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The calculated thermal flux in the core region, as shown in Figure 7 of Chapter II, is seen to be relatively independent of position. By   making the simplifying approximation that the radial flux is constant, the heat generation rate is proportional to the uranium density.


        S(r) = CNu(r) f af (E) (E)dE = C'NU (r)    (8.25)

where


               C'   f af(E)f(E)dE                  (8.26)

The simulated uranium density distribution discussed in Chapter VII is given by

                            2   2
                  (r)-r/2b        + a 2            (7.1)

Substituting (7.1) into (8.25),

                           2   2
               S(r) = A1e-r /2bu + A2              (8.27)

where


               Al E alC',  A2 = a2C'               (8.28)


Using the heat generation rate (8.27) to evaluate the temperature distribution (8.23),

                  1R -    r       e r ,2/2b 2
   T(r) = TR + U   kn (R)   r' (Ajer    U + Ajdr'
            + R            -r'2/2b
               r'Zn(    A e U/2b    + A2)dr'}      (8.29)

             r