What Factors Affect Neutron Flux in a Finite Medium?

AI Thread Summary
The discussion focuses on calculating neutron flux in a slab with a specific thickness containing distributed neutron sources. The user seeks assistance with a homework problem involving the diffusion equation and the diffusion kernel for an infinite slab. They reference the book "Introduction to Nuclear Reactor Theory" by John R. Lamarsh and provide their attempts at solving the problem, including boundary and source conditions. The user expresses difficulty in determining the constants necessary for their solution. Overall, the conversation emphasizes the mathematical approach to neutron flux in a finite medium.
damyoro
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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
 
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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
 
What have you tried so far? This looks to be a homework problem.
 
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
 
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