Approximate One-dimensional Models for Monoenergetic Neutral Particle Transport in Ducts with Wall Migration

The problem of monoenergetic neutral particle transport in a duct, where particles travel inside the duct walls, is treated using an approximate one-dimensional model. The onedimensional model uses three-basis functions, as part of a previously derived weighted-residual procedure, to account for the geometry of particle transport in a duct system (where particle migration into the walls is not considered). Our model introduces two stochastic parameters to account for particle-wall interactions: an albedo approximation yielding the fraction of particles that return to the duct after striking the walls, and a mean-distance travelled in the walls transverse to the duct by particles that re-enter the duct. Our model produces a set of three transport equations with a non-local scattering kernel. We solve these equations using discrete ordinates with source iteration. Numerical results for the reflection and transmission probabilities of neutron transport in ducts of circular cross section are compared to Monte Carlo results computed using the MCNP code.