Flux plot curve

In burn-out experiments, a test section is part of a loop which may be open or closed, and the question arises as to whether or not any of the loop equipment, such as condensers, heaters, pumps, or pipe fittings, have any significant effect on the burn-out flux. This issue came to prominence at the Boulder Heat Transfer Conference in 1961 with a Russian paper by Aladyev (A4) describing burn-out experiments in which a branch pipe, connecting to a small vessel, was fitted close to the test section inlet. The test section itself was a uniformly heated tube 8 mm in diameter and 16 cm long. The results are reproduced in Fig. 9, and show burn-out flux plotted against exit steam quality. Curve (A) was obtained with the branch vessel filled with cold water,... 

In Figures 8 and 9 are shown the data for the dependence of the characteristic film buildup time t on Apg and U. In accord with the model, t is found to be independent of U, with only a very weak dependence on Apg indicated. This latter result could in part be a function of experimental inaccuracy. The data reduction for t introduces no assumptions beyond that needed to draw the exponential flux decline curves such as those shown in Figures 2 and 3. However, an error analysis shows that the maximum errors relative to the exponential curve fits occur at the earlier times of the experiment. This is seen in the typical error curve plotted in Figure 10. The error analysis indicates that during the early fouling stage the relatively crude experimental procedure used is not sufficiently accurate or possibly that the assumed flux decline behavior is not exponential at the early times. In any case, it follows that the accuracy of the determination of 6f is greater than that for t. 

In Fig. 1.10b we plot the total flux emission curve for a mixture of fulleranes (with a number of carbon atoms N = 60-2,160) following a size distribution law n(R) aR with tn — 3.5 it 1,5 Uid compttre it with the Costnic Hcick Toiifid ItYia cv... 

The water permeability coefficient can be obtained via eq. V - 43 using experiments with pure water. Because the osmotic pressure difference is zero, there is a linear relationship between the hydrodynamic pressure AP and the volume (water) flux Jy (eq. V - 43), and from the slope of the corresponding flux-pressure curve the water permeability coefficient Lp can be obtained. Figure V - 3 is a schematic representation of the volume flux plotted as a function of the applied pressure for a more open membrane (high Lp) and a more dense membrane (low Lp). 

Differential scanning calorimetry (DSC) A technique in which the difference in energy inputs into a substance and a reference material is measured as a function of temperature whilst the substance and reference material are subjected to a controlled temperature program. Two modes, power-compensation DSC and heat-flux DSC, can be distinguished, depending on the method of measurement used. Usually, for the power-compensation DSC curve, heat flow rate should be plotted on the ordinate with endothermic reactions upwards, and for the heat-flux DSC curve with endothermic reactions downwards. 

Relationship Between the Height-Time Curve and the Flux Plot... 

Figure 3.15 shows flux plots for a critically loaded thickener. The line of slope F/A represents the relationship between feed concentration and feed flux for a volumetric feed rate, F. The material balance equations [Equations (3.43) and (3.44)] determine that this line intersects the curve for the total flux in the downflow section when the total flux in the upflow section is zero. Under critical loading conditions the feed concentration is just equal to the critical value giving rise to a feed flux equal to the total continuous flux that the downflow section can deliver at that concentration. Thus the combined effect of bulk flow and settling in the downflow section provides a flux equal to that of the feed. Under these conditions, since all particles fed to the thickener can be dealt with by the downflow section, the upflow flux is zero. The material balance then dictates that the concentration in the downflow section, Cb, is equal to Cp and the underflow concentration, Cp is FCp/L. The material balance may be performed graphically and is shown in Figure 3.15. From the feed flux line, the feed flux at a feed concentration, Cp is Ups = FCf/A. At this flux the concentration in the downflow section is Cb = Cp. The downflow flux is exactly equal to the feed flux and so the flux in the upflow section is zero. In the underflow, where there is no sedimentation, the underflow flux, LCl/A, is equal to the downflow flux. At this flux the underflow concentration, Cl is determined from the underflow line.

Figure 17 shows curves for the methane permeate flux plotted against the bore liquid flowrate used to produce the hollow fibres. 

The measured flux of each substance was plotted as a function of pressure and the results compared with the predicted curves. The agreement, in each case, was gratlfyingly good. 

Ultrafiltration equipment suppHers derive K empirically for their equipment on specific process fluids. Flux J is plotted versus log for a set of operation conditions in Figure 6 K is the slope, and is found by extrapolating to zero flux. Operating at different hydrodynamic conditions yields differently sloped curves through C. ... 

Figure 2.42 shows boiling curves obtained in an annular channel with length 24 mm and different gap size (Bond numbers). The heat flux q is plotted versus the wall excess temperature AT = 7w — 7s (the natural convection data are not shown). The horizontal arrows indicate the critical heat flux. In these experiments we did not observe any signs of hysteresis. The wall excess temperature was reduced as the Bond number (gap size) decreased. One can see that the bubbles grew in the narrow channel, and the liquid layer between the wall and the base of the bubble was enlarged. It facilitates evaporation and increases latent heat transfer. 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

Figure Al. a) Porosity distribution for a ID melt column (solid curve) assuming constant melt flux (see Spiegelman and Elliott 1993). Average porosity is shown as the dashed line, b) Emichment factors (a) calculated from the analytical solution (solid curves) and approximate analytical solution (dotted curves) for °Th and Ra. c) Emichment factors (a) calculated from the numerical solution of Spiegelman and Elliott (1993) for °Th and Ra. In these plots, depth (z) is non-dimensionalized. See text for explanation.

