Flat plate mass transfer

TABLE 5-21 Mass Transfer Correlations for a Single Flat Plate or Disk—Transfer to or from Plate to Fluid... 

Peng XF, Wang BX, Peterson GP, Ma HB (1994b) Experimental investigation of heat transfer in flat plates with rectangular micro-channels. Int J Heat Mass Transfer 37 127-137... 

For turbulent flow, we shall use the Chilton-Colburn analogy [12] to derive an expression for mass transfer to the spherical surface. This analogy is based on an investigation of heat and mass transfer to a flat plate situated in a uniform flow stream. At high Schmidt numbers, the local mass transfer rate is related to the local wall shear stress by... 

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. 

For flow parallel to an electrode, a maximum in the value of the mass-transfer rate occurs at the leading edge of the electrode. This is not only the case in flow over a flat plate, but also in pipes, annuli, and channels. In all these cases, the parallel velocity component in the mass-transfer boundary layer is practically a linear function of the distance to the electrode. Even though the parallel velocity profile over the hydrodynamic boundary layer (of thickness h) or over the duct diameter (with equivalent diameter de) is parabolic or more complicated, a linear profile within the diffusion layer (of thickness 8d) may be assumed. This is justified by the extreme thinness of the diffusion layer in liquids of high Schmidt number ... 

It is remarkable that boundary layer flow along a flat plate, much studied and well understood, has not been used in electrochemical mass-transfer... 

The analyses of simultaneous reaction and mass transfer in this geometry are similar mathematically to those of the straight cylindrical pore model considered previously, because both are essentally one-dimensional models. In the general case, the Thiele modulus for semiinfinite, flat-plate problems becomes... 

Mass transfer can produce films of nonuniform thickness because the deposition rate can depend on the velocity field u over the sohd. Regions with high whl have the highest deposition rates in a mass-transfer-hmited process. For flow over a flat plate of length L the average Sherwood number for laminar flow is given by the expression... 

Figure 9-10 Sketches of film profiles for chemical vapor deposition over a flat plate with reactant gases flowing from left to right. Reaction-limited deposition should produce a uniform film (a), while mass-transfer-limited Roi should produce a thicker film near the leading edge (b).

The reaction A, —> Bg occurs on the surface of a flat plate with a rate r" = k"CAn- The concentration of A above the boundary layer of thickness S is C/tb, and the mass transfer coefScient is... 

When heat and mass are transferred simultaneously, the two processes interact through the Gr and Gq terms in Eq. (10-12) and the energy and diffusion equations. Although solutions to the governing equations are not available for spheres, results should be qualitatively similar to those for flat plates (T4), where for aiding flows (Gr /Gq > 0) the transfer rate and surface shear stress are increased, and for opposing flows (Gr Gq < 0) the surface shear stress is predicted to drop to zero yielding an unstable flow. 

Mass Transfer in Flow along a Flat Plate with Homogeneous First-Order Reaction... 

Consider the mass transfer across a flat plate. In this case, the important variables are (dimensions in parentheses) the mass transfer coefficient k (L/T), the bulk fluid velocity u (L/T), the kinematic viscosity of the fluid v (L2/T), the solute diffusion coefficient I) (L2/T), and the plate length / (L). The number of independent variables n = 5 and the number of the involved dimensions m = 2. Hence, die number of dimensionless groups Pi = n — m = 3. 

The mass transfer from a flat plate has been studied by Spalding (S12) for both forced and free convection. 

Data acquired by many investigators have shown a close analogy between the rates of heat and mass transfer, not only in the case of packed beds but also in other cases, such as flow through and outside tubes, and flow along flat plates. In such cases, plots of the /-factors for heat and mass transfer against the Reynolds number produce almost identical curves. Consider, for example, the case of turbulent flow through tubes. Since... 

Zehnder and Trepp [23] studied the evaporation of a-tocopherol and two iso-phythols into a dense gas from a flat liquid plate (Re = 100 to 3000) and observed the surface during evaporation, with an optical fibre device. The regressed mass-transfer equation was as follows ... 

Fractionation, by definition, is simply the mass transfer between a liquid phase and a gas phase in contact with each other. A fractionation column is simply a tall, vertical, cylindrical pressure vessel that contains numerous flat internal metal plates called trays. Each tray allows liquid to flow over it, so the liquid flows from tray to tray by the force of gravity. The liquid thus enters the top tray. The liquid portion not vaporized in the column s trays is taken out in the column s bottom liquid accumulation. Gas enters the column s bottom section and flows through each tray to the top section. Entering vapor pressure is its driving force. Gas not absorbed by the liquid exits the column s top section. 

Szewczyk, A.A.. "Stability and Transition of the Free Convection Layer Along a Vertical Flat Plate", lnt. J. Heat Mass Transfer, Vol. 5, pp. 903-914, 1962. 

To. W.M. and Humphrey. J.A.C.. Numerical Simulation of Buoyant. Turbulent Flow. I. Free Convection Along a Heated, Vertical, Flat Plate . Int. J. Heat Mass Transfer, Vol. 29, pp. 573-592, 1986. 

Wickem. G., Mixed Convection from an Arbitrarily Inclined Semi-Infinite Flat Plate , lnt. J. of Heat and Mass Transfer, Vol. 34, pp. 1935-57, 1991. 

Lin, Hsiao Tsung and Chen, Yao Han, The Analogy Between Fluid Friction and Heat Transfer of Laminar Mixed Convection Flat Plates , lnt. J. Heat and Mass Transfer, Vol. 37, Nd 11, pp. 1683-1686, 1994. 

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