Sherwood number wall effects

The presence of container walls has a much smaller effect on Sherwood number than on drag since the mass transfer coefficient is only proportional to the one-third power of the surface vorticity. For a sphere with given settling on the axis of a cylindrical container, the Sherwood number decreases with 2, but it is still within 8% of the Sherwood number in an infinite fluid for 2 — 0.5. No data are available to test these predictions. 

For Re > 10 there are a number of studies of the effect of walls on heat and mass transfer from solid particles in wind and water tunnels. In these studies it was customary to define a velocity ratio K based on the same Sherwood number in bounded and infinite fluids ... 

Here Kjj is obtained from Fig. 9.5. Equation (9-27) and the equations of Chapter 5 can be used to determine the decrease in Sh for a rigid sphere with fixed settling on the axis of a cylindrical tube. For example, for a settling sphere with 2 = 0.4 and = 200, Uj/Uj = 0.76 and UJUj = 0.85. Since the Sherwood number is roughly proportional to the square root of Re, the Sherwood number for the settling particle is reduced only 8%, while its terminal velocity is reduced 24%. As in creeping flow, the effect of container walls on mass and heat transfer is much smaller than on terminal velocity. 

This problem considers the chemically reactive flow in a long, straight channel that represents a section of an idealized porous media (Fig. 4.32). Assume that the flow is incompressible and isothermal, but that it carries a trace compound A. The compound A may react homgeneously in the flow, and it may react heterogeneously at the pore walls. Overall, the objective of the problem is to characterize the chemically reacting flow problem, including the development of an effective mass-transfer coefficient as represented by a Sherwood number. 

Mass transfer rates attainable In menbrane separation devices, such as gas permeators or dlalyzers, can be limited by solute transport through the menbrane. The addition Into the menbrane of a mobile carrier species, which reacts rapidly and reversibly with the solute of Interest, can Increase the membrane s solute permeability and selectivity by carrier-facilitated transport. Mass separation is analyzed for the case of fully developed, one-dimensional, laminar flow of a Newtonian fluid in a parallel-plate separation device with reactive menbranes. The effect of the diffusion and reaction parameters on the separation is investigated. The advantage of using a carrier-facilitated membrane process is shown to depend on the wall Sherwood number, tfrien the wall Sherwood nunber Is below ten, the presence of a carrier-facilitated membrane system is desirable to Improve solute separation. 

For a straight vessel, Sh cannot drop below these asymptotic values. Equation 9.19 and Equation 9.21 also indicate that the wall boundary condition has little effect on the Sherwood number. 

V is the kinematic viscosity, u the mean gas velocity in the channel, a the thermal diffusivity, Po the gas density, Cpo the heat capacity of the gas, and its thermal conductivity. Correlations (2.1) and (2.2) indicate a strong flowrate dependence. For standard monoliths and operating conditions, Sh ranges from 0.7 to 1.6, and Nu from 0.6 to 2.7 according to the correlations above. These correlations contradict the results of Heck et al. (1974) and other earlier authors on one hand, and the results of the comparison between the Graetz-Nusselt and film models on the other hand. There are several explanations to this discrepancy. As mentioned above, wall irregularity may be invoked. However, we may also invoke a non-uniform flow distribution in the monolith sample (Martin (1978)), or the effect of the small L/Dj, ratio (less than 10) and the small diameter of the monolith sample used by Votruba et al.. Here again, we see that the gas-solid transfer process is not fully understood, and that a refined and detailed description of this process is not presently possible. Consequently, we think that the Nusselt and Sherwood numbers must be considered adjustable parameters. 

Effect of Membrane Resistance The Wall Sherwood Number... 

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