Approximate closed form solution to the fission product diffusion equation in one-dimensional slab geometry Page: 56 of 76
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In the present case we have two solutions, a concentration and a flux.
These, in turn, are functions of two boundary conditions, also a concen-
tration and a flux. Duhamel's theorem is easily extended in this case
to giveC (p) = J
+
J (P) =G ( 'Y'p-p') d C (p ') dp'
1Cp dp
G ( ,y'p-p,) d (JL L) dp'
G2 d JL dp
H 0'Y'p-p' C--(0LD dp'p
+ IThe most obvious approach to this solution is to evaluate the above
integrals numerically using the trapezoidal rule. The result is
n-
CL(n . [GlPPi + GlP n 11 ( + - C)
n-+
2 [ -P _ ) + G2 nP i+ JL i+1 LD , (150)50
and
(148)
(149)
H2 d L~p)d'
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Smith, P.D. Approximate closed form solution to the fission product diffusion equation in one-dimensional slab geometry, report, November 1, 1974; San Diego, California. (https://digital.library.unt.edu/ark:/67531/metadc1019844/m1/56/: accessed May 5, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.