Numerical solution of diffusion equation to study fast neutrons flux distribution for variant radii of nuclear fuel pin and moderator regions

Abstract

Abstract In this symbolic investigation, a cylindrical cell in a LWR, which consists of one fuel pin and moderator (water), is considered. The width of this cylindrical cell is divided into 100 equal units. Since the neutron flux in a cylindrical fuel pin is resulting from the diffusion equation: - 1 r d d r φ ( r ) + ∑ a φ ( r ) = S ( r ) $ - \frac{1}{r}\frac{d}{{dr}}\varphi \left( r \right) + \mathop \sum \nolimits_a \varphi \left( r \right) = S\left( r \right)$ , the amount of fast neutron fluxes are obtained on the basis of the numeric solution of this equation, and the applied boundary conditions are considered: φ ′ ( 0 ) = φ ′ ( 1 ) = 0 $\varphi '\left( 0 \right) = \varphi '\left( 1 \right) = 0$ . This differential equation is solved by the tridiagonal method for variant enrichments of uranium. Neutron fluxes are obtained in variant radii of fuel pin and moderator and are finally compared with each other. There are some interesting outcomes resulting from this investigation. It can be inferred that because of the fuel enrichment increment, the fast neutron flux increases significantly at the centre of core, while many of the fast neutrons produced are absorbed after entering the water region, moderation of lots of them causes the reduced neutron flux to get improved in this region.