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Homework Help: Fick's Law Diffusion HW

  1. Nov 19, 2013 #1
    The problem of the hw 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?
  2. jcsd
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