Mass transfer fluid cylinders

It was shown above that the limiting c.d. increases with velocity raised to the 0.8 power and the pipe diameter raised to the -0.2 power for piping corrosion rates that are controlled by mass transport. In contrast, it is evident that the shear stress increases with the fluid velocity raised to the 1.75 power and the pipe diameter raised to the -0.2 power. Thus equality of shear stress does not give equality of mass transfer rates. In both cases corrosion is enhanced in pipes of smaller diameter for the same solution velocity. Such a relationship can be rationalized based on the effect of pipe diameter on the thickness of the mass transport and hydrodynamic boundary layers for a given fixed geometry. Cameron and Chiu (19) have derived similar expressions for defining the rotating cylinder rotation rate required to match the shear stress in a pipe for the case of velocity-... 

The rotating cylinder is a popular tool for electrochemical research because it is convenient to use and both the primary and mass-transfer-limited current distributions are uniform.A schematic representation of the rotating cylinder is presented in Figure 11.12. At very low rotation speeds, the fluid flows in concentric circles around the rotating cylinder, satisfying a no-slip condition at the rotating inner cylinder and at the stationary outer cylinder. Since there is no velocity component in the radial direction, there is no convective enhancement to mass transfer. 

Yang etal. report an experimental and computational study of mass transfer to a channel wall downstream of a cylinder. The rate of mass transfer was recorded at various locations. Ferricyanide reduction at a mass-transfer-controlled rate from an electrolyte containing a large amount of KCl was used for the experimental measurements. A diagram of the cell is shown in Fig. 7. A cylinder of diameter d is placed a distance b from the bottom wall, and a working electrode of length 2L is placed at a distance x downstream of the center of the cylinder. The fluid flow can be characterized with a Reynolds number defined as... 

N. A. Frankel and A. Acrivos, Heat and mass transfer from small spheres and cylinders freely suspended in shear flow, Phys. Fluids 11, 1913-18 (1968). 

Note that in some problems of heat and mass transfer and chemical hydrodynamics, the velocity fields near the body can be determined by the flow laws of ideal nonviscous fluid. This situation is typical of flows in a porous medium [75, 153, 346] and of interaction between bodies and liquid metals (see Section 4.11, where the solution of heat problem for a translational ideal flow past an elliptical cylinder is given). 

Freely rotating cylinder. Now let us consider convective mass transfer to the surface of a circular cylinder freely suspended in an arbitrary linear shear Stokes flow (Re -> 0). In view of the no-slip condition, the cylinder rotates at a constant angular velocity equal to the angular velocity of the flow at infinity. The fluid velocity distribution is described by formulas (2.7.11). The streamline pattern qualitatively differs from that for the case of a fixed cylinder. For 0 0, there are no stagnation points on the surface of the cylinder and there exist two qualitatively different types of flow. For 0 < Ifigl < 1, there are both closed and open streamlines in the flow, the region filled with closed streamlines is adjacent to the surface of the cylinder, and streamlines far from the cylinder are open (Figure 2.11). For Ifl l > 1, all streamlines are open. 

It is useful to mention another class of problems related to those referred to in the previous paragraphs, but that is not considered here. We do not try to answer the ques- tion of how fast a system will respond to a change in constraints that is, we do not try to study system dynamics. The answers to such problems, depending on the system and its constraints, may involve chemical kinetics, heat or mass transfer, and fluid mechanics, all of which are studied elsewhere. Thus, in the example above, we are interested in the final state of the gas in each cylinder, but not in computing how long a valve of given size must be held open to allow the necessary amount of gas to pass from one cylinder to the other. Similarly, when, in Chapters 10, 11, and 12, we study phase equilibrium and, in Chapter 13, chemical equilibrium, our interest is in the prediction of the equilibrium state, not in how long it will take to achieve this equilibrium state. —... 

O. Miyatake, and H. Iwashita, Laminar-Flow Heat Transfer to a Fluid Flowing Axially Between Cylinders with a Uniform Surface Temperature, Int. 1 Heat Mass Transfer, (33) 417-425,1990. 

Example 2.6 Mass Transfer to Fluid Flow Normal to a Cylinder... 

Answer Begin with the equation of continuity and the mass transfer equation in cylindrical coordinates with two-dimensional flow (i.e., Vr and vq) in the mass transfer boundary layer and no dependence of Ca on z because the length of the cylinder exceeds its radius by a factor of 100. Heat transfer results will be generated by analogy with the mass transfer solution. The equations of interest for an incompressible fluid with constant physical properties are... 

The limited work on heat and mass transfer between power-law fluids and cylinders with their axis normal to the flow has been summarised recently by Ghosh et al. [1994] who proposed the following correlation for heat and mass transfer ... 

In a continuous system, the band of drying material is transported in a serpentine fashion through the fluidized bed of sorbent particles. Heat required for moisture release from the sorbent to fluidizing air is supplied by immersed heaters. The use of fluidized beds of active particles enhances not only the convective but also material-sorbent, sorbent-sorbent, and sorbent-heater contact heat/mass transfer rates. Comparison of the fluid bed dryer with inert sorbent with the cylinder dryer is given in Table 12.1. 

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