Factor plots

For condensing vapor in vertical downflow, in which the hquid flows as a thin annular film, the frictional contribution to the pressure drop may be estimated based on the gas flow alone, using the friction factor plotted in Fig. 6-31, where Re is the Reynolds number for the gas flowing alone (Bergelin, et al., Proc. Heat Transfer Fluid Mech. Inst., ASME, June 22-24, 1949, pp. 19-28). 

Temperature correction factor plots for other arrangements can be found in the TEMA standards and the books by Kern (1950) and Ludwig (2001). Mueller (1973) gives a comprehensive set of figures for calculating the log mean temperature correction factor, which includes figures for cross-flow exchangers. 

Effectiveness factor plot for spherical catalyst particles based on effective diffusivities (first-order reaction). 

Effectiveness factor plot for nth-order kinetics— spherical catalyst particles... 

Figure 8 IR-ATR images of a PA/PTFE polymer blend bright colors PTFE clusters. Left integration of 1,149 cm-1 C-F absorption. Right PCA factor plot — additional clusters appear within the white circles. (See Color Plate Section at the end of this book.)...

Finally, if the initial model is built using the full-spectrum, an examination of factor plots would reveal areas in which there is no activity. 

The friction factor plot is available in many handbooks, so that given a value of Re, one can find the corresponding value of /. In the context of numerical optimization, however, using a graph is a cumbersome procedure. Because all of the constraints should be expressed as mathematical relations, we select the Blasius correlation for a smooth pipe (Bird et al., 1964) ... 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) The RMSEP versus number of factors plot in Figure 5.113 shows a break at three factors and a leveling off after six factors. Tlie RMSEP value with six factors (0,04) is comparable to the estimated error in the reported concentrations (0.033), indicating the model is predicting well At this point we tentatively choose a rank six model. The rank three model shows an RMSEP of 0.07 and may well have been considered to be an adequate model, depending on how well the reference values are known. 

The analysis of the mean response and the s/n ratio can be performed employing the usual ANOVA and/or hypothesis tests to detect which factors or interactions have statistical significance. Taguchi proposed a conceptual approach based on the graphical display of the effects (they are called factor plots or marginal means followed by a qualitative evaluation. This provides objective information and a test for the significance of each design factor on the two observed responses mean and s/n ratio. 

The answers need an analysis of the s/n ratio. Table 2.17 summarises the Pareto analysis of variance (see Figure 2.7 for the calculations involved) and Figure 2.8 displays the factor plots associated with the calculations. 

Figure 2.8 Factor plots for a worked example of the Taguchi methodology.

Calculate the ideal volumes for the gas at each pressure and use them to calculate the z-factors. Plot the z-factors against pressure. 

The partial derivative, (3z/dp)r, is the slope of z-factor plotted against pressure at constant temperature. The slopes of the isotherms of Figures 3-2, 3-3, and 3-4 show that the second term of Equation 6-8 can be significantly large. 

Cooper ef al. (C15), 1934 Earlier film thickness data correlated in form of film friction factor plot. 

Fallah el al. (FI), 1934 Flow of water films inside tubes, with second phase of air, white oil, stationary and countercurrent kerosine. Film thicknesses of this and previous work correlated by film friction factor plot. 

Figure 15-9. Shift factor plotted against temperature Predictions using these models take no account of differences in the...

The effects of strain rate and temperature are correlated, and can be modeled (Kinloch and Young, 1983, Kinloch, 1985). For different temperatures and strain rates, GIc and the time to failure, tf, were measured. Using the time-temperature superposition principle, shift factors (aT) applicable to the time to failure tf, were determine. Shift factors plotted against (T — Tg) are independent of the type of test used (Fig. 12.14). The construction of a typical master curve GIc versus tf/aT is shown in Fig. 12.15 (Hunston et al., 1984). The value of GIc may be predicted for any strain rate/temperature combination. This model can also be applied to rubber-modified epoxies (See chapter 13). 

Note that the shape factors plotted in Fig. 6.13 are a function of only the II/W ratio. The effect of the flight on the pressure flow is stronger than that on drag flow. When the ratio Il/W diminishes, both approach unity. In this case, Eq. 6.3-19 reduces to the simplest possible model for pumping in screw extruders, that is, isothermal flow of a Newtonian fluid between two parallel plates. 

Fig. 10-8 Correction-factor plot for exchanger with one shell pass and two, four, or any multiple of tube passes.

Fig. 10-10 Correction-factor plot for single-pass c.ross-flow exchanger both fluids unmixed...

Figure 2. Effectiveness factor plots for Reactions 1 and 2. Example 2.

Nevertheless, there are some notable differences between An0 and Anv As discussed previously, An0 is important for the low 17 region, and hence is of interest from a theoretical view-point, whereas An, is important for the high rj region and thus of interest in practice. There are other differences as well To illustrate these it is necessary to discuss and understand effectiveness factor plots that are somewhat more exotic than those described so far. 

In Figure 6.11 effectiveness factor plots are given for wth-order kinetics in a slab. The lines were calculated with the formulae given in Table 6.5. The effectiveness factor in... 

From Figure 6.11 shows that three basically different effectiveness factor plots can be obtained ... 

---