Convection flow systems

Our development in this chapter is primarily analytical in character and is concerned only with forced-convection flow systems. Subsequent chapters will present empirical relations for calculating forced-convection heat transfer and will also treat the subjects of natural convection and boiling and condensation heat transfer. 

The Grashof number may be interpreted physically as a dimensionless group representing the ratio of the buoyancy forces to the viscous forces in the free-convection flow system. It has a role similar to that played by the Reynolds number in forced-convection systems and is the primary variable used as a criterion for transition from laminar to turbulent boundary-layer flow. For air in free convection on a vertical flat plate, the critical Grashof number has been observed by Eckert and Soehngen [1] to be approximately 4 x 10". Values ranging between 10" and 109 may be observed for different fluids and environment turbulence levels. ... 

The foregoing analysis of free-convection heat transfer on a vertical flat plate is the simplest case that may be treated mathematically, and it has served to introduce the new dimensionless variable, the Grashof number, which is important in all free-convection problems. But as in some forced-convection problems, experimental measurements must be relied upon to obtain relations for heat transfer in other circumstances. These circumstances are usually those in which it is difficult to predict temperature and velocity profiles analytically. Turbulent free convection is an important example, just as is turbulent forced convection, of a problem area in which experimental data are necessary however, the problem is more acute with free-convection flow systems than with forced-convection systems because the velocities are usually so small that they are very difficult to measure. Despite the experimental difficulties, velocity measurements have been performed using hydrogen-bubble techniques [26], hot-wire anemometry [28], and quartz-fiber anemometers. Temperature field measurements have been obtained through the use of the Zehnder-Mach interferometer. The laser anemometer [29] is particularly useful for free-convection measurements because it does not disturb the flow field. 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

In this section the application of the total mass balance principles is presented. Consider some arbitrary balance region, as shown in Fig. 1.14 by the shaded area. Mass accumulates within the system at a rate dM/dt, owing to the competing effects of a convective flow input (mass flow rate in) and an output stream (mass flow rate out). 

Low-permeability passive perimeter gas control systems (Figure 16.7) effectively block gas flow into the areas of concern by using barriers (such as synthetic membranes or natural clays) between the contaminated site and the area to be protected. In the low-permeability system, gases are not collected and therefore cannot be conveyed to a point of controlled release or treatment. The low-permeability system can also alter the paths of convective flow. 

Maulbetsch, J. S., and P. Griffith, 1965, A Study of System-Induced Instabilities in Forced Convection Flows with Subcooled Boiling, MIT Engineering Projects Lab. Rep. 5382-35, Massachusetts Institute of Technology, Cambridge, MA. (5)... 

The other parameters in Eqs. (67) and (68) are evaluated in the same manner as in Section II,B,3, with the single exception of qwn. The evaluation of the wall heat flux for nucleate boiling in flowing systems has been described briefly in the reviews by Westwater (W4, W5) and Leppert and Pitts (L2). Less quantitative information is available for this case than for pool boiling. According to these authors, the heat flux in forced-convection nucleation is independent of the fluid velocity. Westwater (W5) and Roh-senow (R1) have presented a number of correlations for calculating the total heat flux in forced-convection nucleation the general form of these correlations is... 

For a flow system, streams with curved streamlines may carry angular momentum into and/or out of the system by convection. To account for this, the general macroscopic angular momentum balance applies ... 

If, indeed, Eqs. (6.171) and (6.172) adequately predict the burning rate of a droplet in laminar convective flow, the droplet will follow a d3/2 burning rate law for a given relative velocity between the gas and the droplet. In this case (3 will be a function of the relative velocity as well as B and other physical parameters of the system. This result should be compared to the d2 law [Eq. (6.172)] for droplet burning in quiescent atmospheres. In turbulent flow, droplets will appear to follow a burning rate law in which the power of the diameter is close to 1. 

Convection-based systems fall into two fundamental classes, namely those using a moving electrode in a fixed bulk solution (such as the rotated disc electrode (RDE)) and fixed electrodes with a moving solution (such as flow cells and channel electrodes, and the wall-jet electrode). These convective systems can only be usefully employed if the movement of the analyte solution is reproducible over the face of the electrode. In practice, we define reproducible by ensuring that the flow is laminar. Turbulent flow leads to irreproducible conditions such as the production of eddy currents and vortices and should be avoided whenever possible. 

