1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Neutron flux in a finite medium

  1. Oct 18, 2012 #1
    Deaar all
    good morning

    I am very interested to the flux in a slab of extrapolated thickness a, containing distributed sources of neutron. A I have an example in which the source is given as s(x)=S(x+a/2) where S is a constant and x distance from the center of the slab.
    You mentioned in one of your post that you would do it but I could find.
    I would really appreciate any help of reference from you
    Thank you in advance
  2. jcsd
  3. Oct 19, 2012 #2
    I wanted to add the reference of the book : Introduction to Nuclear reactor theory by John R. Lamarsh

    CHp5 Problem
    a)By using the diffusion equation for a planar source located at x', show that the diffusion kernel for an infinite slab of thickness a is given by

    G(x,x^' )=L/(Dsinh(a/L)) {█(sinh 1/L (a/2-x)sinh 1/L (a/2+x^' ),x>x',
    sinh 1/L (a/2+x)sinh 1/L (a/2-x^' ),x<x'
    b) using this kernel calculate the flux in a slab containing uniformly distributed souces emitting S neutrons/cm3.sec
  4. Oct 19, 2012 #3
    What have you tried so far? This looks to be a homework problem.
  5. Oct 19, 2012 #4
    You are right and thank you for your reply
    This is my try
    general solution is C=A*e^(-x/L)+Be^(x/L)
    And I use as boundary conditions φ(a/2)==0
    and as source condition
    J(a/2-x')=J(x') +1
    What I found is the following
    Ф+(x,x^' )=-(Le^((x-a/2)/L))/2D[cosh x^'/L-cosh((x^'-a/2)/L) ] +(Le^((-x+a/2)/L))/(2*D[cosh x^'/L-cosh((x^'-a/2)/L) ] )

    I really tried hard but until now I could not get it right.
    One of my problems is to find the conditions for determining the constants.

    thank you in advance
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook