Parallel flow flat plates

Mass transfer in flow parallel to flat plates. The mass transfer and vaporization of liquids from a plate or flat surface to a flowing stream is of interest in the drying of inorganic and biological materials, in evaporation of solvents from paints, for plates in wi nd tunnels, and in flow channels in chemical process equipment. 

Consider the case of a Newtonian fluid undergoing laminar, pressure-driven flow between two parallel, infinite flat plates separated by a distance B (Figure 1.10). The bottom plate is stationary and the top plate moves at a constant velocity Fup. For a constant dynamic pressure gradient, AP/Ax, P = p - g -r,-we wish to calculate the resulting velocity profile. 

Parallel-Leaf Cartridge. A parallel-leaf cartridge consists of several flat plates, each having membrane sealed to both sides (Fig. 13). The plates have raised (2—3 mm) rails along the sides in such a way that, when they are stacked, the feed can flow between them. They are clamped between two stainless-steel plates with a central tie rod. Permeate from each leaf drains into an annular channel surrounding the tie rod (33). 

It is convenient first to consider the flow over a thin plate inserted parallel to the flow of a fluid with a constant stream velocity us. It will be assumed that the plate is sufficiently wide for conditions to be constant across any finite width w of the plate which is being considered. Furthermore, the extent of the fluid in a direction perpendicular to the surface is considered as sufficiently large for the velocity of the fluid remote from the surface to be unaffected and to remain constant at the stream velocity m.,. Whilst part of the fluid flows on one side of the flat plate and part on the other, the flow on only one side is considered. 

For flow parallel to an electrode, a maximum in the value of the mass-transfer rate occurs at the leading edge of the electrode. This is not only the case in flow over a flat plate, but also in pipes, annuli, and channels. In all these cases, the parallel velocity component in the mass-transfer boundary layer is practically a linear function of the distance to the electrode. Even though the parallel velocity profile over the hydrodynamic boundary layer (of thickness h) or over the duct diameter (with equivalent diameter de) is parabolic or more complicated, a linear profile within the diffusion layer (of thickness 8d) may be assumed. This is justified by the extreme thinness of the diffusion layer in liquids of high Schmidt number ... 

Example 5-9 Flow Down an Inclined Plane. Consider the steady laminar flow of a thin layer or film of liquid down a flat plate that is inclined at an angle 6 to the vertical, as illustrated in Fig. 5-10. The width of the plate is W (normal to the plane of the figure). Flow is only in the v direction (parallel to... 

Flat plate, flow parallel to, 15 7191 Flat-screen printing, 26 398 Flat wall paint, 7 137-139 Flavanthrone dye, 9 336 Flavanthrone Yellow, pigment for plastics, 7 366t... 

Figure 1.25 shows the boundary layer that develops over a flat plate placed in, and aligned parallel to, the fluid having a uniform velocity upstream of the plate. Flow over the wall of a pipe or tube is similar but eventually the boundary layer reaches the centre-line. Although most of the change in the velocity component vx parallel to the wall takes place over a short distance from the wall, it does continue to rise and tends gradually to the value vx in the fluid distant from the wall (the free stream). Consequently, if a boundary layer thickness is to be defined it has to be done in some arbitrary but useful way. The normal definition of the boundary layer thickness is that it is the distance from the solid boundary to the location where vx has risen to 99 per cent of the free stream velocity v . The locus of such points is shown in Figure 1.25. It should be appreciated that this is a time averaged distance the thickness of the boundary layer fluctuates owing to the velocity fluctuations.

Couette and Poiseuille flows are in a class of flows called parallel flow, which means that only one velocity component is nonzero. That velocity component, however, can have spatial variation. Couette flow is a simple shearing flow, usually set up by one flat plate moving parallel to another fixed plate. For infinitely long plates, there is only one velocity component, which is in the direction of the plate motion. In steady state, assuming constant viscosity, the velocity is found to vary linearly between the plates, with no-slip boundary conditions requiring that the fluid velocity equals the plate velocity at each plate. There... 

Initial developments in this area consisted ot a series of parallel flat plates called parallel plate interceptors (PPI) which were installed at an angle of 45° to the direction of flow in an API separator. 

Free-Flow Electrophoresis. Free-flow electrophoresis is the most common technique for scaling up electrophoresis for commercial application, in this technique, sample compounds are injected into a curtain of buffer which flows between two flat plates, with electrodes parallel to the flow at each end. The electric field is then applied perpendicularly to the flow direction, so that as compounds flow down between the electrodes they separate horizontally and exit the flow field at different locations. 

If a fluid such as air flows over a flat plate placed with its surface parallel to the stream, particles in the vicinity of the surface are slowed down by viscous forces. Fluid particles adjacent to the surface stick to it and have zero velocity relative to the boundary. Other fluid particles are retarded as a result of sliding over the immobilised particles. The effects of viscous forces originating at the boundary extend for a certain distance (5, the boundary layer thickness). The effects of viscous forces originating at the boundary are not extensive and the velocity soon approaches free stream velocity. 

S Ostrach. An Analysis of Laminar Free-Convection Flow and Heat Transfer About a Flat Plate Parallel to the Direction of the Generating Body Force. NACA Report 1111, 1953. 

Air flows parallel to the surface of a flat plate which is unheated (adiabatic) up to a... 

The plate represents an infinite source of mass, such that the concentration at the plate surface is constant. The fluid represents a mass sink. Flow over the flat plate is uniform and parallel to the surface. Hence, the x component of the Navier-Stokes equation and the continuity equation in two dimensions (x and y) describe flow over the plate. These equations are given as... 

Let us therefore discuss about spatial instability of parallel flows, mainly the flow past a flat plate at zero angle of attack- a problem that enjoys a canonical status for instability analyses. For the spatial instability problem associated with two-dimensional disturbance held of two-dimensional primary flows, the disturbance quantities will have the appearance of Eqn. (2.3.28) with /3 = 0. Thus for a fixed Re, one would be looking for complex a when the shear layer is excited by a fixed frequency source of circular frequency, lvq- If we define Re in terms of the displacement thickness S as the length scale, then Re = and the results obtained will be plotted as contours of constant amplification rates Oj in Re — lvo)— plane, as shown in Fig. 2.2. 

Some other tJiJes of valves arc the check valve, which permits flow in one direction only the butterfly valve, which operates in damperlike fashion by rotating a flat plate to either a parallel or a perpendicular position relative to the flow the plug valve, in which a rotating tapered plug provides on-off service the needle valve, which is a variation of the globe valve that gives... 

Flat plate parallel to flow Plate length 10 to3xltf >0.6 0.648 0.50... 

Let us consider a steady flow for which a Cartesian coordinate system (x, y, z) can be established such that -h x is the principal flow direction and all flow properties are independent of z. In this two-dimensional (x, y) flow, it will further be assumed that except in a layer extending parallel to the principal flow direction, all flow properties vary so slowly that transport effects are negligibly small. For convenience, the viscous, diffusive, and heat-conducting layer will be placed in the vicinity of the plane y = 0 (which, for example, may represent a stationary flat plate, or may divide two parallel... 

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