Universal correlation

The heat-transfer coefficient depends on particle size distribution, bed voidage, tube size, etc. Thus a universal correlation to predict heat-transfer coefficients is not available. However, the correlation of Andeen and Ghcksman (22) is adequate for approximate predictions ... 

A typical temperature dependence of is shown in fig. 53. Clough et al. [1981] have found a universal correlation between the temperature at which has a minimum, r in, and A, when the measurements are performed at the same Zeeman frequency. This correlation, demonstrated in fig. 54, holds for all molecular solids studied so far, with A covering a range of four orders... 

Fig. 54. Universal correlation between T , and tunneling frequency A. The values of A are given in peV (1 peV 8.066 X 10 cm = 2.42 x 10 Hz). The Zeeman frequency equals 21 MHz. The points correspond to different chemical species.

In the nucleate boiling region the heat-transfer coefficient is dependent on the nature and condition of the heat-transfer surface, and it is not possible to present a universal correlation that will give accurate predictions for all systems. Palen and Taborek (1962) have reviewed the published correlations and compared their suitability for use in reboiler design. 

Coal is an extremely heterogeneous material, both from a macroscopic and microscopic point of view. Correlation of liquefaction reactivity with coal properties is, as a result, inherently difficult and any truly "universal correlations that will be developed will need to be based... 

Despite various attempts, no single universal correlation between bulk properties and catalytic activity of solids has been found. It is now recognized that the geometric factor and the electronic factor cannot be separated from one another and that catalytic activity should be considered along with catalyst selectivity to arrive at an understanding of heterogeneous catalysis (Sachtler, 1981). 

There is a natural draw rate for a rotating disk that depends on the rotation rate. Both the radial velocity and the circumferential velocity vanish outside the viscous boundary layer. The only parameter in the equations is the Prandtl number in the energy equation. Clearly, there is a very large effect of Prandtl number on the temperature profile and heat transfer at the surface. For constant properties, however, the energy-equation solution does not affect the velocity distributions. For problems including chemistry and complex transport, there is still a natural draw rate for a given rotation rate. However, the actual inlet velocity depends on the particular flow circumstances—there is no universal correlation. 

Universal Correlations between Tc and tig/m (Carrier Density over Effective Mass) in EEgh-Tc Cuprate Superconductors, Phys. Rev. Lett. (1989) 2317. 

In order to obtain a universal correlation for the linear growth rate in the full temperature region between Tg and Tm written in dimensionless variables, we introduce the variables... 

In summary, while a number of dimensionless group correlations have been proposed to transfer mass-transfer and corrosion-rate data from one hydrodynamic geometry to another, all of these correlations are system-specific and are not generally valid for use outside of the ranges of conditions (Re, Sc, T) for which they have been derived. Clearly, a universal correlation is lacking (and is perhaps unattainable), particularly one that can be used to correlate mass-transfer geometries at elevated temperatures. Again, we emphasize that the development of correlations of this type is vitally important for the quantitative comparison of different series of experimental data. 

The solid curve in Fig. 2 indicates that all three data sets are represented reasonably well by a single quadratic function. We (include diat the [ oposed universal correlation between and a is rrect to first order. The positive sign of the quadratic term may serve as a detailed test trf competing models, for example, from the dependence on a of the parameters in the MacMillan formula. 

A universal correlation (equation 19) was suggested to exist between the excited-state proton-transfer rate constant and photoacidity in aqueous solutions ... 

Whether a sample is dextrorotatory (abbreviated "(+) ) or levorotatory (abbreviated (-)") is determined experimentally by a polarimeter. Except for the molecule glyceraldehyde, there is no direct, universal correlation between direction of optical rotation ((-i-) and (-)) and designation of configuration (R and 5). In other words, one dextrorotatory compound might have R configuration while a different dextrorotatory compound might have S configuration. 

This is an interesting challange from the standpoint of developing geometry-insensitive universal correlations for all catalyst shapes. As illustrated above, the critical value of the intrapellet Damkohler number is... 

One common characteristic of these length scales is that the dimensionless spatial coordinate is identically zero at the plane, axis, or point of symmetry, and r] reaches its maximum value of unity on the external surface of the catalyst. In terms of a universal correlation, a typical characteristic length scale for all catalyst shapes is L = V cataiyst/>S extemai, where Vcataiyst is the volume of catalyst and 5extemai IS the total external surface area. This definition of L reduces to ... 

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