The Effect on Burn-Out of Nonuniform Heating

All the references to burn-out have thus far been concerned with uniformly heated channels, apart from some of the rod bundles where the heat flux varies from one rod to another, but which respond to analysis in terms of the average heat flux. In a nuclear-reactor situation, however, the heat flux varies along the length of a channel, and to find what effect this may have, some burn-out experiments on round tubes and annuli have been done using, for example, symmetrical or skewed-cosine axial heat-flux profiles. Tests with axial non-uniform heating in a rod bundle have not yet been reported. 

One result of nonuniform heating is that burn-out does not always occur at the channel outlet as it does with uniform heating, provided instabilities are avoided and the flow is vertically upwards. Consequently, the problem of analysis is made that much more difficult. The obvious first step is to see if 

The Barnett local-conditions hypothesis has been applied to the above example by rewriting the general burn-out correlation for uniformly heated round tubes [Eq. (22)] as follows  

This is derived by substituting from the heat-balance expression, Eq. (20). Now, the skewed-cosine heat-flux profile being considered gives a known functional relationship between the flux and the quality at any position along the channel. By equating this relationship with Eq. (35), a solution can be obtained giving the local values of (j and k at the predicted burn-out position. The corresponding peak flux can then be evaluated, and in this way the predicted burn-out lines for the three mass velocities in Fig. 40 can be drawn. 

There is an exception to the above generalization which is shown in Russian data reported by Smolin et al. (S5) for a round tube of 0.291-in. diameter and 150-in. long with water at pressures of 1420 and 2560 psia. In 

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