Aris number zeroth

The zeroth Aris number Ana is defined as the number which becomes equivalent to 1/ if if the effectiveness factor 17 goes to zero. Hence ... 

Table 6.1 Effectiveness factor 17 as a function of the zeroth Aris number An, for first-order kinetics an infinitely long slab, an infinitely long cylinder and a sphere...

Figure 6.18 Effectiveness factor t] versus zeroth Aris number An0 for first-order kinetics in an infinite slab and several values of .

Figure 7.1 Schematic plot of the effectiveness factor versus the zeroth Aris number Ana for an exothermic nth-order reaction (n > 0 and > n). Notice the occurrence of a maximum for the effectiveness factor.

Figure 7.2 Effectiveness factor ij versus the zeroth Aris number An, for an exothermic zeroth-order reaction in an infinite slab. Lines for several values of (t a 0) are drawn.

Figure 7.4 Effectiveness factor r versus zeroth Aris number Anc for a bimolecular reaction with (1,1) kinetics occurring in an infinite slab, and for several values off).

Figure 7.7 Effectiveness facto j/ versus zeroth Aris number An for a simple, first-order reaction occurring in an infinite slab. The figure was drawn for nondiluted gases lines for several values of y are given.

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. 

When the two branches meet (concentration profile as in Figure 6.12b), the t]-An0 graph is nondifferentiable. For this specific point the zeroth Aris number has a critical value ... 

Derivation of a Formula for the Zeroth Aris Number An0 for Simple Reactions... 

Therefore, if the effectiveness factor for first-order reactions t]l is known as a function of the zeroth Aris number An0, the effectiveness factor in the high rj region can be estimated from ... 

This last number follows from the zeroth Aris number An0 for first-order reactions, by replacing the reaction rate constant k with (see the formulae in Table 6.4)... 

Since the generalized zeroth Aris number equals... 

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