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Once the uranium distribution is specified, the parameters Nu(o), Nu(R) and bu are determined and A,/A2 can be evaluated from (8.33). The expression (8.35) represents the temperature distribution for the case of a constant diffusion coefficient and a constant radial neutron flux. For this simplest case, a completely analytical expression for the temperature distribution was not obtained since the integral I(r) must be evaluated numerically. For the more realistic cases involving fewer approximations, it is even less likely that analytical solutions will be obtained. Opacity with Explicit Temperature Dependence

        If the Rosseland opacity is expressed as some explicit function of temperature, KR = f(T), then the method of the preceding section can be used to obtain an expression for the temperature distribution. Using the explicit form of the opacity, the diffusion coefficient given by (8.5) is

                  <R <RT) -16a
               KR   KR(T) =3 g(T)                   (8.36)

where


                    g(T) =   T                      (8.37)

The energy balance equation (8.10) then becomes


               V    (g(T)VT) + 3 S = 0              (8.38)
                              l6c