ANS is committed to advancing, fostering, and promoting the development and application of nuclear sciences and technologies to benefit society.
Explore the many uses for nuclear science and its impact on energy, the environment, healthcare, food, and more.
Explore membership for yourself or for your organization.
Conference Spotlight
2025 ANS Winter Conference & Expo
November 9–12, 2025
Washington, DC|Washington Hilton
Standards Program
The Standards Committee is responsible for the development and maintenance of voluntary consensus standards that address the design, analysis, and operation of components, systems, and facilities related to the application of nuclear science and technology. Find out What’s New, check out the Standards Store, or Get Involved today!
Latest Magazine Issues
Oct 2025
Jul 2025
Latest Journal Issues
Nuclear Science and Engineering
November 2025
Nuclear Technology
Fusion Science and Technology
Latest News
Nuclear momentum continues to grow across Canada
The Canadian provinces of Alberta and Saskatchewan were the subject of two different announcements yesterday about new nuclear developments.
Samuel L. Gralnick
Nuclear Science and Engineering | Volume 60 | Number 3 | July 1976 | Pages 302-310
Technical Paper | doi.org/10.13182/NSE76-A26886
Articles are hosted by Taylor and Francis Online.
This paper presents a derivation of the conservation-law form of the single energy group transport equation in an axisymmetric toroidal coordinate system formed by rotating a nest of smooth, simply closed, plane curves of arbitrary parametric description about an axis that does not intersect the nest. This general equation can be used for generating equations specific to particular cross-section geometries or as the basis of a finite difference equation for the general case. The effect of both the toroidal and poloidal curvatures of the system are investigated, and criteria for the validity of cylindrical and planar approximations are established. The diffusion equation for this geometry is derived, and it is shown to be formally homologous to the “r-θ” cylindrical diffusion equation if the coordinate system is orthogonal and if the azimuthal coordinate, , can be ignored.