Heat Generation Rate in Fuel

Even for a reactor in which all fuel elements are identical, the local heat generation rate will vary because of the variation of thermal neutron flux with position in the core. We illustrate by calculating the maximum local rate of heat generation as a function of total core power for the case of a bare reactor with vertical fuel elements, all of which contain fuel of the same enrichment. 

The fueled length of the element is H, while the extrapolated height of the core is H (see Fig. 6.1). The cross-sectional area of the element is 

If the width of the element is small compared with the core radius, we may ignore the radial variation of neutron flux across it. It is then only necessary to consider the axial variation, which depends on the function cos(7rz/if ), as shown in Table 3.4. The central plane of the reactor is taken as z = 0. 

Using the standard heat transfer notation, the heat generation rate per unit volume, at height z, for the element at the radial position r, is (z). If the fuel is uniformly distributed in the element, the heat generation rate per unit volume of fuel is proportional to the flux and, hence, 

The heat generation rate in a small slice of the element, of height dz, is qr(z)As dz and the total heat generation rate for the whole element at the radial position r is therefore 

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