  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 one-dimensional 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.
