Exothermic, Zeroth-order Reaction in a Ring-shaped Catalyst

11 Exothermic, Zeroth-order Reaction in a Ring-shaped Catalyst 

A zeroth-order reaction is carried out in a ring-shaped catalyst. The following numbers have been evaluated from measurements  

For this situation the Aris numbers follow from (Equations 7.13 and 7.14) 

Since An 0, approximation 6.59 cannot be used. To calculate the effectiveness factor exactly involves solving partial differential equations, which is very time consuming. The effectiveness factor is therefore estimated as follows construct an infinite slab in such a way, that for an exothermic zeroth-order reaction, it has the same Aris numbers as given above. Since the Aris numbers are generalized the hollow cylinder under consideration and the constructed slab will have almost the same effectiveness factor. Calculation of the effectiveness factor for a slab is relatively easy. Hence an estimate for the effectiveness factor for the hollow cylinder is obtained relatively easily. 

construct the slab. Changing the geometry from a hollow cylinder to a slab changes the geometry factor from T = 1.11 to T=2/3. To arrive at the same Aris numbers we must change the values of f 2 en . For the slab those values follow from  

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