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1d diffusion equation solution for slab with non symmetric source

  1. Mar 5, 2016 #1
    • Thread moved from the technical forums, so no HH Template is shown.
    Disclaimer: This is a homework problem

    I need to analytically solve the diffusion equation for a 1d 1 group slab with width a, and source distribution Se^(-k(x+a/2))

    I've gone through the math, and come up with my homogeneous and particular solution and attempted to apply the boundary conditions of the flux set to 0 at -a/2 and a/2 but my constants are functions of each other. I was thinking of solving the source for the average, and setting the neutron current at that point to 0 but I didn't think that would work. Is there any other boundary condition I can use? I read in another text (I went through about 4 texts and 7 power points to no avail) "There always exists a physically realizable solution (no critical buckling!)") (http://www.mit.edu/~lululi/school/22.211_Nuclear_Reactor_Physics_I/notes/__all__.pdf) But I am not sure how to use this condition, or if it applies to this problem. I would greatly appreciate any insight into this.
     
  2. jcsd
  3. Mar 10, 2016 #2

    Twigg

    User Avatar
    Gold Member

    If you haven't tried it already, I would try finding a Green's function and taking it's convolution with the source term.
     
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