Free convection mass transfer

Of course, in free-convection mass transfer the transition time is dependent on the density difference generated at the electrode. The dimensionless time variable of the transient process is... 

In free-convection mass transfer at electrodes, as well as in forced convection, the concentration (diffusion) boundary layer (5d extends only over a very small part of the hydrodynamic boundary layer <5h. In laminar free convection, the ratio of the thicknesses is... 

Grashof number, Grm (mass transfer) gp L P Ax P coefficient of density change with concentration Ax concentration of driven force / buoyancy force V viscous force / Free convection mass transfer... 

Concentration difference driven free convection mass transfer. Analogous to the previous development of thermal density driven free convection, density variations also occur near fluid-solid interfaces as a result chemical concentration difference. These density imbalances generate fluid motion that enhances chemical transport is a more subtle conduction process. For example, at the aquatic boundary layer, chemical concentrations in the interface fluid may be very different from those in the water column above. This in turn produces a water density difference, ACa (kg/m ), where Ca is the concentration in water. Similar to the thermal coefficient of volume expansion given by Equation 2.26 it is termed the mass coefficient of volume expansion defined as... 

The effective diffusivities determined from limiting-current measurements appear at first applicable only to the particular flow cell in which they were measured. However, it can be argued plausibly that, for example, rotating-disk effective diffusivities are also applicable to laminar forced-convection mass transfer in general, provided the same bulk electrolyte composition is used (H8). Furthermore, the effective diffusivities characteristic for laminar free convection at vertical or inclined electrodes are presumably not significantly different from the forced-convection diffusivities. 

The usual specific flow-rates for extraction are very small. In terms of space velocities, these are about 5 to 15 kg/h per litre of extractor volume, with superficial velocities in the range of 0.5 to 10 mm/s. With these small velocities, natural convection mass transfer is the favoured mechanism of transport. Gas densities are in the range of 500 to 800 kg/m3, and viscosities are about 5 x 10 7 kg/(m s), thus giving kinematic viscosities of about 10 9 m2/s, which is a very small value for a fluid. For example, the kinematic viscosity of water is 10"7 m2/s and that of ambient air is 2 x 10 5 m2/s. This makes free convection a principal mechanism for mass-transfer in high pressure gases. 

Yen, Y.C., Effects of Density Inversion on Free Convective Heat Transfer in Porous Layer Heated from Below , Int. J. Heat Mass Transfer. Vol. 17. pp. 1349-1356,... 

Singh, S. N., R. C. Birkebak, and R. M. Drake Laminar Free Convection Heat Transfer from Downward-facing Horizontal Surfaces of Finite Dimensions, Prog. Heat Mass Transfer, vol. 2, p. 87, 1969. 

Hollands, K. G. T., G. D. Raithby, and L. Konicek Correlation Equations for Free Convection Heat Transfer in Horizontal Layers of Air and Water, Int. J. Heat Mass Transfer, vol. 18, p. 879, 1975. 

In the preceding chapters we considered forced and free convection heal transfer involving a single phase of a fluid. The analysis of such convectior processes involves tlie thermophysical properties p, p, k, and Cp of the fluid The analysis of boiling heat transfer involves these properties of the liquic (indicated by the subscript 0 or vapor (indicated by the subscript v) as well a the properties (the latent heat of vaporization) and cr (the surface tension) The hf represents the energy absorbed as a unit mass of liquid vaporize ... 

Since convective mass transfer is negligible in porous catalytic pellets, it is reasonable to let /i = 0 in (21-47) and add the diffusivities inversely. If the pore diameter is much smaller than the mean free path of the gas, then colhsions with the walls are more frequent than collisions with other molecules, and Knudsen diffusion provides the dominant resistance. If the pores are much larger than the mean free path, then collisions with other molecules are more frequent than colhsions with the walls of the channel, and ordinary molecular diffusion provides the dominant resistance. Usually, one arrives at a sum of resistauces in series by following the trajectory of a single gas molecule within a catalytic pore. It is important to emphasize that one obtains the correct result by tracking a single molecule only if there are no other pathways by which diffusion supplies the... 

Figure 7.16 shows Crank s idealized model [25] for moving boundaries towards an aqueous bulk of solution and schematic concentration distribution. This diffusion problem requires that the medium be free of convective mass transfer and that boundary motion occurs along stationary xj and X2 axes. In this case, the boundary motion occurs perpendicular to x and x. ... 

The convection mass transport of species i may also take place if there exists a bulk fluid motion. The convection mass transfer is analogous to convection heat transfer and occurs between a moving mixture of fluid species and an exposed solid surface. Like hydrodynamic and thermal boundary layers, a concentration boundary layer forms over the surface if the free stream concentration of a species i, differs from species concentration at the surface, Qs, in an external flow over a solid surface as demonstrated in Figure 6.13. 

Like free convective heat transfer, the mass transport in gases is supported by free convection due to the very low cinematic viscosity data at high pressures. 

Free convection heat transfer as a source of forced convection mass transfer. It has been demonstrated on numerous occasions that the Chilton-Colburn analogy appearing in Table 2.3 is applicable for converting a forced-convection Nusselt number to a forced-convection Sherwood number as a means of converting the imbedded HTC into its equivalent MTC. In the present situation, the thermal buoyant forces provide the momentum source, which in effect provides the forced-convective flow that drives the mass transfer process. In addition, Grj Gta and Sc > Pr. For this case the alternative equation is... 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

Kato H NtSHtWAKi, N. and Hirata, M. Im. Jl. Heat Mass Transfer 11 (1968) 1117. On the turbulent heat transfer by free convection from a vertical plate. 

Garner, F.H. andKEEY, R.B. Chem. Eng. Sci. 9 (1959) 218. Mass transfer from single solid spheres — H. Transfer in free convection. 

In binary solutions, for example, CuS04 in H20, the limiting current exceeds that due to convective diffusion alone by a factor of about two. The excess mass transfer is caused by migration of the reacting ion in the electric field. In both forced and free convection it is important to know the ion flux contributed by migration, which can never be suppressed completely. 

The diffusivities thus obtained are necessarily effective diffusivities since (1) they reflect a migration contribution that is not always negligible and (2) they contain the effect of variable properties in the diffusion layer that are neglected in the well-known solutions to constant-property equations. It has been shown, however, that the limiting current at a rotating disk in the laminar range is still proportional to the square root of the rotation rate if the variation of physical properties in the diffusion layer is accounted for (D3e, H8). Similar invariant relationships hold for the laminar diffusion layer at a flat plate in forced convection (D4), in which case the mass-transfer rate is proportional to the square root of velocity, and in free convection at a vertical plate (Dl), where it is proportional to the three-fourths power of plate height. 

Transition Times (sec) to Steady-State Mass Transfer in Laminar Free and Forced Convection along a Planar Electrode, for a Solution of 0.05 M CuS04, 1.5 M H2S04 at 25°C ... 

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