Similar flows natural convection

Open Tube Sections (Air Cooled) Plain or finned tubes No shell required, only end heaters similar to water units. Condensing, high level heat transfer. Transfer coefficient is low, if natural convection circulation, but is improved with forced air flow across tubes. 0.8-1.8... 

The flow artifacts detected in the droplet size measurements are similar to those reported by Goux et al. [79] and Mohoric and Stepisnik [80]. In their work natural convection effects led to an increase in the decay of signal attenuation curves, causing over-prediction in the self-diffusion coefficient of pure liquids. In order to avoid flow effects in droplet size distributions, flow compensating pulse sequences such as the double PGSTE should be used. It has been demonstrated recently that this sequence facilitates droplet size measurements in pipe flows [81]. 

The interaction of forced and natural convective flow between cathodes and anodes may produce unusual circulation patterns whose description via deterministic flow equations may prove to be rather unwieldy, if possible at all. The Markovian approach would approximate the true flow pattern by subdividing the flow volume into several zones, and characterize flow in terms of transition probabilities from one zone to others. Under steady operating conditions, they are independent of stage n, and the evolution pattern is determined by the initial probability distribution. In a similar fashion, the travel of solid pieces of impurity in the cell can be monitored, provided that the size, shape and density of the solids allow the pieces to be swept freely by electrolyte flow. 

Intershell flow is the slowest step in a V-blender because it is dispersive in nature while intrashell flow is convective. Both processes can be described by similar mathematics, typically using an equation such as... 

Eqs. (8.120) and (8.121) represent the limiting boundary layer solution for natural convective flow through a vertical plane duct. For the particular case of Pr = 0.7, the similarity solution for natural convective boundary layer flow on a vertical plate... 

Available analyses of turbulent natural convection mostly rely in some way on the assumption that the turbulence structure is similar to that which exists in turbulent forced convection, see [96] to [105]. In fact, the buoyancy forces influence the turbulence and the direct use of empirical information obtained from studies of forced convection to the analysis of natural convection is not always appropriate. This will be discussed further in Chapter 9. Here, however, a discussion of one of the earliest analyses of turbulent natural convective boundary layer flow on a flat plate will be presented. This analysis involves assumptions that are typical of those used in the majority of available analyses of turbulent natural convection. 

To proceed further, relationships for the wall shear stress, tw> and the wall heat transfer rate, qw, must be assumed. It is consistent with the assumption that the flow near the wall in a turbulent natural convective boundary layer is similar to that in a turbulent forced convective boundary layer to assume that the expressions for tw and qw that have been found to apply in forced convection should apply in natural convection. It will therefore be assumed here that the following apply in a natural convective boundary layer ... 

The set of three partial differential equations (the continuity, momentum, and the energy equations) iliai govern natural convection flow over vertical isothermal plates can be reduced to a set of two ordinarj nonlinear differential equations by the introduction of a similarity variable. But the resulting equations must still be solved numerically [Ostrach (1953)]. Interested readers arc referred to advanced books on the topic for detailed discussions [e.g., Kays and Crawford (1993)],... 

Consider a heated vertical plate in a quiescent fluid. The plate heats the fluid in its neighborhood, which then becomes lighter and moves upward. The force resulting from the product of gravity and density difference and causing this upward motion is called buoyancy. The fluid moving under the effect of buoyancy develops a vertical boundary layer about the plate. Within the boundary layer the temperature decreases from the plate temperature to the fluid temperature, while the velocity vanishes on the plate walls and beyond the boundary layer and has a maximum in between (Fig. 5.13). Actually, in a manner similar to forced convection, the momentum boundary layer of natural convection is expected to be thicker for larger Prandtl numbers than the thermal boundary layer. However, the characteristic velocity for the enthalpy flow across should be scaled relative to Ss rather than 5,... 

Convection, sometimes identified as a separate mode of heat transfer, relates to the transfer of heat from a bounding surface to a fluid in motion, or to the heat transfer across a flow plane within the interior of the flowing fluid. If the fluid motion is induced by a pump, a blower, a fan, or some similar device, the process is called forced convection. If the fluid motion occurs as a result of the density difference produced by the temperature difference, the process is called free or natural convection. 

