الفهرس 
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Abstract
After a short review for the published methods used for cell calculation given special attention to the determination of flux distribution in square cells with cylindrical fuel elements, we propose an analytical spherical harmonics method based on choosing a coordinate system which provides the outer boundary surface of the cell as a cOjjrdinate surfaces. In this proposed method a periodic solutions are derived for one velo¬city neutron transport equation in an infinite, douply periodic lattice of fuel elements imbedded in a moderating medium. The angular flux is expanded in a complete set of spherical harmo¬nics for the angular dependence and a set of doubly periodic exponentials for the space dependence. The integrodifferential equation is thus transformed into a set of linear algebraic system.
Naturally occurring reflecting boundary conditions were applied properly on the outer boundary of the cell. ~he in¬ternal boundary conditions in this method are implicitly taken into consideration during integration process over the cell. The presented method allows for exact treatment of a number of common fuel cell configurations, namely concentric annuli, ster of cylindrical pins and stack of parallel plates. The
actual shape and composition of the fuel element, clad, and structural materials can be taken into consideration. In additlon, anisotropic scattering of any order may be included in
our proposed method.
Special codes were written to implement the suggested method for one limensional and two dimensional cases. The con- ergence and accuracy of proposed method is assessed by compa-rison with exact analytic results which are obtainable for one
dimensional problem. In addition fluxes and disadvantage fac-
tors for the well known Thie lattices are computed by our method and compared with the results obtained by previous wor- kers who used various transport methods most of which rely on
the cylindrical cell approximation. The variation of the dis_ advantage factor as function of the ratio of cell volume tofuel volume is studied. For single rod cells as the cell width
decreases, when the fuel re~ion becomes the inscribed circle,
a minimum in the dieadvantage factor Occurs at certain fuel to
moderator ratio, this agrees with some published results of other method. Some of the cases which we treated by our method have published results and comparison of these with our results