Flat-plate geometry

For the simplest one-dimensional or flat-plate geometry, a simple statement of the material balance for diffusion and catalytic reactions in the pore at steady-state can be made that which diffuses in and does not come out has been converted. The depth of the pore for a flat plate is the half width L, for long, cylindrical pellets is L = dp/2 and for spherical particles L = dp/3. The varying coordinate along the pore length is x ... 

Turn now to the flat-plate geometry. The coefficients A, B, and C, and the mixing-cup averaging technique must be revised. This programming exercise is left to the reader. Run the modified program with ki = I but without... 

This velocity profile is commonly called drag flow. It is used to model the flow of lubricant between sliding metal surfaces or the flow of polymer in extruders. A pressure-driven flow—typically in the opposite direction—is sometimes superimposed on the drag flow, but we will avoid this complication. Equation (8.51) also represents a limiting case of Couette flow (which is flow between coaxial cylinders, one of which is rotating) when the gap width is small. Equation (8.38) continues to govern convective diffusion in the flat-plate geometry, but the boundary conditions are different. The zero-flux condition applies at both walls, but there is no line of symmetry. Calculations must be made over the entire channel width and not just the half-width. 

The equivalent of radial flow for flat-plate geometries is Vy. The governing equations are similar to those for Vy. However, the various corrections for Vy are seldom necessary. The reason for this is that the distance Y is usually so small that diffusion in the y-direction tends to eliminate the composition and temperature differences that cause Vy. That is precisely why flat-plate geometries are used as chemical reactors and for laminar heat transfer. 

For flat-plate geometry wher only one side of the plate is exposed to reactant gases, one may proceed as in previous subsections to show that for mechanistic equations of the form... 

Figure 8.10 (a) Representation of flat-plate geometry (b) concentration profile z) (dimensionless) for various values of Thiele modulus (j>... 

Equation 8.5-11 applies to a first-order surface reaction for a particle of flat-plate geometry with one face permeable. In the next two sections, the effects of shape and reaction order on p are described. A general form independent of kinetics and of shape is given in Section 8.5.4.5. The units of are such that is dimensionless. For catalytic reactions, the rate constant may be expressed per unit mass of catalyst (k )m. To convert to kA for use in equation 8.5-11 or other equations for d>, kA)m is multiplied by pp, the particle density. 

Repeat Example 9-1 and problem 9-1 for an isothermal particle of flat-plate geometry rep-... 

Donaldson and Snedickar (1971) studied jet impingement on flat plates as well as on convex- and concave-shaped objects. Base pressure changes were measured for all considered geometries and velocity measurements reported for the flat-plate geometry. The study indicated that wall jets are... 

The MCM has been used to simulate tubular solar photocatalytic reactors, like parabolic troughs (Arancibia-Bulnes et al., 2002a), CPC (Arancibia-Bulnes et al., 2002b), and also of flat plate geometry (Cuevas et al., 2004). Also it has been used to simulate flat lamp reactors (Brucato et al., 2006) or to obtain optical coefficients by comparison with transmission results from an experimental cell (Yokota et al., 1999). 

For flat plate geometry, the overall mass trasnfer flux,y (moles/area/ time), resulting from the total partial pressure profile over the boundary layer and across the pores is given by... 

Figure 16.9 Mixing-cup average concentration profiles for a second-order reaction in the flat-plate geometry of Figure 16.8.

Flat plate geometry, corresponding to layer deposition of porous medium on monoliths, was selected as the basis for the analysis of diffusion effects. Other catalyst geometries would yield similar results and conclusions. A component mass balance for CO in the catalyst pore under isothermal conditions yields ... 

The chains were placed on a cubic lattice and parallel flat plate geometry was assumed. 

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