Internal flow, definition

The temperature of the fluid t F far away from the wall, appears in (1.23), the definition of the local heat transfer coefficient. If a fluid flows around a body, so called external flow, the temperature t F is taken to be that of the fluid so far away from the surface of the body that it is hardly influenced by heat transfer, i) F is called the free flow temperature, and is often written as diDC. However, when a fluid flows in a channel, (internal flow), e.g. in a heated tube, the fluid temperature at each point in a cross-section of the channel will be influenced by the heat transfer from the wall. The temperature profile for this case is shown in Figure 1.8. i) F is defined here as a cross sectional average temperature in such a way that t F is also a characteristic temperature for energy transport in the fluid along the channel axis. This definition of F links the heat flow from the wall characterised by a and the energy transported by the flowing fluid. 

This method also considers the stage temperatures as the independent variables. The algorithm is applied to a single-feed, two-product column with a partial condenser and reboiler. As in the original Thiele-Geddes method, the problem definition is such that the feed component flow rates, are known and fixed. The column pressure profile is also fixed, as well as its configuration, which defines the number of stages and feed location. In addition, one product rate (the distillate) and one internal flow (such as the reflux rate, Lj) are specified. The solution method, outlined below, is described in detail by Holland (1975). 

To date, no definitive explanation exists for why bag breakup occurs at low levels of aerodynamic forces and sheet-thinning breakup occurs at higher levels. Some have proposed that unstable surface waves dictate the breakup modes. However, as discussed in [4], this explanation fails to fully explain aU of the modes and is not supported by recent numerical simulations. Other possibilities may include a competition between internal flow in the deforming drop and surface tension [4], or strong backflow in the wake at high We which prevents bag growth [12]. More research is warranted. 

The first and most important single feature of a flow pattern in a container is whether slip takes place on all contact surfaces between the contents and the container walls during a fiilly developed discharge condition. If it does, it is termed mass flow by virtue of the movement of the entire mass (see Fig. 5.1). If it does not mass flow, it is often termed fimnel flow after the characteristic shape this type of flow channel takes in some cases (see Fig. 5.2), or cote flow . The first two definitions were laid down by Jenike in 1960, in his fundamental work on the gravity flow of bulk solids. Arnold Redler, in his UK and USA patents of 1920 relating to chain-type extractors, had previously defined the latter flow mode, and his term core flow is common parlance in the UK. This form is sometimes referred to as internal flow . 

Fig. 2.2 Schematic of the/i-vortex formation and definition scotch Initially the vorticity is organized spanwise at it is uniformly distributed in flow direction. By an instability process, the vorticity starts to wrap up into a vortex which by stretching takes the idealized form of a A composed mainly of two side-vortex-rods with an internal flow behaviour as described by eq.(2.2). This process ends when the vorticity cannot be concentrated anymore and viscous diffusion processes start to dominate the flow field in the event, which starts from thereon to decay. Since this model also has to account for the non-slip condition, the wall near flow can be described by a viscous tornado. Therefore the question arises whether by incorporating the model of the viscous tornado into the 1-vortex model it would be possible to describe the flow field completely.

Discrepancy between the conventional theory and the microchannel measurements of friction factor/ in gaseous flow has been attributed to compressibility [6]. In general it appears that/Re for compressible slip flow is less than that for the incompressible case [3]. In a comprehensive study of results of microscale single-phase internal flows [1], it has been found that the only definitive conclusion that can be reached from the currently available data is that gaseous slip flow data indicate an approximate 60% reduction in / compared to macroscale theory at the same Re (while for laminar non-slip water flow/ appears to be approximately 20% higher than the theoretical predictions). The finding for compressible slip flow seems to be supported by a simple analytical correlation with the factor c 0.6 0.05 [3] ... 

In order to maintain a definite contact area, soHd supports for the solvent membrane can be introduced (85). Those typically consist of hydrophobic polymeric films having pore sizes between 0.02 and 1 p.m. Figure 9c illustrates a hoUow fiber membrane where the feed solution flows around the fiber, the solvent—extractant phase is supported on the fiber wall, and the strip solution flows within the fiber. Supported membranes can also be used in conventional extraction where the supported phase is continuously fed and removed. This technique is known as dispersion-free solvent extraction (86,87). The level of research interest in membrane extraction is reflected by the fact that the 1990 International Solvent Extraction Conference (20) featured over 50 papers on this area, mainly as appHed to metals extraction. Pilot-scale studies of treatment of metal waste streams by Hquid membrane extraction have been reported (88). The developments in membrane technology have been reviewed (89). Despite the research interest and potential, membranes have yet to be appHed at an industrial production scale (90). 

