Runaway insensitive

If AT between gas and wall is incrementally larger than this, a runaway starts. It remains insensitive if it is incrementally lower. This is shown on Figure 9.7.2 and with the temperature derivatives on 9.7.3 and 9.7.4 (figures Bashir et al 1992). 

This result means that the reactor is insensitive if the temperature profile is concave toward the reactor length axis, and the inflection point is avoided. If the AT exceeds that permitted by the previous criterion—the limit set by RT /E— an inflection of the temperature vs., tube length will occur and thermal runaway will set in. Just before runway sets in the temperature at the hot spot can be 1.4 times higher than RT /E. 

In each case, the pressure is mainly fixed by the density and quite insensitive to temperature. A consequence of this is that, when a new nuclear reaction (e.g. helium-burning) sets in in degenerate material, the additional heat cannot be taken up (as it would be in an ideal gas) by expansion and there is a thermal runaway (Mestel 1952). The temperature rises very strongly until it becomes high enough for the degeneracy to be removed, and the star adjusts to a new structure with lower central density. 

Balakotaiah, Kodra, and Nguyen also studied the CSTR. They found that the boundary between the insensitive and runaway region is where there are two limit points (a point of infinite slope - there are two such limit points in Fig. 2) in the reaction path connecting the initial and final states. They foimd identical criteria to the batch reactor in the special limit of 7 —> oo and Og = 0. That is, the safe criteria under adiabatic conditions (a = 0) is given... 

Comparison with the runaway diagram (Figure 4.10.25) shows that particularly for low values of Nad (low value of Ua and/or of ATad) the criterion according to Eq. (4.10.58) is too strict, at least for reactions with a reaction order > 0 (see Topic 4.10.2). Hence, the reactor is already insensitive for values of of... 

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