Sherwood number natural convection

Each of these is a ratio of a convective transfer rate to the corresponding diffusion rate of transfer. Dimensionless analysis indicates that, for fixed geometry and constant properties, the Nusselt number and the Sherwood number depend on the Reynolds number (forced convection), Rayleigh number (natural convection), flow characteristics, Prandtl number (heat transfer), and Schmidt number (mass transfer). 

This relationship indicates that the Sherwood number takes the value 2 for Ap 0, as is the case in natural convection. A generalized correlation for mass and heat transfer coefficients is recommended by Calderbank and Moo-Young (1961). This correlation relates the mass-transfer coefficient to the power per unit volume and Schmidt number. The relationship is mainly applicable to low-viscosity liquids. 

In natural convection mass transfer, the analogy betsveen the Nusselt and Sherwood numbers still holds, and thus Sh =y(Gr, Sc). But the Grashof number in this case should be determined directly from... 

A common approach to mixed convection is to compute the Sherwood number as the sum of the powers of pure natural and forced convection (18) ... 

Combined forced and free convection at a vertical flat plate, where the forced convection velocity is in the same direction as the natural convection flow (the so-called assisting mixed convection case). Here, researchers have combined Sherwood numbers for the pure forced and natural convection cases in the following way [15, 24-26] ... 

Karabelas et al." reviewed many of the published correlations for fixed-bed coefficients and proposed different correlations to be used depending on the flow regime that is, at low Reynolds number the effects of molecular diffusion and natural convection must be considered. Kato et al. reviewed mass transfer coefficients in fixed and fluid beds and observed considerable deviations from established correlations in both the literature and their own data for Re < 10. In some cases it appeared that the limiting Sherwood number could be less than 2 for gas-particle transfer. They suggested that for small Re and Sc i the concentration boundary layers of the individual particles in a fixed bed would overlap considerably. They proposed two correlations for different flow regimes which also inclutted a particle diameter to bed height term. 

Presenting the process model as a mass transfer correlation is also conunon. This requires an understanding of the process s physical properties, namely, the density and viscosity of the SC-CO2 and the mass diffusion of the solute in SC-CO2. Dimensionless numbers, namely, Reynolds (Re) (Equation 5.16), which is related to fluid flow Schmidt (Sc) (Equation 5.17), which is related to mass diffusivity Grashof (Gr) (Equation 5.18), which is related to mass transfer via buoyancy forces due to difference in density difference between saturated SC-CO2 with solute and pure SC-CO2 and Sherwood (Sh) (Equation 5.19), which is related to mass transfer, are important in these correlations. In supercritical extraction, natural convection is not significant (Shi et al., 2007) and in this case, Shp is related only to Re and Sc, as shown in Equation 5.19. 

In addition, the Sherwood Number Sh can be semi-empirically defined for natural (free) and forced convection for the case shown in Figure 7.17. 

Friedlander [10] has demonstrated on the basis of theoretical considerations that at low Reynolds numbers and in the absence of natural convection, the Sherwood number is given by the following ... 

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