An analytical discrete-ordinates solution for an improved one-dimensional model of three-dimensional transport in ducts

•An improved 1-D model of 3-D particle transport in ducts is studied.•The cases of isotropic and directional incidence are treated with the ADO method.•Accurate numerical results are reported for ducts of circular cross section.•A comparison with results of other authors is included.•The ADO method is found to be very efficient.

An analytical discrete-ordinates solution is developed for the problem of particle transport in ducts, as described by a one-dimensional model constructed with two basis functions. Two types of particle incidence are considered: isotropic incidence and incidence described by the Dirac delta distribution. Accurate numerical results are tabulated for the reflection probabilities of semi-infinite ducts and the reflection and transmission probabilities of finite ducts. It is concluded that the developed solution is more efficient than commonly used numerical implementations of the discrete-ordinates method.