Cylinders mass-transfer coefficients

However, flow generated by a cylinder rotating at high speed was subsequently used by others, and in particular by King and co-workers (K3, K4a), to demonstrate that dissolution and electrochemical corrosion may both be transport limited. The dependence of the mass-transfer coefficient on the rotation rate and on the diffusivity of the dissolving species was established by correlation of experimental data (see Table VII, System 43). 

Knaff and Schlunder [9] studied the evaporation of naphthalene and caffeine from a cylindrical surface (a sintered metallic rod impregnated with the solute) to high-pressure carbon dioxide flowing over an annular space around the rod. They studied the diffusion flux within the bar and in the boundary layer. The mass-transfer coefficient owing to forced convection from cylinder to the gas flowing in the annular duct was correlated, using the standard correlation due to Stephan [7]. For caffeine, it does not require a free-convection correction, as the Reynolds dependence is that expected by a transfer by forced convection. This is... 

Silverman has defined a number of useful expressions that allow one to utilize the rotating cylinder method with a variety of practical geometries (12,15). Both shear stresses and mass transfer coefficients are included in the derivations described (12). Table 1 in NACE standard TM-0270-72 summarized the various features of experimental systems for studying flow induced corrosion (22). 

J. Rotating cylinder in an infinite liquid, no forced flow ji> = — Ngf4 = 0.07911V j 30 V Results presented graphically to NRe = 241,000. A/jjg = where v = —= peripheral velocity P 2 [E] Used with arithmetic concentration difference. Useful geometry in electrochemical studies. 112 < NRe <, 100,000. 835 < NSc < 11490 k = mass-transfer coefficient, cm/s co = rotational speed, radian/s. [60] [138] p. 238... 

Table 2. Velocity of a rotating cylinder that yields the same mass-transfer coefficients for the indicated geometries (after Silverman [21]).

The problem of transferring corrosion rate data from one hydrodynamic system to another has also been considered in some depth by Chen et al. [18], by using the corrosion of 90 10 Cu Ni alloy in aerated 1 m NaCl solution at 25 °C in pipe-flow, annular-flow, and rotating-cylinder systems. The authors recognized that two mass-transfer processes should be distinguished transfer through the diffusion boundary layer in e solution (mass-transfer coefficient, h), and transfer through the corrosion product film ( f). The overall mass-transfer coefficient was defined as... 

Rotating cylinders, described in Section 11.8, are popular experimental systems because the system setup is relatively simple to use and, at moderate rotation speeds, the flow is turbulent and yields a uniform mass-transfer-controlled current density. Empirical correlations are available that relate the cylinder rotation speed to the mass-transfer coefficient. ... 

As the previous illustrations showed, the heat and mass transfer coefficients for simple flows over a body, such as those over flat or slightly curved plates, can be calculated exactly using the boundary layer equations. In flows where detachment occurs, for example around cylinders, spheres or other bodies, the heat and mass transfer coefficients are very difficult if not impossible to calculate and so can only be determined by experiments. In terms of practical applications the calculated or measured results have been described by empirical correlations of the type Nu = f(Re,Pr), some of which have already been discussed. These are summarised in the following along with some of the more frequently used correlations. All the correlations are also valid for mass transfer. This merely requires the Nusselt to be replaced by the Sherwood number and the Prandtl by the Schmidt number. 

Schmidt give data in tree convection for wires and Satterfield and Cortez give data in forced convection for gauzes. The latter conclude that the data are better correlated according to the Reynolds number based on wire diameter (A Re.d) rather than that based on hydraulic radius. Values found were similar to values for infinite cylinders. From their work the mass transfer coefficient at low Reynolds numbers (<10 ) is proportional to Values of mass... 

