Forced convection Schmidt number

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). 

For problems involving gradients in chemical species, the convection-diffusion equations for the species are also solved, usually for N— 1 species with the Nth species obtained by forcing the mass fractions to sum to unity. Turbulence can be described by a turbulent diffusivity and a turbulent Schmidt number, Sct, analogous to the heat transfer case. 

Frossling studied vaporizing droplets without combustion and found that KjK = 1 + 0.276 Re Sc, where Sc is the Schmidt number (Appendix E), Re is the Reynolds number, and is the value of K for evaporation in the same atmosphere without forced convection. Here... 

For a given geometry, the average Nusselt number in forced convection depends on the Reynolds and Prandtl numbers, whereas the average Sherwood number depends on the Reynolds and Schmidt numbers. That is. 

This relation is analogous to the expression for the heat transfer by forced convection given earlier. The dimensionless group kd/D corresponds to the Nusselt group in heat transfer. The parameter rj/pD is known as the Schmidt number and is the mass-transfer counterpart of the Prandtl number. For example, the evaporation of a thin liquid film at the wall of a pipe into a turbulent gas is described by the equation... 

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... 

In this chapter, we return to forced convection heat and mass transfer problems when the Reynolds number is large enough that the velocity field takes the boundary-layer form. For this class of problems, we find that there must be a correlation between the dimensionless transport rate (i.e., the Nusselt number for heat transfer) and the independent dimensionless parameters, Reynolds number Re and either Prandtl number Pr or Schmidt number Sc of the form... 

The Sherwood. Re noldx, and Schmidt numbers are used in forced convection mass transfer currctalions. 

Dissolution rate data obtained under forced convection conditions can be correlated by means of equation 6.64 or 6.65. As described in section 6.2.2, equation 6.64 is the preferred relationship on theoretical grounds, since Sh = 2 for mass transfer by convection in stagnant solution (Re = 0), whereas equation 6.65 incorrectly predicts a zero mass transfer rate (Sh = 0) for this condition. However, at reasonably high values of Sh (>100) the use of the simpler equation 6.65 is quite justified. The exponent of the Schmidt number b is usually taken to be and for mass transfer from spheres the exponent of the Reynolds number a =... 

For forced convection, Sh is calculated on the basis of the Reynolds number Re and the Schmidt number S. For laminar flow and Re < 50, the following correlation is valid for cylindrical cmcibles with an overflow of a gas ... 

Preparatory work for the steps in the scaling up of the membrane reactors has been presented in the previous sections. Now, to maintain the similarity of the membrane reactors between the laboratory and pilot plant, dimensional analysis with a number of dimensionless numbers is introduced in the scaling-up process. Traditionally, the scaling-up of hydrodynamic systems is performed with the aid of dimensionless parameters, which must be kept equal at all scales to be hydrodynamically similar. Dimensional analysis allows one to reduce the number of variables that have to be taken into accoimt for mass transfer determination. For mass transfer under forced convection, there are at least three dimensionless groups the Sherwood number, Sh, which contains the mass transfer coefficient the Reynolds number. Re, which contains the flow velocity and defines the flow condition (laminar/turbulent) and the Schmidt number, Sc, which characterizes the diffusive and viscous properties of the respective fluid and describes the relative extension of the fluid-dynamic and concentration boundary layer. The dependence of Sh on Re, Sc, the characteristic length, Dq/L, and D /L can be described in the form of the power series as shown in Eqn (14.38), in which Dc/a is the gap between cathode and anode Dw/C is gap between reactor wall and cathode, and L is the length of the electrode (Pak. Chung, Ju, 2001) ... 

In a forced-convection system, the Sherwood number is a function of the Reynolds number, Re, and the Schmidt number. Sc. 

In view of the convection induced by the ion mass transfer, the force responsible for the momentum transfer is proportional to the product of the Grashoff and Schmidt numbers ... 

The correlations for fluid-solid interfaces often show mathematical forms like those for fluid fluid interfaces. The mass transfer coefficient is most often written as a Sherwood number, though occasionally as a Stanton number. The effect of diffusion coefficient is most often expressed as a Schmidt number. The effect of flow is most often expressed as a Reynolds number for forced convection, and as a Grashof number for free convection. 

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. 

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