Channel width

For a given fixed flow rate Q = Vbh, and channel width profile b(x), Eq. (6-56) may be integrated to determine the liquid depth profile h(x). The dimensionless Fronde number is Fr = VVg/j. When Fr = 1, the flow is critical, when Fr < 1, the flow is subcritical, and when Fr > 1, the flow is supercritical. Surface disturbances move at a wave velocity c = V they cannot propagate upstream in supercritical flows. The specific energy Ejp is nearly constant. 

TABLE 14-19 Experimental Values for j, Channel Width in Packing as a Fraction of Packing Diameter... 

In both cases, AB =dz, element width = dx and channel width = T Fig. 4.7 Melt Flow between parallel plates... 

It should also be noted that in some cases correction factors, Fj, and Fp are applied to the drag and pressure flow terms. They are to allow for edge effects and are solely dependent on the channel width, T, and channel depth, h, in the metering zone. Typical values are illustrated in Fig. 4.11. 

Inlet channel width to each pump is considered optimum at 2 to prevent secondary turbulence effects. [3]... 

Avoid placing several pumps in one open channel removing w ater in series fashion. If this must be done, velocity at each pump must be kept at same value as for single pump. The channel width at each pump would be taken from Reference [17]. 

This velocity profile is commonly called drag flow. It is used to model the flow of lubricant between sliding metal surfaces or the flow of polymer in extruders. A pressure-driven flow—typically in the opposite direction—is sometimes superimposed on the drag flow, but we will avoid this complication. Equation (8.51) also represents a limiting case of Couette flow (which is flow between coaxial cylinders, one of which is rotating) when the gap width is small. Equation (8.38) continues to govern convective diffusion in the flat-plate geometry, but the boundary conditions are different. The zero-flux condition applies at both walls, but there is no line of symmetry. Calculations must be made over the entire channel width and not just the half-width. 

Flow in the transverse (y) direction is negligible. Although flow in the transverse (y) direction will actually be non-zero, because the channel width increases it is assumed to be negligible, relative to Vx. After solving the problem based on Vy=0, an estimate of Vy can be obtained by then solving the continuity equation. 

To understand the mechanism of flame quenching in narrow channels in detail, one should first examine the data of flames in mixtures of constant composition, but in charmels of different sizes (Figure 6.1.2). The measured propagation velocities in stoichiometric propane/ air mixture are shown in Figure 6.1.2a. For channel widths slightly larger than the quenching distance, the... 

Measured quenching distance as a function of equivalence ratio for propane/air mixture (top), and pictures of (a) downward and (b) upward propagating flames in channels, close to quenching. Channel widths as in the graph. Frame numbers correspond to the numbers of experimental points. 

It can be observed that the dominant mechanism of heat transfer from the flame to the walls is different for channel widths up to 7 mm as well as for wider channels. 

The radius of curvature of flame is shown in Figure 6.1.7 as a function of the quenching distance (Figure 6.1.7a) and of the equivalence ratio (Figure 6.1.7b). The radius was determined from the flame pictures. For lean mixtures, the radius increases linearly with the channel width, both for the downward and upward propagating flames. For rich mixtures and downward propagation, the increase is linear for quenching distances up to Dq = 7 mm, but the increase is not as steep as that of lean mixtures. However, the increase accelerates. For rich... 

Effectively, Eqs. (86) and (87) describe two interpenetrating continua which are thermally coupled. The value of the heat transfer coefficient a depends on the specific shape of the channels considered suitable correlations have been determined for circular or for rectangular channels [100]. In general, the temperature fields obtained from Eqs. (86) and (87) for the solid and the fluid phases are different, in contrast to the assumptions made in most other models for heat transfer in porous media [117]. Kim et al. [118] have used a model similar to that described here to compute the temperature distribution in a micro channel heat sink. They considered various values of the channel width (expressed in dimensionless form as the Darcy number) and various ratios of the solid and fluid thermal conductivity and determined the regimes where major deviations of the fluid temperature from the solid temperature are found. 

Mixing channel width depth 148-469 pm 200 pm Reaction plate thickness 300 pm... 

Reactor type Multi-plate-stack in cylindrical housing Reaction channel width depth length 700 pm 300 pm 50 mm... 

Heating Cross-flowing gas Reaction channel width depth length 400 pm 300 pm 10 mm... 

Reactor type Ceramic platelet reactor Micro channel width length (type A + B) 500 pm 25 mm... 

Micro channel width depth length 500 pm 100 pm 8 mm Outer device dimensions 32 mm x 32 mm X 26 mm... 

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