Flow rate boundary conditions

As before, we assume a distributed line source having a pressure of the form +1 

Following Equations 2-16a and 2-16b, we evaluate Equation 2-87 for large distances away from the fracture, yielding 

Since the integral in Equation 2-90 is known from inputs, the flow rate problem is solved. The net result on combining Equations 2-87 and 2-90 is +1 

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Intra-bundle microvoid is the most common microvoid type which occurs due to the lower permeability of the fiber bundles than the permeability of the empty spaces between the bundles. The resin flow is faster between the fiber bundles than inside the bundles, and the resin encircles itself when it reaches a stitch or another bundle perpendicular to the flow direction, and entraps a microvoid inside the bundle as shown in Fig. 9.21. To avoid this type of microvoid, the common practice is to slow the resin flow down by decreasing the injection pressure/flow rate boundary condition. This allows sufficient time for the encircled microvoids to shrink and collapse due to the higher resin pressure around the microvoids than inside the voids. 

Next, consider the same problem, except that we impose flow rate boundary conditions along the length of the source. As before. Equation 5-80 applies. For convenience, we introduce the variable then, for... 

Flow rate boundary conditions. In constant density flow, a producing well always results in flow across the farfield boundary a nonproducing well always implies that the farfield flow is stagnant. This is not the case when the fluid is compressible. Even when a well is shut-in, fluid may continue to migrate across farfield boundaries because of expansion effects. Both pressure and flow rate boundary conditions may be used at the well or at the farfield radius. The differencing procedure is straightforward. For example, if an input volume flow rate Q(t) is assumed at the well, then,... 

The previous set of equations is applied to a computational domain using finite difference, finite volume, or finite element methods. The input is either the cell voltage or the average current density. In addition, the flow rates and conditions at the inlet must also be prescribed, as well as the boundary conditions at the outside walls. The boundary conditions depend on the model domain. Several typical computational domains may be of interest, namely ... 

Numerical simulation of hood performance is complex, and results depend on hood design, flow restriction by surrounding surfaces, source strength, and other boundary conditions. Thus, most currently used method.s of hood design are based on experimental studies and analytical models. According to these models, the exhaust airflow rate is calculated based on the desired capture velocity at a particular location in front of the hood. It is easier... 

These systems can be inside large halls and may have no fixed limits for their influence, except for some parts of the system (inlet device surface, etc.) They can also be situated inside small rooms, where walls, floors, and ceilings are the natural boundaries. The systems usually consist of one exhaust hood and one supply inlet, which interact. There are also special combinations, as two or more inlets and one exhaust hood, or one supply inlet and two or more exhausts. All of these combinations need careful design and an accurate relation between supply and exhaust flow rates and velocities. Some systems also need stable temperature conditions to function properly. All combinations are dependent on having a defined contaminant concentration in the inlet air. This usually implies clean supply air, but some systems may use recirculated air with or without cleaning. 

In relatively low-reactive fuel-air mixtures, a detonation may only arise as a consequence of the presence of appropriate boundary conditions to the combustion process. These boundary conditions induce a turbulent structure in the flow ahead of the flame front. This turbulent structure is a basic element in the feedback coupling in the process by which combustion rate can grow more or less exponentially with time. This fundamental mechanism of a gas explosion has been described in Section 3.2. 

Any rheometric technique involves the simultaneous assessment of force, and deformation and/or rate as a function of temperature. Through the appropriate rheometrical equations, such basic measurements are converted into quantities of rheological interest, for instance, shear or extensional stress and rate in isothermal condition. The rheometrical equations are established by considering the test geometry and type of flow involved, with respect to several hypotheses dealing with the nature of the fluid and the boundary conditions the fluid is generally assumed to be homogeneous and incompressible, and ideal boundaries are considered, for instance, no wall slip. 

To scrutinize the sensitivity of the flame structure to the description of the outer-flow field, we compared the flame structure obtained from the two limiting boundary conditions at the extinction state, which can be considered to be the most aerodynamically and kinetically sensitive state of the flame for a given mixture concentration, and demonstrated that they were basically indistinguishable from each other. This result thus suggests that the reported discrepancies in the extinction stretch rates as mentioned in the work by Kee et al. [19] are simply the consequences of the "errors" associated with the evaluation of the velocity gradients. 

Traditionally, an average Sherwood number has been determined for different catalytic fixed-bed reactors assuming constant concentration or constant flux on the catalyst surface. In reality, the boundary condition on the surface has neither a constant concentration nor a constant flux. In addition, the Sh-number will vary locally around the catalyst particles and in time since mass transfer depends on both flow and concentration boundary layers. When external mass transfer becomes important at a high reaction rate, the concentration on the particle surface varies and affects both the reaction rate and selectivity, and consequently, the traditional models fail to predict this outcome. 

No slip Is used as the velocity boundary conditions at all walls. Actually there Is a finite normal velocity at the deposition surface, but It Is Insignificant In the case of dilute reactants. The Inlet flow Is assumed to be Polseullle flow while zero stresses are specified at the reactor exit. The boundary conditions for the temperature play a central role in CVD reactor behavior. Here we employ Idealized boundary conditions In the absence of detailed heat transfer modelling of an actual reactor. Two wall conditions will be considered (1) adiabatic side walls, l.e. dT/dn = 0, and (11) fixed side wall temperatures corresponding to cooled reactor walls. For the reactive species, no net normal flux Is specified on nonreacting surfaces. At substrate surface, the flux of the Tth species equals the rate of reaction of 1 In n surface reactions, l.e. 

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