Brett, C. M. A. and Brett A. M. C. F. O., Hydrodynamic Electrodes , in Comprehensive Chemical Kinetics, Vol. 27, Bamford, C. H. and Compton R. G. (Eds), Elsevier, Amsterdam, 1986, pp. 355-441. This monograph provides a thorough and useful introduction to the topics of mass transport and convection-based electrodes. It also contains one of the better discussions on flow systems, in part because it can be read quite easily despite the overall treatment being so overtly mathematical. 

The microreactor system consists of a pumping module (R2+) and a four-channel heated component (R4). Two independently conducted flow streams are mixed in a T-piece and driven through a convection-flow coil (CFC, volume 10 ml) made of poly(fluoroacetate) (PFA). After the CFC, the flow is guided through Omnifit glass columns [41] packed with immobilized scavengers. 

For similar solvent polymeric membranes (78 wt.% dicresyl butyl phosphate in polyvinyl chloride) self-diffusion coefficients of the order of 10-7 cm2s 1 have been reported.12 These diffusion coefficients, as well as measurements of rotational mobilities,14 indicate that the solvent polymeric membranes studied here are indeed liquid membranes. This liquid phase is so viscous, however, that convective flow is virtually absent. This contrasts with pure solvent membranes where an organic solvent is interposed between two aqueous solutions either by sandwiching it between two cellophane sheets or by fixing it in a hole of a Teflon sheet separating the aqueous solutions.15 The extremely high convective flow is one of the reasons why the term membrane for extraction systems... 

Free convection is fluid flow, induced by density gradients owing, for example, to temperature gradients. In gas extraction the supercritical solvent is subject to density variation with only slight changes in pressure and temperature. Furthermore, flow velocities within the processing equipment are low, so that flow owing to free convection may be important. Therefore, conditions for free convective flow must be considered in such types of systems. For isothermal vertical plates ... 

The study of rotating disk electrode behavior provides a unique opportunity to develop a model that predicts the effect of diffusion and convection on the current. This is one of the few convective systems that have simple hydrodynamic equations that may be combined with the diffusion model developed herein to produce meaningful results. The effect of diffusion is modeled exactly as it has been done previously. The effect of convection is treated by integrating an approximate velocity equation to determine the extent of convective flow during a given At interval. Matter, then, is simply transferred from volume element to volume element in accord with this result to simulate convection. The whole process repeated results in a steady-state concentration profile and a steady-state representation of the current (the Levich equation). 

The governing heat transfer modes in gas-solid flow systems include gas-particle heat transfer, particle-particle heat transfer, and suspension-surface heat transfer by conduction, convection, and/or radiation. The basic heat and mass transfer modes of a single particle in a gas medium are introduced in Chapter 4. This chapter deals with the modeling approaches in describing the heat and mass transfer processes in gas-solid flows. In multiparticle systems, as in the fluidization systems with spherical or nearly spherical particles, the conductive heat transfer due to particle collisions is usually negligible. Hence, this chapter is mainly concerned with the heat and mass transfer from suspension to the wall, from suspension to an immersed surface, and from gas to solids for multiparticle systems. The heat and mass transfer mechanisms due to particle convection and gas convection are illustrated. In addition, heat transfer due to radiation is discussed. 

The mechanism of absorption after SC or IM administration is thought to occur via the lymphatic system. The mAbs enter the lymphatic system by convective flow of interstitial fluid into the porous lymphatic vessels. The molecular mass cut-off of these pores is >100-fold the molecular mass of mAbs. From the lymphatic vessels, the mAbs are transported unidirectionally into the venous system. As the flow rate of the lymphatic system is relatively low, mAbs are absorbed over a long time period after administration. The resulting time of maximum concentration (tmax) is much later (typically 1-8 days), and the systemically available fraction (F) is equal or lower (typically 0.5-1.0) compared to the IV administration of mAbs. For example, SC injection of 40 mg adalimumab results in a tmax of approximately 5 days, and F is approximately 64%. 

For relatively porous nanofiltration membranes, simple pore flow models based on convective flow will be adapted to incorporate the influence of the parameters mentioned above. The Hagen-Poiseuille model and the Jonsson and Boesen model, which are commonly used for aqueous systems permeating through porous media, such as microfiltration and ultrafiltration membranes, take no interaction parameters into account, and the viscosity as the only solvent parameter. It is expected that these equations will be insufficient to describe the performance of solvent resistant nanofiltration membranes. Machado et al. [62] developed a resistance-in-series model based on convective transport of the solvent for the permeation of pure solvents and solvent mixtures ... 

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