NE 455555 Nuclear Reactor Analysis II

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NE 455/555Nuclear Reactor Analysis II

• Lecture 2 1/7/00
• Review of one-group diffusion analytic solutions

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Review problem

• Just to help get the juices flowing again from
  last term, lets work a problem togetherSolve
  the following finite homogeneous -medium
  spherical-geometry diffusion problem with a
  shell source

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So, you remember the procedure, right?

• Put the diffusion equation in the proper form
• divide through by the diffusion coefficient
• eliminate any delta functions by using jump
  conditions
• Integrate the diffusion equation over an
  infinitesimally small volume around the location
  of the source r0

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The procedure...

• Choose the appropriate fundamental solutions
• What are they in this case? To the left of r0 ,
  we useTo the right of r0 we use

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The procedure...

• Now we must have four boundary conditions to
  determine the four coefficients. They are

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So, lets apply the boundary conditions and
determine the coefficients!

• Lets do the easy ones first
• implies
• impliesThe sinh/r goes to 1 as r
  goes to zero, which means that

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The procedure...

• Continuity of flux implies
• The jump condition implies

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So, after a little algebra, we can solve for the
coefficients.
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Lets examine the solution for a particular
problem
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Here is a plot of the solution