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Constant Diffusion Coefficient Approximation

        To examine the possibility of obtaining analytic solutions to (8.9), the simplest case in which the diffusion coefficient is a constant, is considered first. In this approximation, the diffusion coefficient, KR, is independent of position and temperature and the heat balance equation reduces to a form of Poisson's equation,


               V2T(r) + S(r) = 0                    (8.10)
                         KR

The boundary conditions are T(O) = To

                    T(R) = TR                       (8.11)

where T and TR are the temperatures at the reactor centerline and the inside face of the graphite, respectively.

        The method of Green's function is used to obtain the temperature distribution in the constant diffusion coefficient approximation. Equation (8.10) is written as L(r)T(r)                    = f(r)                 (8.12)

where


                    L(r)   1 d   (r d               (8.13)


                    f(r) = -    S(r)                (8.14)
                             KR