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.