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G (x,y; X' y') = 2 knz + 2  1Iz            > Iz'I
                        n=l



                 2nz' + 2    n         Iz < Iz'j   (8.20)
                         n=l
                         i0         iG'

The transformation z = re  , z' = r'e   is used to express the Green's function in polar coordinates:



G(r,O; r',O') = 2knr + 2 0  1 (rI n cos n(O-e'), r > r' n=l



                  2Znr' + 2    k ( r n cos n(O'-O), r < r' n=l
                                                   (8.21)

For a point source of heat S(r',6') where r' < R, the steady state temperature distribution is given by the Green's function (8.21), modified by the solution of Laplace's equation which satisfies the boundary condition T = TR(O) at r = R. Let the modified Green's function be denoted by T(r,e; r','). Since the fission heat generation rate is distributed over the reactor core, the resulting temperature distribution will be the integral of T(r,O; r',6') over the entire core region. The resulting expression becomes



T(r,O) = TR () +  1      do' {{ r'dr'[9,n