Anisotropic diffusion coefficients and the streaming problem in slab lattices: A new approach

• The diffusion of neutrons in a slab lattice is reformulated.
• A new method based on a Fourier expansion of the fluxes in the cell is developed.
• Extensive numerical results are given for the transverse and parallel diffusion coefficients.
• The void problem is discussed in detail.

The problem of anisotropic diffusion in slab lattices is reformulated and revisited with a view to obtaining some exact solutions of the associated transport equations using the method of finite Fourier transforms. The question of replacing a heterogeneous system by an equivalent homogeneous one is discussed and some of the problems that arise are outlined and in some cases solved. The classic problem of the existence of an infinite parallel diffusion coefficient when a void region is present is examined and a new integral equation formulation is given which shows precisely how this divergence arises and how to ‘quench’ it by means of an axial height or buckling. Extensive numerical values are reported to illustrate the behaviour of the leakage effect and the convergence properties of the Fourier transform. We also examine the convergence of the terms in the series solution of the parallel diffusion coefficient due to the effect of neighbouring cells.