Effectiveness factor

We define the effectiveness factor as the average reaction rate with diffusion divided by the average reaction rate if the rate of reaction is evaluated at the bulk-stream (or boundary condition) values. This last quantity is the average reaction rate if diffusion is very fast, presenting no limitation to the mass transfer. The effectiveness factor is thus

The parameter a = 1, 2, or 3, respectively, for planar, cylindrical, or spherical geometry. We can integration the differential equation

over the domain r = 0 to 1 to obtain

Hence, we can rewrite the effectiveness factor as

Exact solutions give the same result using both formula, but numerical or perturbation solutions may not.

For planar geometry, when the Thiele modulus approaches zero (f­>0), we get

while for large f

A typical effectiveness factor is displayed in the figure; both asymptotes are clearly visible.

figure

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