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The problem of the homework states:
Mono-energetic sources of neutrons emitting S neutrons/cm3 are distributed throughout an infinite moderator with diffusion coefficient, D (cm), and absorption cross section Ʃa (cm-1)
Show that the neutron flux in the moderator is given by:
[itex]\Phi[/itex] = S/Ʃa
I know that the Diffusion equation is
dn/dt = S - Ʃa[itex]\Phi[/itex] + D[itex]\nabla[/itex]2[itex]\Phi[/itex]
For Steady-State the equation becomes
0= S - Ʃa[itex]\Phi[/itex] + D[itex]\nabla[/itex]2[itex]\Phi[/itex]
and [itex]\nabla[/itex]J =0 if space independent thus giving the following equation as
dn/dt = S - Ʃa[itex]\Phi[/itex]
So, my question to this problem is can you assume the following diffusion equation to be steady state and space independent to get this:
[itex]\Phi[/itex] = S/Ʃa ? or do I need to consider other variables?
Mono-energetic sources of neutrons emitting S neutrons/cm3 are distributed throughout an infinite moderator with diffusion coefficient, D (cm), and absorption cross section Ʃa (cm-1)
Show that the neutron flux in the moderator is given by:
[itex]\Phi[/itex] = S/Ʃa
I know that the Diffusion equation is
dn/dt = S - Ʃa[itex]\Phi[/itex] + D[itex]\nabla[/itex]2[itex]\Phi[/itex]
For Steady-State the equation becomes
0= S - Ʃa[itex]\Phi[/itex] + D[itex]\nabla[/itex]2[itex]\Phi[/itex]
and [itex]\nabla[/itex]J =0 if space independent thus giving the following equation as
dn/dt = S - Ʃa[itex]\Phi[/itex]
So, my question to this problem is can you assume the following diffusion equation to be steady state and space independent to get this:
[itex]\Phi[/itex] = S/Ʃa ? or do I need to consider other variables?