Flow between plates

Plates are pressed from stainless steel, titanium, HasteT loy or any material ductile enough to be formed into a pressing. The specious design of the trough pattern strengthens the plates, increases the effective heat transfer area and produces turbulence in the liquid flow between plates. Plates are pressed in materials between 0.5 and... 

In order to predict Lhe transition point from stable streamline to stable turbulent flow, it is necessary to define a modified Reynolds number, though it is not clear that the same sharp transition in flow regime always occurs. Particular attention will be paid to flow in pipes of circular cross-section, but the methods are applicable to other geometries (annuli, between flat plates, and so on) as in the case of Newtonian fluids, and the methods described earlier for flow between plates, through an annulus or down a surface can be adapted to take account of non-Newtonian characteristics of the fluid. 

FLOW BETWEEN PLATES WITH WALL INJECTION... 

J5 Consider the wall-injection problem in an axisymmetric setting, where a uniform injection velocity flows through the wall of a cylindrical tube. There is a mean velocity U that enters through one end of the tube. Following a procedure analogous to the flow-between-plates problem (Section 5.6), develop a solution for the velocity profiles and the wall shear stress as characterized by the product of a Reynolds number and a friction factor. 

The power-law solution for squeezing flow between plates of radius a for a power-law liquid of original thickness ho and current thickness h at time t is given by... 

In this paragraph, we consider the element of an exchanger, either a tube, or a flow between plates, or even a more complex configuration incorporating a hydraulic radius (i.e., the ratio of the cross-section of the passage to the wet perimeter). 

Fypass Flow Effects. There are several bypass flows, particularly on the sheUside of a heat exchanger, and these include a bypass flow between the tube bundle and the shell, bypass flow between the baffle plate and the shell, and bypass flow between the shell and the bundle outer shroud. Some high temperature nuclear heat exchangers have shrouds inside the shell to protect the shell from thermal transient effects. The effect of bypass flow is the degradation of the exchanger thermal performance. Therefore additional heat-transfer surface area must be provided to compensate for this performance degradation. 

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). 

Under conditions of limiting current, the system can be analyzed using the traditional convective-diffusion equations. For example, the correlation for flow between two flat plates is... 

Most plate columns operate under conditions such that gas is completely mixed as it flows between the plates, but few operate with pure plug flow of liquid. Departure from plug flow of liquid has been studied by Gautreaux and O Connell [Chem. Eng. Pi oq., 51, 232 (1955)] by assuming that hquid mixing can be represented as occurring in a series of stages of completely mixed liquid. For this model,... 

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

If the clearance between the rolls is small in relation to their radius then at any section x the problem may be analysed as the flow between parallel plates at a distance h apart. The velocity profile at any section is thus made up of a drag flow component and a pressure flow component. 

The velocity component due to pressure flow between two parallel plates has already been determined in Section 4.2.3(b). 

It is worth noting that the equations for flow between parallel plates may also be used with acceptable accuracy for flow along a circular annular slot. The relevant terms are illustrated in Fig. 5.6. 

Here I /G. is the heat exchanger contact resistance. The reason for rhe contact resistance is that there exists a resistance to heat flow between the outer surface of the pipe and the collar of the plate tins. Normally, the fins are attached to the pipes by mechanical expansion of the tubes out into rhe plate-fin collars. Because of this manufacturing method, the contact will not be ideal. Small gaps between the pipe surface and rhe collar of the tins will occur. 

Liquids are able to flow. Complicated stream patterns arise, dependent on geometric shape of the surrounding of the liquid and of the initial conditions. Physicists tend to simplify things by considering well-defined situations. What could be the simplest configurations where flow occurs Suppose we had two parallel plates and a liquid drop squeezed in between. Let us keep the lower plate at rest and move the upper plate at constant velocity in a parallel direction, so that the plate separation distance keeps constant. Near each of the plates, the velocities of the liquid and the plate are equal due to the friction between plate and liquid. Hence a velocity field that describes the stream builds up, (Fig. 15). In the simplest case the velocity is linear in the spatial coordinate perpendicular to the plates. It is a shear flow, as different planes of liquid slide over each other. This is true for a simple as well as for a complex fluid. But what will happen to the mesoscopic structure of a complex fluid How is it affected Is it destroyed or can it even be built up For a review of theories and experiments, see Ref. 122. Let us look into some recent works. 

One particularly important feature of the plate heat exchanger is that the turbulence induced by the troughs reduces the Reynolds number at which the flow becomes laminar. If the characteristic length dimension in the Reynolds number is taken as twice the average gap between plates, the Re number at which the flow becomes laminar varies from about 100 to 400, according to the type of plate. 

Flow between each parallel plate surface... 

Figure 3.12. Streamline flow between parallel plates...

The problem of axial conduction in the wall was considered by Petukhov (1967). The parameter used to characterize the effect of axial conduction is P = (l - dyd k2/k ). The numerical calculations performed for q = const, and neglecting the wall thermal resistance in radial direction, showed that axial thermal conduction in the wall does not affect the Nusselt number Nuco. Davis and Gill (1970) considered the problem of axial conduction in the wall with reference to laminar flow between parallel plates with finite conductivity. It was found that the Peclet number, the ratio of thickness of the plates to their length are important dimensionless groups that determine the process of heat transfer. 

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

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