Effectiveness factor for first-order irreversible reaction-diffusion system

This linear differential equation has the general solution 

The effectiveness factor 17 is a measure of how much the reaction rate is lowered because of the diffusion resistance, and Eq. (9.24) is defined by 

Coupled systems of chemical reactions and transport processes 

For a spherical pellet, from the steady-state mass balance 

For a cylinder and other geometries, a general modulus for a first-order reaction is 

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Example 9.3 Effectiveness factor for first-order irreversible reaction-diffusion system Consider a first-order reaction occurring on the pore walls of a catalyst with equimolar counter diffusion. Assume that isothermal conditions are maintained, and a catalyst with simple slab geometry is used (Figure 9.1). If the -coordinate is oriented from the centerline to the surface, the steady-state reaction diffusion equation for reaction A — B between reactant A and product B is... 

Example 9.2 Effectiveness factor for first-order irreversible reaction-diffusion system... 

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