Sherwood number, definition

Based on the Sherwood number definition and the solutions for a range of inlet velocities, evaluate the mass fraction of TMG at the surface. 

Based on the Sherwood number definition and the solutions for a range of inlet velocities, evaluate the surface mass transfer (kg/m2 s) of gallium to the surface. Assume that only gallium remains on the surface and that methyl groups desorb back to the gas,... 

This is simply the definition of the mass transfer coefficient km, the subject of mass transfer courses is to find suitable correlations in order to estimate k A (units of lengthAime). The mass transfer coefficient is in turn defined through the Sherwood number,... 

A similar definition is frequently used for the continuous phase Sherwood number... 

Careful reading of papers is required to determine which definition has been used. Measurements of the continuous phase resistance around bubbles frequently use photographic, volumetric, or pressure change techniques to yield instantaneous rates of mass transfer, and thus kA. Here too, both definitions of the Sherwood number, Eqs. (7-43) and (7-45), have been used. 

These groups have a definite, important, physical meaning. The Reynolds number is the ratio of inertial forces to viscous forces, the Sherwood number the ratio of mass transfer resistance in fluid film to mass transfer in bulk fluid, and Schmidt number the ratio of momentum diffusivity to mass diffusivity. 

As shown in Table III, several authors (Fidaleo and Moresi, 2005a Kraaijeveld et al., 1995 Kuroda et al., 1983 Sonin and Isaacson, 1974) established power function relationships between the Sherwood number (Sh) and the Reynolds (Re) and Schmidt (Sc) numbers in ED cells equipped with different eddy promoters, even if different definitions of the equivalent diameter were used to calculate the Reynolds number. 

Which is less than 2300 and thus the flow is laminar. Therefore, based on the analogy between heat and mass transfer, the Nusselt and the Sherv/ood numbers in this case are Nu = Sh = 3.66, Using the definition of Sherwood number, itie mass transfer coefficient is determined to be... 

The heat- and mass-transfer coefficients were then calculated from the definitions of the Nusselt and Sherwood numbers. 

The mass transfer coefficient for the vapor phase is computed from the definition of the Sherwood number (Eq. 12.3.39), as... 

Equation (9 274) can now be interpreted as a relationship between the Peclet number and the Sherwood number, and the constant c in (9 274) can be calculated from the definition... 

Provide three separate definitions of the Sherwood number, without using equation format. 

This definition provides a simple relation between the Sherwood number and the thickness of the diffusion layer, 5. 

The semi-empirical global transport correlation proposed by Hawthorn [15] is the most commonly used for the definition of local Nusselt and Sherwood numbers, applicable to laminar flows in square ducts ... 

The mass-transfer coefficient, kpp, may be estimated from correlations of the Sherwood number, Sh, in a packed bed (where the diameter based definition is used) ... 

The values of some of the parameters in these equations, such as the diffusion coefficient D and the characteristic length parameter d, will depend on specific models and definitions (see below). Using the definitions of the Sherwood number, Sh = kd/D, the ratio of total and molecular mass transfer (with k the mass transfer coefficient), and the Schmidt number. Sc = r]/pD the ratio of momentum and molecular mass transfer, the equation can be written as ... 

A key point about each of these groups is that its exact definition implies a specific physical system. For example, the eharaeteristic length I in the Sherwood number... 

Heat and mass transfer coefficients are usually reported as correlations in terms of dimensionless numbers. The exact definition of these dimensionless numbers implies a specific physical system. These numbers are expressed in terms of the characteristic scales. Correlations for mass transfer are conveniently divided into those for fluid-fluid interfaces and those for fluid-solid interfaces. Many of the correlations have the same general form. That is, the Sherwood or Stanton numbers containing the mass transfer coefficient are often expressed as a power function of the Schmidt number, the Reynolds number, and the Grashof number. The formulation of the correlations can be based on dimensional analysis and/or theoretical reasoning. In most cases, however, pure curve fitting of experimental data is used. The correlations are therefore usually problem dependent and can not be used for other systems than the one for which the curve fitting has been performed without validation. A large list of mass transfer correlations with references is presented by Perry [95]. 

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