External and Internal Flows

External Flow Internal Flow External and internal flows. 

A flow having some characteristics of both an external and an internal flow. 

Heat transfer involving a change of phase is classified as convective heat transfer even though when the solid phase is involved, the overall process involves combined and interrelated convection and conduction. Heat transfer during boiling, condensation, and solidification (freezing) all, thus, involve convective heat transfer. 

Convective flows are conventionally broken down into those that involve external flow and those that involve internal flow. These two types of flow are illustrated in Fig. 1.6. 

External flows involve a flow, that is essentially infinite in extent, over the outer surface of a body. Internal flows involve the flow through a duct or channel. It is not always possible to clearly place a convective heat transfer problem into one of these categories since some problems have several of the characteristics of both an internal and an external flow. An example of such a case is shown in Fig. 1.7. 

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In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

There is a fundamental difference between external and internal flows. In external flow, considered in Chapter 7, the fluid has a free surface, and thus the boundary layer over the surface is free to grow indefinitely. In internal flow, however, the fluid is completely confined by the inner surfaces of the tube, and thus there is a limit on how much Ihe boundary layer can grow. 

P = 1 yields maximum productivity under ideal conditions, while larger values provide a more robust design up to the maximum P = VKj/Ka. For a given P, external and internal flow velocities are calculated from... 

The situation is illustrated in Figiue 17.14 for an equivalent TMB and neglecting axial dispersion. Under steady-state, we have a step gradient, with a liquid phase of composition X2 in sections I and II and X3 in sections 111 and IV. These values depend on xp) and xp and also on the external and internal flow rates. They can be calculated through the mass balances of the weak solvent at the desorbent and the feed nodes. 

Here (9.44) and (9.45) are the equations of motion and (9.46) is the continuity equation for both the external and internal flows. Parameters of the current inside the drop will be denoted below by primed symbols. 

Significant deformation of the drop surface precedes the process of drop breakage. This deformation is caused by the action on the surface of stresses from external and internal flow, for which significant gradients of velocity and dynamic... 

The entire temperature progress, fr (a,T), is the subject of external and internal flows of heat and their contributions are usually reduced to that which is simply provided by externally applied temperature program, T, + f(t) u,e,, specifying the external restraint of the reaction progress in relation to the reaction rate, r ", derived from the factually measured properties of the sample. 

In this section, the detailed analysis of reacting or soluble flat plate in external and internal flow situation is presented. The analytical expression for diffusion boundary layer thickness is compared with that from the order of magnitude estimate derived in the previous section. 

In order to operate a process facility in a safe and efficient manner, it is essential to be able to control the process at a desired state or sequence of states. This goal is usually achieved by implementing control strategies on a broad array of hardware and software. The state of a process is characterized by specific values for a relevant set of variables, eg, temperatures, flows, pressures, compositions, etc. Both external and internal conditions, classified as uncontrollable or controllable, affect the state. Controllable conditions may be further classified as controlled, manipulated, or not controlled. Excellent overviews of the basic concepts of process control are available (1 6). 

Figure 4 Calibration of external and internal standard method. Chromatographic conditions — column 30 cm x 3.9 mm p-Bondapak C18 (10-pm particle size) mobile phase water acetonitrile (50 50) flow rate 1.5 ml/min column temperature ambient detector wavelength 254 nm. (A) External standard method, (B) internal standard method.

Bennett etal. have presented a model for gaseous pollution sorption by plants. The model includes all the known factors that might have a significant effect on pollution sorption by plant leaves, including gas concentration (ambient air and internal leaf), gas fluxes (external and internal), resistance to flow (leaf boundary layer, stomatal, and internal), nature of leaf surfaces (stomatal presence, cutin, and surface properties), importance of gas solubility and thus solute concentration within the leaf, and ability of the plant to metabolize pollutants (decontaminate itself). They mentioned the reactivity of ozone as another factor to consider. They believe that surface sorption may be important, at least over short periods. They presented a possible mathematical representation of these factors, which they suggested is equivalent to the mathematical statement of Ohm s law. This material is well int ated in the review by Bennett and Hill. ... 