For flow over a flat plate or around a cylinder or sphere, the velocity profile is linear near the surface but the gradient decreases as the velocity approaches that of the main stream at the outer edge of the boundary layer. Exact calculations show that the mass-transfer coefficient still varies with if is low or the Schmidt number pLjpD is 10 or larger. For Schmidt numbers of about 1, typical for gases, the predicted coefficient varies with a slightly lower power of Z>p. For boundary-layer flows, no matter what the shape of the velocity... 

External mass transfer, such as diffusion to particles or to the outside of pipes or cylinders, requires different correlations from those for internal mass transfer, because there is boundary-layer flow over part of the surface, and boundary-layer separation is common. The mass-transfer coefficients can be determined by studying evaporation of liquid from porous wet solids. However, it is not easy to ensure that there is no effect of internal mass-transfer resistance. Complications from diffusion in the solid are eliminated if the solid is made from a slightly soluble substance that dissolves in the liquid or sublimes into a gas. This method also permits measurement of local mass-transfer coefficients for different points on the solid particle or cylinder. 

In typical applications, pure solid naphthalene is melted and poured into a mold so it will have the desired shape such as a flat plate [127], a circular cylinder [128], or a turbine blade [129]. For average mass transfer measurements on a test surface, the section coated with naphthalene can be weighed before and after exposure to air flow to determine the mass transfer rate. Local mass transfer coefficients can be determined from the sublimation depth, which is the difference in surface profiles, measured using a profilometer, before and after each test run. Once the vapor density of naphthalene is known, the local mass transfer coefficient hD can be evaluated from the following expression ... 

Estimate convective mass-transfer coefficients for the following situations (a) flow paralell to a flat surface, (b) flow past a single sphere, (c) flow normal to a single cylinder, (d) turbulent flow in circular pipes, (e) flow through packed and fluidized beds, and (f) flow through the shell side of a hollow-fiber membrane module. 

In theory it is not necessary to have experimental mass-transfer coefficients for laminar flow, since the equations for momentum transfer and for diffusion can be solved. However, in many actual cases it is difficult to describe mathematically the laminar flow for geometries, such as flow past a cylinder or in a packed bed. Hence, experimental mass-transfer coefficients are often obtained and correlated. A simplified theoretical derivation will be given for two cases in laminar flow. 

As noted above, the mass transfer kinetics of temperature gradient loops are usually described with reference to dissolution in the hot leg. It is possible to quantitatively study the dissolution step using the rotating cylinder technique. Unlike loop studies, this technique allows one to study dissolution in a system where the hydrodynamic conditions are fully defined. Experimentally, solid cylinders of the test material are rotated at various speeds in an isothermal liquid-metal bath. Changes in the concentration of solid in the liquid and changes in the cylinder radius are determined as a function of time. With these data it is possible to determine the mass transfer coefficient and the rate-controlling step for dissolution. 

A falling film reactor is essentially a vertical cylinder, where liquid flows downward in a thin film along the wall, and gas flows in the core. Relatively high mass transfer coefficients are obtained both in the liquid and in the gas phases. The liquid phase can be cooled effectively via the wall. Therefore this type of reactor is preferred for very rapid exothermic gas liquid reactions. There are two variations, one consists of a tube bundle, the other consists of one cylinder with a rotor. 

Particularly when fluids flow past immersed objects, the local mass-transfer coefficient varies with position on the object, due especially to the separation of the boundary layer from the downstream surfaces to form a wake. This phenomenon has been studied in great detail for some shapes, e.g., cylinders [8]. The average mass-transfer coefficient in these cases can sometimes best be correlated by adding the contributions of the laminar boundary layer and the wake. This is true for the second entry of item 5, Table 3.3, for example, where these contributions correspond respectively to the two Reynolds-number terms. 

C.4. Instead of assuming a given Sherwood nnmber for the external mass transfer coefficients, use FEMLAB to compute the laminar velocity profile aronndthe cylinder to directly model the effect of forced convection on the external mass transfer rate. Report your results for Reynolds numbers of 10 ", 10, 10, 1, 10, using a viscosity jx = 10 Pas and density p = lO kg/m ... 

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