Equivalent Examples with Different Characteristic Length Scales

18-4 EQUIVALENT EXAMPLES WITH DIFFERENT CHARACTERISTIC LENGTH SCALES 

Radial diffusion and first-order irreversible chemical reaction in spherical catalysts can be solved analytically or numerically for the effectiveness factor when the 

Notice that the geometric factor a is unity in the effectiveness factor calculation given by equation (18-17) for all catalyst geometries when the characteristic length L is V cataiyst/6 extemai- Specifically for spheres, the dimensionless independent spatial variable rj ranges from 10 near the center of the catalyst to 3 at the external surface. 

These two example problems are identical, even thongh the characteristic length differs by a factor of 3. The exact dimensionless molar density of reactant A at the center of the catalyst is obtained from the analytical solution, given by equation (17-30) or (18-13). 

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