divided by the moles of Si per molecule ( Si) gives the rate at which the radius of a spherical particle or half the length of a cube will disappear by the dissolution process (9). 

Wetland and tundra flux time series should also continue and possibly be expanded at carefully selected high-latitude wetland sites, preferably sites in the Hudson s Bay Lowlands and Siberian... 

Whalen S. C. and Reeburgh W. S. (1988) A methane flux time series for tundra environments. Global Biogeochem. Cycles 2, 399-409. 

In summary, four experimental/calculational techniques, ICP-OES, ICP-MS, SIMS-SEM-EDX and NAA with radiochemical analysis, were used to determine the concentration of Li in reactor steels either by direct measurement or by calculation from measured values. Li measurements from the first two techniques, ICP-OES, and ICP-MS, were discarded due to excessive values/excessive limit of detection. SIMS/SEM-EDX measurement of Li and two approaches to neutron activation of steels samples with radiochemical measurement of values used to calculate Li concentrations yielded 10 valid data points spread over one order of magnitude, see Table 4. In particular, the two neutron activation approaches using differing flux, time and temperature conditions yielded good consistency of calculated values of Li. Consequently, the average Li concentration in Magnox RPV steel is considered to be < 1 ng g" and estimated as 0.4 0.2 ngg- x(lB). 

Similar steel samples irradiated under differing flux, time and temperature conditions yielded good consistency of calculated values of Li precursor. 

FIGURE 8.8 Flux-time profile with and without Dean fiow for filtration of S/DVB particles. (From Figure 3 in Mallubhotla, H. and Belfort, G., J. Membr. Sci., 125, 75, 1997. With permission.)... 

Figure 8.19 shows the flux-time profiles obtained in filtration of 5% yeast cell suspension using a mbular membrane of 6 mm i.d. (inside diameter) and 0.14 pm pore size with a helical baffle (HB), a rod baffle (RB), and the mbular membrane without baffle (NB) [35]. The comparison has been made at the same hydraulic-dissipated power, which is defined as the product of the flow rate and the pressure drop along the mbular membrane, or the energy consumed to generate the crossflow through the mbular membrane. Using the hydraulic-dissipated power rather than the crossflow rate as a control parameter for the comparison of the mbular membrane with and without inserts eliminates the effect of the reduced crossflow section by... 

FIGURE 11.2 Diagram of typical flux-time dependency during cyclic operation in large-scale ultrafiltration systems. (From Koltuniewicz, A. and Noworyta, A., Indus. Eng. Chem. Res., 33, 1771, 1994.)... 

The mathematical model derived from the network in Figpre 13.6 together with the specification of aU the local fluxes, time-dependent variables, and parameters is presented in Table 13.1 The model consists of ordinary differential equations (ODE) describing the evolution of aU capacitances (local concentrations) characteristic for a membrane and external solutions. 

Next, a mass balance is performed on the drop. The change in mass equals the flux times the surface area. 

When we have obtained steady state, the rate of heat transfer (flux times area) through the surrounding fluid is constant with respect to the radial position ... 

Thermal conductivity (k with units W m 1 K 1) describes the ability of a material to transport thermal energy because of temperature gradient. Steady-state thermal conductivity is a constant of proportionality between the heat flux (time rate of heat flow per unit area) through a solid and the imposed temperature gradient as described by (4) [52] ... 

The cross section of low-cross-section fission products, Op, has a single constant value independent of the fissile nuclide from which the fission products were produced and independent of the flux time to which the fission products were exposed. This assumption is an oversimplification, because the yield of individual fission products is different from each fissile nuclide, and individual fission products with hi er cross sections tend to be converted to those of lower cross section as irradiation progresses. Walker [Wl] has given tables from which may be determined the effective cross sections of fission products from U, U, Pu, and Pu as a function of the flux and flux time to which the fission products have been exposed. 

The value of 80 b given for fission-product pairs is an approximate, constant value to be used independent of the fuel from which the fission products are formed and independent of the flux time to vidiich the fission products are exposed after formation. For the present PWR, the effect of these variables on the cross sections of fission-product pairs, evaluated by extrapolation of Walker s [Wl] tables, is as follows ... 

Thermal flux time, n/kb Effective cross section Op, in bams, of fission-product pairs from ... 

The flux time is the fundamental variable used to express the extent of exposure to irradiation. Even when the flux varies with time, Eq. (3.44) is strictly conect. The flux time thus defined is in units of neutrons per square centimeter. Expressed in these units its magnitude is around 10 in a typical reactor, as when fuel has been irradiated in a flux of 10 w/(cm s) for 10 s. Consequently, it has become customary to express flux time in units of 10 n/cm, termed neutrons per kilobarn and written n/kb. The flux time is often called the fluence. 

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