When molecules have the insoluble BCS classification, the expected absorption profile is exemplified in Fig. 2.2. The upper horizontal line (solid) in Fig. 2.2, representing log Pq, can be determined by the methods described in Chapter 7. The slope 0, 1 segments curve (dashed), representing log Co, the concentration of the uncharged form of an ionizable molecule, can be determined by the methods described in the Chapter 6. The summation of log P0 and log C0 curves produces the log flux-pH profile. Such plots indicate under what pH conditions the absorption should be at its highest potential. 

Inverse mass flux effects. Critical heat fluxes at three different mass fluxes obtained on uniformly heated test sections at Argonne National Laboratory (Weatherhead, 1962) are plotted in Figures 5.44 and 5.45. The crossing over of the curves in Figure 5.44 is generally referred to as the inverse mass flux effect, in a... 

The raw data of the thermocouples consist of the temperature as a function of time (Fig. 8.9, left). In the raw data, the passing of the conversion front can be observed by a rapid increase in temperature. Because the distance between the thermocouples is known, the velocity of the conversion front can be determined. The front velocity can be used to transform the time domain in Fig. 8.9 (left) to the spatial domain. The resulting spatial flame profiles can be compared with the spatial profiles resulting from the model. The solid mass flux can also be plotted as a function of gas mass flow rate. The trend of this curve is similar to the model results (Fig. 8.9, right). 

If a tangent is drawn from the point on the abscissa corresponding to the required underflow concentration C , it will meet the if curve at a concentration value CL at which fT has the minimum value (A/v. and will intersect the ordinate axis at a value equal to irTL. The construction is dependent on the fact that the slopes of the tangent and of the iru line are equal and opposite ( uu). Thus, in order to determine both Cl and (An, it is not necessary to plot the total-flux curve (ibatch sedimentation (if ) curve. The value of (A/ /, determined in this way is then inserted in equation 5.46 to obtain the required area A. 

Figure 18 displays mass flux curves plotted against time. This particular selection of curves shows the difference in conversion gas rates with respect to wood fuel. Wood chips are significantly easier to convert than 6 mm wood pellets, which in turn have higher mass flux of conversion gas than fuel wood for a given volume flux of primary air through the conversion system. 

Fig. 10.4 Measured breakthrough curve of bromide with CTRW and advection-dispersion equation (ADE) fits. Here, the quantity j represents the normafized, flux-averaged concentration (top) Complete breakthrough curve, (bottom) Region identified by the bold-framed rectangle in the top plot. Note the difference in scale units between the plots. Pressure head h=-10cm water velocity v=2.82 cm/h. The dashed tine is the best advection-dispersion equation solution fit. The soUd line is the best CTRW fit. (Cortis and Berkowitz 2004)...

The membrane composition of Quantro II has been under continuous research for 19 months. Early samples were put on test in order to establish a long-term data base for this chemistry. While that early composition has been modified to achieve higher flux and rejection, its durability can be judged from Table I. Table I plots data obtained daily over the time period indicated. Curves on all tables have been smoothed to avoid daily fluctuations. It should be understood that fluctuations of as much as 0.2% rejection and 0.2 gfd in flux are routinely experienced and are not shown. 

FIGURE 2 The flux control coefficient, (a) Typical variation of the pathway flux, )ymeasured at the step catalyzed by the enzyme ydh, as a function of the amount of the enzyme xase, xase, which catalyzes an earlier step in the pathway. The flux control coefficient at (e,j) is the slope of the product of the tangent to the curve, d/ydh/3 xase/ and the ratio (scaling factor), e/j. (b) On a double-logarithmic plot of the same curve, the flux control coefficient is the slope of the tangent to the curve. 

Fig. 2.50. Generation of /-resolved two-dimensional 13C NMR spectra (a) flux diagram (b) /-modulation of Cl l doublets, CH2 triplets and CH3 quartets during evolution, vector diagrams in the x y plane and cosine curves described by the signal maxima (c) series of 13C NMR spectra of CHn groups with t1 dependent /-modulation of the signal amplitudes (d) series of /-resolved two-dimensional 13C NMR spectra formethine, methylene and methyl carbon atoms, stacked plots and contour plots (e).

A convenient way to illustrate the behavior of the model for the example of ZnS deposition is to plot the measured deposition rate, r(d, ZnS), as a function of the incident-flux rate of one element when the incident-flux rate of the second element is fixed. An example is shown in Figure 13 for the deposition of ZnS as a function of the incident-flux rate of sulfur at a substrate temperature of 200 °C. Experimental data points and curves representing the best-fit model predictions are shown for each of four zinc incident-flux rates. A nonlinear least-square procedure was used to obtain the following values for the model parameters that best fit equation 40 to the experimental data 8(Zn) = 0.6-0.7, 8(S) = 0.5-0.7, and K(ZnS) > 1015 cm2-s/ZnS. 

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