Bed profiles

FIG. 16-3 Bed profiles (top and middle) and hreakthroiigh curve (hottom). The Led profiles show the mass-transfer zone (MTZ) and eqiiilihriiim section at hreakthroiigh. The stoichiometric front divides the MTZ into two parts with contrihiitions to the length of equivalent eqiiihhriiim section (LES) and the length of equivalent unused hed (LUB). 

This equation, evaluated at = 1, is plotted for r = 2 and r = 0.5 in Fig. 16-20. Clearly, the solution for r= 0.5 is not physically correct. Equation (16-132), with dZi/d = Xi/, is apphed to this case to give the shock indicated by the dashed line. Alternatively, we could have obtained bed profiles by evaluating equations at Ti = const. 

The resulting eontours of the stream lines, a elose-up of a veetor plot near the top eover plate and the profile of radial veloeity at the inner edge of the eatalyst bed (Profile C, Figure 10-15) all show us that these last-named proposed ehanges would have many benefits. The main ones are ... 

In the stationary regime and for a non-reactive solid, the volumetric solid flow rate is constant and equal to the inlet flow rate given by the vibrating feeder (Qv ). From Eq. (1), the following ordinary differential equation is directly obtained and can be solved with a boundary condition (exit height fixed) in order to compute the bed profile along the kiln ... 

The Tadmor model assumes Newtonian fluids and shallow channels. The channel cross section and that of the solid bed are assumed to be rectangular. The width of the solid bed profile is denoted by X(z), which is the the main objective that we are seeking with the model. The solid bed that develops at steady state conditions is the focal interest here. Furthermore, Tadmor assumed that melting only occurs at the barrel surface and the solid bed is homogeneous, continuous and deformable. 

Solid bed profile prediction for a plasticating single screw extruder. In this example we would like to use Tadmor s model to predict the solid bed profile of a low density polyethylene in a plasticating single screw extruder, based on experiments published by Tadmor and Klein [27], In their experiments they used the following screw geometry ... 

The remaining two sections are computed in a similar fashion. Figure 6.71 presents a comparison between the measured and the predicted solid bed profiles. 

Equations 9.3-22 and 9.3-26 are the basic equations of the melting model. We note that the solid-bed profile in both cases is a function of one dimensionless group ijj, which in physical terms expresses the ratio of the local rate of melting per unit solid-melt interface JX /X to the local solid mass flux into the interface Vszps, where ps is the local mean solid bed density. The solid-bed velocity at the beginning of melting is obtained from the mass-flow rate... 

Equation 9.3-28 indicates that the solid bed profile in a constant-depth channel is parabolic. The total (down-channel) length, ZT, of melting is obtained from Eq. 9.3-28 by setting X = 0 to give... 

There are many barrier-type screws that differ from each other by the channel depth profiles of the melt and solids channels, by the helix angles, profiles, and the number of flights. We briefly review here just a few if these types of screw. The first barrier-screw design is due to C. Maillefer14 and is shown in Fig. 9.40, in which the auxiliary channel follows roughly the solid-bed profile. Clearly, at certain conditions the auxiliary flight can restrict flow rate, but at all times it prevents solids from leaving the screw. 

Figure 3 T)rpicai CSS solution of pressure and gas composition bed profiles for the Ot VSA process...

FIG. 16-21 Bed profiles fortwo-component isothermal adsorption, Example 10. 

The spikes are repeated over a nximber of hours to simulate vehicle ageing The expected temperature profiles are shown. At temperatures less than 700 °C, the gas-in temperature profile is as shown, while at hi er temperatures, it is similar to the mid bed profile but 60 - 80 °C lower. 

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