The flux distribution in a cylindrical reactor is given by the expression:

Ф = Ф max jo (ar) cos bz (1,11)

where Ф = neutron flux
г = radius

z = distance along channel a, b — constants

Within the fuel the number of fissions and hence the heat generated per volume of fuel (Qv) is propor­tional to the neutron flux, therefore:

Q" = Q max Jo (ar) cos (bz) (1.12)

Similar expressions can be written for other factors which are proportional to the neutron flux, e. g., heat generated/unit length of fuel element (Q), heat trans­ferred through unit surface area of sheath (q), heat generated per unit mass of fuel (Qw). Equation (1.12) shows that the heat distribution in a cylindrical core is a first order Bessel function in a radial direction and a cosine function axially with allowance for the extrapolation radii and lengths in each dimension (see Fig 1.15).