Diffusion Theory

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EngNewbit
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This is in the beginning of a long set of problems, and I am lost. I don't get anything like this answer. Any guidance? I have a feeling its simple but haven't done much of these.

Write down the diffusion equation for the neutron flux in a multiplying sphere of radius R containing a constant distributed source of strength Q neutrons/cm3/s. Assuming that the flux vanishes at the sphere surface and that it remains finite at the origin:
Solve the diffusion equation when k inf = 1 and show that the neutron flux is given by:
(Q/6D)(R^2 − r^2)
 

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  • #2
Astronuc
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One has to write the diffusion equation (in spherical coordinates) with a constant, distributed source, and apply the boundary conditions, that the flux [tex]\phi[/tex] is finite at r = 0, and 0 at r = R.

The current should also be 0 at r = 0.
 

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