The angle of internal friction, a, is defined as the equilibrium angle between flowing particles and bulk or stationary solids in a bin. Figure 4 illustrates the definition. The angle of internal friction is greater than the angle of repose. 

Dissipative systems whether described as continuous flows or Poincare maps are characterized by the presence of some sort of internal friction that tends to contract phase space volume elements. They are roughly analogous to irreversible CA systems. Contraction in phase space allows such systems to approach a subset of the phase space, C P, called an attractor, as t — oo. Although there is no universally accepted definition of an attractor, it is intuitively reasonable to demand that it satisfy the following three properties ([ruelle71], [eckmanSl]) ... 

Porter s value chain is one basis for the development of the supply chain. The term supply chain was created by consultant Keith Oliver in 1982 according to Heckmann et al. (2003). Compared to the company-internal focus of Porter s value chain, the supply chain extends the scope towards intra-company material and information flows from raw materials to the end-consumer reflected in the definition of Christopher (1992) a supply chain is a network of organizations that are involved through upstream and downstream linkages in different processes and activities that product value in the form of products and services in the hand of the ultimate consumer . Core ideas of the supply chain concept are ... 

Skeggs innovative step, the introduction of air bubbles into the flowing stream, attempted to minimize the time taken for a steady-state condition to be reached in the detector. The definitive description of dispersion in segmented streams (Snyder [37]) showed a complex relationship between internal diameter, liquid flow rate, segmentation frequency, residence time in the flow system, viscosity of the hquid and surface tension. 

The product selectivity is strongly affected by the flow rate, reactor geometry (i.e., internal diameter and "heated zone) and weight of catalyst. On this account, the space time yield to HCHO - or HCHO productivity -( HCHO Scat h ) appears to be the more definite parameter to evaluate the reactivity of the partial oxi tion catalysts. 

Assume that the water contains a radioactive substance that causes internal volumetric heat generation q (W/m3). With the objective of deriving a total energy equation for the annular flow, state the first law. Be careful with the signs and the definitions of positive heat transfer and work. 

Using the definition of enthalpy, h = e + p/p, we may combine the flow work with the internal-energy flux at the inlet and outlet to yield... 

D.J. Mason, P. Marjanovic, Re-Visit of the fundamental definitions of fluid-solids flow properties in freight pipelines, Proceedings of the 9th International Symposium on Freight Pipelines, Monterrey, Mexico, April 1998. 

Fractionation, by definition, is simply the mass transfer between a liquid phase and a gas phase in contact with each other. A fractionation column is simply a tall, vertical, cylindrical pressure vessel that contains numerous flat internal metal plates called trays. Each tray allows liquid to flow over it, so the liquid flows from tray to tray by the force of gravity. The liquid thus enters the top tray. The liquid portion not vaporized in the column s trays is taken out in the column s bottom liquid accumulation. Gas enters the column s bottom section and flows through each tray to the top section. Entering vapor pressure is its driving force. Gas not absorbed by the liquid exits the column s top section. 

The definition of RTD functions is credited to Danckwerts (55). We first differentiate between the internal RTD function g(t) dt and the external RTD function /(f) dt. The former is defined as the fraction of fluid volume in the system with a residence time between t and t + dt, and the latter is defined as the fraction of exiting flow rate with a residence time between t and t + dt. From these definitions we can define the cumulative functions G(t) and F(t), respectively, as follows ... 

Next, we define a parallel set of NPD function in continuous flow recirculating systems. We restrict our discussion to steady flow systems. Here, as in the case of RTD, we distinguish between external and internal NPD functions. We define fk and 4 as the fraction of exiting volumetric flow rate and the fraction of material volume, respectively, that have experienced exactly k passages in the specified region of the system. The respective cumulative distribution functions, and /, the means of the distributions, the variances, and the moments of distributions, parallel the definitions given for the batch system. 

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