In the case of airlift reactors, the flow pattern may be similar to that in bubble columns or closer to that two-phase flow in pipes (when the internal circulation is good), in which case the use of suitable correlations developed for pipes may be justified [55]. Blakebrough et al. studied the heat transfer characteristics of systems with microorganisms in an external loop airlift reactor and reported an increase in the rate of heat transfer [56], In an analytical study, Kawase and Kumagai [57] invoked the similarity between gas sparged pneumatic bioreactors and turbulent natural convection to develop a semi-theoretical framework for the prediction of Nusselt number in bubble columns and airlift reactors the predictions were in fair agreement with the limited experimental results [7,58] for polymer solutions and particulate slurries. 

Mass transfer in laminar flow in a tube. We consider the case of mass transfer from a tube wall to a fluid inside in laminar flow, where, for example, the wall is made of solid benzoic acid which is dissolving in water. This is similar to heat transfer from a wall to the flowing fluid where natural convection is negligible. For fully developed flow, the parabolic velocity derived as Eqs. (2.6-18) and (2.6-20) is... 

A difference which might be anticipated, so far as size is concerned, is the response of the system as the function of height above the bottom. It appears from our results that in our experimental system we still are experiencing the influence of the bottom corner. In tanks of larger size, for heights to radius ratios equivalent to ours, it is entirely possible that one would be removed from the influence of the bottom corner, which would result in a free-convection process more similar to that of turbulent flow over vertical flat plates in natural convection. 

Mixing processes and 3-D natural convection flow is important for deboration accidents for PWRs. For BWRs similar complicated flow fields exist for sequences with boron injection. For these processes experiments with detailed instrumentation are underway the data can be used also for code validation. 

For a number of flow situations, the mass-transfer rate can be derived directly from the equation of convective diffusion (see Table VII, Part A). The velocity profile near the electrode is known, and the equation is reduced to a simpler form by appropriate similarity transformations (N6). These well-defined flows, therefore, are being exploited increasingly by electrochemists as tools for the kinetic characterization of electrode reactions. Current distributions at, or below, the limiting current, transient mass transfer, and other aspects of these flows are amenable to analysis. Especially noteworthy are the systematic investigations conducted by Newman (review until 1973 in N7 also N9b, N9c, H6b and references in Table VII), by Daguenet and other French workers (references in Table VII), and by Matsuda (M4a-d). Here we only want to comment on the nature of the velocity profile near the electrode, and on the agreement between theory and mass-transfer experiment. 

Synthesis of nano-structured alloys by the inert gas evaporation technique A precursor material, either a single metal or a compound, is evaporated at low temperature, producing atom clusters through homogeneous condensation via collisions with gas atoms in the proximity of a cold collection surface. To avoid cluster coalescence, the clusters are removed from the deposition region by natural gas convection or forced gas flow. A similar technique is sputtering (ejection of atoms or clusters by an accelerated focused beam of an inert gas, see 6.9.3). 

In general, it can be very difficult to determine the nature of the boundary terms. A specific result in an exactly solvable case is discussed in Section IV.A.2. Equation (55) is the Gallavotti-Cohen FT derived in the context of deterministic Anosov systems [28]. In that case, Sp stands for the so-called phase space compression factor. It has been experimentally tested by Ciliberto and co-workers in Rayleigh-Bemard convection [52] and turbulent flows [53]. Similar relations have also been tested in athermal systems, for example, in fluidized granular media [54] or the case of two-level systems in fluorescent diamond defects excited by light [55]. 

Movement of the Huid may be generated by means external to the heat transfer process, us by fans, blowers, or pumps. It may also be created by density differences connected with the heat transfer process itself. The first mode is culled timet cniireeiirtn the second one natural or free t ttttveclion. Convection heal transfer may also be classified as heat transfer in iltni /fnn. or in interna flow (over cylinders, spheres, air foils, and similar objects). In ilie case of external flow, the heal transfer process is essentially concentrated in a thin fluid layer surrounding the object (boundary layer . 

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