Fig.3 A migrating zone of solute molecules (spots) interacting with lipid bilayers (rings) in a chromatographic or electrophoretic separation system. The free solute molecules move (arrows) relative to the liposomes or vesicles in a flow of eluent or in an electric field. The solute molecules may either partition into the membranes and diffuse between the external and internal aqueous compartments of the structures as depicted, or interact with the external surface of the membranes and stay outside.

The spraying device works in the following way. The prepared liquid mixture of reactive components flows to channel 3 through pipeline 4, and is distributed in a circular direction by the rotation of core 2. This movement simultaneously reduces the apparent viscosity of the liquid. Then the liquid goes to the ring nozzle 5. Porous rings 6 and 7 are placed on the external and internal surfaces of nozzle 5 at a distance of (1 - 20)h from the exit (where h is the distance between the... 

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. 

The bed void volume available for flow and for gas and liquid holdup is determined by the particle size distribution and shape, the particle porosity, and the packing effectiveness. The total voidage and the total liquid holdup can be divided into external and internal terms corresponding to interparticle (bed) and intraparticle (porosity) voidage. The external liquid holdup is further subdivided into static holdup eLs (holdup remaining after bed draining due to surface tension forces) and dynamic holdup eLrf. Additional expressions for the liquid holdup are the pore fillup Ft and the liquid saturation SL ... 

A summary of reactor models used by various authors to interpret trickle-bed reactor data mainly from liquid-limiting petroleum hydrodesulfurization reactions (19-21) is given in Table I of reference (37). These models are based upon i) plug-flow of the liquid-phase, ii) the apparent rate of reaction is controlled by either internal diffusion or intrinsic kinetics, iii) the reactor operates isothermally, and iv) the intrinsic reaction rate is first-order with respect to the nonvolatile liquid-limiting reactant. Model 4 in this table accounts for both incomplete external and internal catalyst wetting by introduction of the effectiveness factor r)Tg developed especially for this situation (37 ). 

A few reactor models have recently been proposed (30-31) for prediction of integral trickle-bed reactor performance when the gaseous reactant is limiting. Common features or assumptions include i) gas-to-liquid and liquid-to-solid external mass transfer resistances are present, ii) internal particle diffusion resistance is present, iii) catalyst particles are completely externally and internally wetted, iv) gas solubility can be described by Henry s law, v) isothermal operation, vi) the axial-dispersion model can be used to describe deviations from plug-flow, and vii) the intrinsic reaction kinetics exhibit first-order behavior. A few others have used similar assumptions except were developed for nonlinear kinetics (27—28). Only in a couple of instances (7,13, 29) was incomplete external catalyst wetting accounted for. 

If we consider the change of local entropy of a system at steady state ds/dt = 0, the local entropy density must remain constant because external and internal parameters do not change with time. However, the divergence of entropy flow does not vanish div J, = . Therefore, the entropy produced at any point of a system must be removed or transferred by a flow of entropy taking place at that point. A steady state cannot be maintained in an adiabatic system, since the entropy produced by irreversible processes cannot be removed because no entropy flow is exchanged with the environment. For an adiabatic system, equilibrium state is the only time-invariant state. 

Convection is classified as natural (or free) and forced convection, depend ing on how the fluid motion is initiated. In forced convection, the fluid is forced to flow over a surface or in a pipe by external means such as a pump or a fan. In natural convection, any fluid motion is caused by natural means such as the buoyancy effect, which manifests itself as the rise of warmer fluid and the fall of the cooler fluid. Convection is also classified a.s external and internal, depending on whether the fluid is forced to flow over a surface or in a pipe. 

For first-order reactions we can use an overall effectiveness factor to help us analyze diffusion, flow, and reaction in packed beds. We now consider a situation where external and internal resistance to mass transfer to and within the pellet are of the same order of magnitude (Figure 12-9). At steady state, the transport of the reactant(s) from the bulk fluid to the external surface of the catalyst is equal to the net rate of reaction of the reactant within and on the pellet. 

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