Lumped constant, calculation

Hasselbalch, S. G., Madsen, P. L., Knudsen, G. M. etal. Calculation of the FDG lumped constant by simultaneous measurements of global glucose and FDG metabolism in humans. /. Cereb. Blood Flow Metab. 18 154-160,1998. 

Modeling of High-Speed Interconnections. Modeling the electrical behavior of an interconnection involves two steps. First, the transmission line characteristics, such as the characteristic impedance, propagation constant, capacitance, resistance, dielectric conductance, and coupling parameters, must be calculated from the physical dimensions and material properties of the interconnection. In addition, structures, such as wire bonds, vias, and pins, must be represented by lumped resistance (R), inductance (L), and capacitance (C) elements. 

The results for a 55 amp load change are shown in Figures 9.10 and 9.11. Figure 9.10 shows the temperature histories for the cell, interconnect, anode exit gas and cathode exit gas. As can be seen the thermal conditions reach their new equilibrium by approximately / = 800 s, resulting in an exponential time constant of r = 266 s. The temperature change for the gas stream is about 150°C. A calculation of the thermal time constant based on the fully lumped model (Equation (9.28) shows... 

To our knowledge, the control of most FCCUs in refineries is based today on a 10- or 11-lump model (14, 15) with 20 kinetic cracking constants. We think that these 20 kinetic constants cannot be calculated with precision from kinetic tests and that they are only empirical parameters... 

When the Bom, double-layer, and van der Waals forces act over distances that are short compared to the diffusion boundary-layer thickness, and when the e forces form an energy hairier, the adsorption and desorption rates may be calculated by lumping the effect of the interactions into a boundary condition on the usual ccm-vective-diffusion equation. This condition takes the form of a first-order, reversible reaction on the collector s surface. The apparent rate constants and equilibrium collector capacity are explicitly related to the interaction profile and are shown to have the Arrhenius form. They do not depend on the collector geometry or flow pattern. 

To estimate the isomerization rate coefficients, eqn 5.8 is applied to the time required for close approach to the straight-line behavior of the first-order curves. Judging this time to be about 25 minutes for a 90% approach to the steady-state isomer distribution, eqn 5.8 yields k 0.1 min-1. With this value and an isomerization equilibrium constant Kn = 20 at 150°C calculated from thermochemical data [5,6] (with 2-cis and 2-trans pentene lumped into a single pseudo-component), eqns 5.40 give as rough estimates... 

Note that the rate coefficient kf used in Eq. 6.82 was defined in Eq. 5.70 and has dimensions LT. By contrast, in the lumped kinetic models, the rate coefficient km in Eq. 6.43 or fcy in Eq. 14.3) has dimensions T . The third, fourth, and fifth moments are given by more complicated expressions and can be formd in the literature [30,31], In practice, only the first and second moments of a band are determined, the first to characterize its retention and calculate the equilibrium constant, the second to characterize and study the band spreading, hence the mass transfer kinetics. 

Calculate the rate constant of the lumped metathesis reaction ... 

Calculate the rate constants and the fractional stoichiometric coefficients of the lumped oxidation reactions ... 

It seems to us that the preceding calculations show that the measurement of the resonance absorption of lumps may in many cases yield the average values of the constants of resonance levels more directly and, perhaps, even more easily than a detailed measurement of several levels. 

The so-called lattice calculations are designed to obtain the geometries (carbon to U ratio and size of lumps) in which the sum of the resonance and thermal losses is least. It turns out, for instance, that a carbon to uranium mass ratio of 6 with uranium spheres of 2" diameter gives a particularly small premature loss of neutrons. The calculations are based on numerous experimentally established nuclear constants. They have been, on the whole, well confirmed by direct observations. 

An investigation to improve prediction capability of Doppler reactivity experiment in critical assemblies was performed. The calculation/experiment (C/E) values were extremely underestimated by the conventional method with a cell group constant set and isolated lump nwdel. A new calculation with ultra-fine energy group cross-sections was applied to the Doppler experiments, and resulted in the improvement of CYE values by 13%. From the present survey, it is found quite significant for the Doppler reactivity analysis to take into account the interaction effect between Doppler samples and core fuel. 

The curves calculated in this way at constant for different combinations of Pe and S [i.e., for different combinations of axial dispersion and mass transfer resistance but the same linear combination 1/Pe + 5(1 + 5/0/15] show close agreement with each other and with the curve calculated from the simple linearized rate model using an overall lumped coefficient to account for the combined effects of axial dispersion, diffusion, and external mass transfer resistance. 

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