- 2

- 0

I need help with the following assignment:

It states:

Consider an ideal moderator with zero absorption cross section, Ʃ

_{a}= 0, and a diffusion coefficient, D, which has a spherical shape with an extrapolated radius, R. If neutron sources emitting S neutrons/cm

^{3}sec are distributed uniformly throughout the moderator, the steady neutron diffusion equation is given by,

D∇

^{2}[itex]\phi[/itex] -Ʃ

_{a}[itex]\phi[/itex]=-S

a) Simplify the above neutron diffusion equation for this moderator in spherical coordinates and state the appropriate boundary conditions.

By solving the simplified diffusion equation, obtain the neutron flux profile, [itex]\phi[/itex](r).

I know I need to divided the neutron diffusion equation and cancel out the absorption cross section and end up with something like:

∇

^{2}[itex]\phi[/itex] = -S/D

and the particular solution would be something like S/Ʃ

_{a}

but what's the general solution to:

D∇

^{2}[itex]\phi[/itex] =0

in spherical coordinates?