Plug flow variable area

PLUG FLOW WITH VARIABLE AREA AND SURFACE CHEMISTRY 657... 

The plug-flow problem may be formulated with a variable cross-sectional area and heterogeneous chemistry on the channel walls. Although the cross-sectional area varies, we make a quasi-one-dimensional assumption in which the flow can still be represented with only one velocity component u. It is implicitly assumed that the area variation is sufficiently small and smooth that the one-dimensional approximation is valid. Otherwise a two- or three-dimensional analysis is needed. Including the surface chemistry causes the system of equations to change from an ordinary-differential equation system to a differential-algebraic equation system. 

Fig. 16.3 Illustration of a plug-flow channel with variable cross sectional area.

Consequently, we see that Equation (1-11) applies equally well to our model of tubular reactors of variable and constant cross-sectional area, although it is doubtful that one would find a reactor of the shape shown in Figure 1-11 unless it were designed by Pablo Picasso. The conclusion drawn from the application of the design equation to Picasso s reactor is an imponant one the degree of completion of a reaction achieved in an ideal plug-flow reactor tPFR) does not depend on its shape, only on its total volume. 

The hydrodynamic diameters of microchannels usually range from 10 to 1000 rm. In such confined flowing spaces, the multiphase flow patterns of Newtonian fluids are more variable compared with the common bubbly or droplet flows in larger vessels and columns. The confined flowing channel first affects the shape of droplets therefore, the flow patterns of liquid/hquid dispersed systems are usually categorized as plug flow and droplet flow, as shown in Fig. 1A and B. Usually, the droplet flow has larger specific surface area, which is fit for the mass transfer enhancement process (Mary et al,... 

A control valve is a specially designed globe valve that acts as a variable resistance in the line to control the flow rate. Closing down on the valve decreases the area between the plug and the... 

The value of this variable is set to zero at the outflow boundary and its values represent the time it will take fluid at any location to travel to the outflow boundary given the velocity field u. Multiplying this variable by 4-q/(jzD ), the flow rate divided by the pipe cross sectional area, produces a variable that can be used to indicate where each drawn litre starts from. The starting point of the water that contributes to the nth litre drawn from the pipes is identified by the positions where the value of P = AqContour plots of P for the four combinations of 12 mm or 18 mm diameter pipes and plug or laminar flow are contained in Figure 3.1 to 3.4. Each shade in those images represents a different litre. 

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