Transient region

Leva s correlation (Leva 1949) is the easiest to use in manual calculation, especially when the particle diameter-based Reynolds number is high, i.e., above Rep>l,000. A changing exponent n in the Leva expression, shown below, accounts for the transient region as turbulence of flow increases. The dependence of n on Rep was specified by Leva graphically (1949) as n growing with the Rep between 1.0 and 2.0. The value reaches n = 1.95 at Rep =1,000 thus approximating 2.0 closely. 

Solution of the linear approximation (4.1.48) reveals the transient region Ar 1, in which the correlation function Yo(r,t) increases from zero to unity. For the auto-model variable r/ = r/ o in equation (4.1.48) the transient region width Arj = 1 / o —> 0, which corresponds to the step-like function. The function Y (r, i) in the superposition approximation reveals the transient region Ar increasing in the time which is confirmed by computer simulations shown in Figs 5.5 and 5.6. 

Fig. 9 Current transients (regions DE and de) characteristic of rapid recombination of the charge carriers near the illuminated electrode in an anthracene crystal with damaged surface (a)...

Due to the overall symmetry constraints on a nonrotating molecular liquid sample, ( (0) = ( ( )) = 0 even in the transient region. It is difficult to evaluate the nonstationaiy correlation function ... 

J.A. Balschi, 23Na NMR demonstrates prolonged increase of intracellular sodium following transient regional ischemia in the in situ pig heart, Basic Res Cardiol 94, 60-69 (1999). 

Prom the results above, one can conclude that the MHMT method for trend analysis correctly classifies the different process operating conditions. There are a few ambiguities in the transient region, which result from the similar responses of manipulated variables to different process events. In other words, the information contained in two variables is not enough to immediately discern the transient part of the process. To eliminate such ambiguities, additional variables may be needed in the HMT model. Sun et al. [286] have shown the extension of the method to the multivariate case for the CSTR simulation example. 

The low activation energies for aldehydes and carbon dioxide formation might be due to the fact that these reactions occur in the diffusion or transient regions. The activation energies for the formation of aldehydes and acids from propene over V206 were measured in the kinetic region by Kutzeva and Margolis (147) and were found to be 13 and 14 kcal/ mole, respectively. 

Indeed, judging from the modified Reynolds number, A/jt, which extends from 10 to 10 regarding the experimental condition for the data points in Fig. 8, the liquid flow in the agitated vessel (Fig. 1) is in a transient region between laminar and turbulent. 

The composition dependence of the diffusion coefficient in the transient region from stoichiometric to nonstoichiometric composition has been discussed by Lidiard on (293). 

In order to establish the self-limiting nature of the transient and to ensure that there is no second transient after the first one, testes were conducted. Reactor was operated beyond the transient region for more than 30 m and the power was found to be stable. While lowering the power the negative transient of similar magnitude took place and the power was stable thereafter. 

Electric arc pyrolysis as a means of coal decomposition is accomplished by passing a high-intensity electric arc between two electrodes, one of which is made of coal. The limited data so far available indicate that the products are mainly methane, acetylene, and ethylene with a notable absence of liquid products. Shock tubes produce transient regions of high temperature and high pressure. The products from shock tube experiments have tended to be higher in the proportion of unsaturated hydrocarbons but the overall conversion is usually extremely low. 

Isobilateral dicot leaves, conifer needles, and many monocot leaves, receive light on both surfaces. The light response curves of photosynthesis of such leaves have sharper transition when the leaves are irradiated from both sides simultaneously than when irradiated unilaterally (18-20). This may also be ascribed to the differentiation of tissues in terms of optical properties and the gradient in properties of chloroplasts. Thus, it can be generalised that the leaf is constructed so as to maximise the sharpness of the transient region under natural light conditions. 

The principal advantages of this type of cyclic system with transient operating techniques are apparent in bioprocesses whose maximum productivity is in a transient region. The products of secondary metabolism (Pirt, 1974) are a typical example of this group of processes. Another group consists of processes whose optimal operation requires an optimal substrate concentration— biomass production with bakers yeast, for example (Aiba et al., 1976)—or where the process is subject to substrate inhibition. An important area of application for this is in biological waste water purification. These periodic modes of operation generally show increased productivity. More systematic and detailed study is needed in this area. 

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