Stanton number with mass transfer

Effects of Temperature on kG and k, The Stanton-number relationship for gas-phase mass transfer in packed beds, Eq. (5-301), indicates that for a given system geometry the rate coefficient kG depends only on the Reynolds number and the Schmidt number. Since the Schmidt number for a gas is approximately independent of temperature, the principal effect of temperature upon kG arises from changes in the gas viscosity with changes in temperature. For normally encountered temperature ranges, these effects will be small owing to the fractional powers involved in Reynolds-number terms (see Tables 5-17 to 5-24). It thus can be concluded that for all... 

With the matrix of low flux mass transfer coefficients related to the matrix of Stanton numbers by Eq. 10.4.25 we may write... 

FIGURE 6.44 Compressibility effects on the reduction of the Stanton number by surface mass transfer on bodies with zero axial pressure gradient and including effects of foreign gas injection. 

With the knowledge of U and I and the measured conversion of hydrogen and synthesis gas, respectively, the Stanton number is obtained from eq. (29). From the solubility data of H2 in molten paraffin provided by Peter cind Weinert (64) the overall resistance 1/K can be computed. The liquid holdup can be estimated from eq. (8) and the specific interfacial area follows from eq. (10). The liquid side mass transfer coefficient is calculated from Calderbank and Moo-Young s correlation for small bubbles, i.e. eq. (14). The H2 diffusivity in paraffin can be estimated from a relation given by Satterfield and Huff (81). With consideration of this relation eq. (14) reduces to... 

Forms of the Peclet number are shown with both column length L and particle diameter dp because both forms are used. It is obviously inportant to know whether L or dp is being enployed in the definition of Pe. Sometimes a dimensionless group called the Stanton number St, the ratio of mass-transfer velocity to flow velocity, is used. 

Other studies of mass transfer for rotating cylinders have appeared in the literature. These include outer rotating cylinders, as well as fanned, wiped, and rough cylinders. With rough surfaces in the turbulent regime, the Stanton number becomes independent of the Reynolds 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]. 

FIG U RE 12.1 Product of the mass transfer Stanton number (St = k/ut) and Schmidt number (Sc = v/D) vs plate Reynolds number (Re = u LIv) with Schmidt number as parameter (Modified from the original Higashino, M. and M.G. Stefan. 2004. Water Environmental Research 76, 292-300.) kc is the water-side mass transfer coefficient at the sediment-water interface (cmh ), V is the kinematic viscosity of water (cm h ), Z) is the diffusivity of gypsum in water (cm h ), is the friction velocity at the sediment-water interface (cmh ), L is the gypsum plate length (cm). 

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