Spherical catalysts critical Damkohler number

TABLE 16-2 Effect of the Intrapellet Damkohler Number on the Critical Dimensionless Radius for Radial Diffusion and Pseudo-Homogeneous Zeroth-Order Chemical Kinetics in Porous Catalysts with Spherical Symmetry... 

Problem. Consider zeroth-order chemical kinetics in pellets with rectangular, cylindrical and spherical symmetry. Dimensionless molar density profiles have been developed in Chapter 16 for each catalyst geometry. Calculate the effectiveness factor when the intrapellet Damkohler number is greater than its critical value by invoking mass transfer of reactant A into the pellet across the external surface. Compare your answers with those given by equations (20-50). 

Catalysts with Spherical Symmetry. This analysis is based on the mass transfer equation with diffusion and chemical reaction in spherical catalysts. For zeroth-order kinetics, the molar density of reactant A is equated to zero at the critical value of the dimensionless radial coordinate, iciiticai = /(A). The relation between the critical value of the dimensionless radial coordinate and the intrapellet Damkohler number is obtained by solving the following nonlinear algebraic equation ... 

Obtain an analytical expression for the effectiveness factor (i.e., E vs. tjcriticai) in Spherical catalysts when the chemical kinetics are zeroth-order and the intrapeUet Damkohler number is greater than its critical value. Use the definition of the effectiveness factor that is based on mass transfer via diffusion across the external surface of the catalyst. 

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