Effect of geometric parameters

Fig. 4.7a,b Trapezoidal micro-channels, (a) Effect of surface roughness on Nusselt number (Wu and Cheng 2003). (b) Effect of geometric parameters on Nusselt number (Wu and Cheng 2003). Reprinted from Wu and Cheng (2003) with permission... 

The effect of geometric parameters on the adiabaticity of a test reactor can be deduced from Table V. It can be seen that for improperly designed laboratory reactors the axial and radial heat flows can be quite appreciable even when the net heat loss is zero. From this table it follows that the radial heat flow is reduced as the bed diameter is increased, whereas the axial heat flow diminishes as the reactor length is increased. Hence, long pilot plant reactors of wide diameter will perform best as adiabatic reactors even with suboptimal design of compensation heaters. 

Table V. Effect of Geometric Parameters on Adiabaticity of Pilot Reactors According to a Computer Simulation Model by Anderson and Sapre 13) (Parameters varied relative to base case are underlined)...

The highly simplified model for water-filled agglomerates allows to rationalize effects of geometrical parameters (composition, radius R ), boundary conditions ( co2(f a), %+( a), and reaction kinetics (transfer coefficient... 

Ansari, R., and Motevalli, B. The effects of geometrical parameters on force distributions and mechanics of carbon nanotubes A critical study, Commun. Nonlinear. Sci. Numer. Simulat., 14,4246 263 (2009). 

Moholkar et al. [11] studied the effect of operating parameters, viz. recovery pressure and time of recovery in the case of hydrodynamic cavitation reactors and the frequency and intensity of irradiation in the case of acoustic cavitation reactors, on the cavity behavior. From their study, it can be seen that the increase in the frequency of irradiation and reduction in the time of the pressure recovery result in an increment in the lifetime of the cavity, whereas amplitude of cavity oscillations increases with an increase in the intensity of ultrasonic irradiation and the recovery pressure and the rate of pressure recovery. Thus, it can be said that the intensity of ultrasound in the case of acoustic cavitation and the recovery pressure in the case of hydrodynamic cavitation are analogous to each other. Similarly, the frequency of the ultrasound and the time or rate of pressure recovery, are analogous to each other. Thus, it is clear that hydrodynamic cavitation can also be used for carrying out so called sonochemical transformations and the desired/sufficient cavitation intensities can be obtained using proper geometric and operating conditions. 

The effect of crown ethers on the geometrical orientation in base-promoted E2 eliminations has been studied by several groups. Bartsch et al. (1973) have investigated the effect of several parameters on the potassium alkoxide-promoted eliminations of HBr from 2-bromobutane (Table 45). In the absence of crown ethers the relative amount of 1-butene formed increases, while the trans/cis ratio of the 2-butenes decreases, with decreasing solvent polarity. Furthermore, the proportion of 1-butene increases and the trans/cis ratio decreases on increasing the base concentration. These effects were explained in terms of steric interactions between the base and a- and /7-alkyl groups in the... 

The rate of cyclotrimerization of PhC=CMc catalysed by the camphor-derived complexes of PdCl2 has been found to be highly dependent on the R group, decreasing in the order R = Me2N, i-Pr, C6H5. The effects of geometric and/or electronic parameters on the catalytic activity of the complexes were evaluated on the basis of X-ray and electrochemical data.91... 

Quantum chemical calculations on RE + /3-diketonate complexes are presently restricted to two approaches the effective core potential (ECP) and the SMLC/AMl method. The SMLC/AMl method is a very powerful addition to the semi-empirical molecular orbital method AMI in that it allows the prediction of geometric parameters of rare-earth /3-diketonate complexes of very difficult experimental determination. In this method the RE3+ ion is a sparkle represented by a -i-3e charge in the center of a repulsive spherical potential of the form exp(—ar). Recently, ab initio effective core potential calculations have also succeeded in reproducing the coordination polyhedron geometries of RE + /S-diketonate complexes with high accuracy . 

There is, at present, no realistic theoretical model of the effect of geometrical disorder. A proper model must take into account the complicated orientation dependence of the matrix element (K) [63g], as well as the distribution of positions and orientations of the CTM. The simple treatment adopted by the Gaussian Disorder Model predicts a dependence of the prefactor mobility (//q) on the geometrical disorder parameter Z, namely //q oc exp(i2 ) [63a], and this relationship has been used often to analyze experimental data. The comparison of TTA and TAPC at low concentrations disagrees with this prediction, and it appears to be untenable a priori anyway [60b, 63e]. A worthy challenge for future work will be to construct a model with enough realism to have predictive value. Recent reports indicate progress in this direction [641,o]. 

Weak interaction potentials can be constructed specihc to a single system, such as the dimer of two molecules of water or the trimer of hydrogen huoride. They may contain terms that correspond to the usual contributing elements and may incorporate cooperative effects. In any case, the objective is a potential that is expressed in terms of geometrical parameters of the specihc system as a whole. The alternative approach is to construct potentials with parameters tied to the molecule building blocks. This alternate approach imposes a type of constraint in that functional forms used to represent a surface must rehect the types of parameters. The contributing element of permanent moment interactions is... 

The hypothesis that ground-state geometry can be used to quantify chemical reactivity was also examined for a number of bimolecular processes. Here, the emphasis was invariably on the effect of steric hindrance, which can be extrapolated to the transition state in a fairly straightforward manner. For instance, Seeman et al. evaluated a variety of geometrical parameters and steric congestion models for the methylation of a wide series of alkyl pyridines [191]. 

Fully developed laminar flow and heat transfer in a parallel plate duct with spanwise-periodic rectangular corrugations at one wall have been investigated by Sparrow and Chukaev [291]. The end effect is also ignored in their analysis. The fully developed / Re is shown in Fig. 5.61, which is based on the results reported by Sparrow and Chukaev [291] and the extension by Shah and Bhatti [2]. The heat transfer characteristics for the three pairs of geometric parameters can be found in Sparrow and Chukaev [291]. 

The effect of geometric ratios on the Nusselt number is difficult to quantify, although some investigators have incorporated the principal length parameters... 

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