Exact solutions for laminar pressure-driven flow through a pipe with a concentric internal grating

This paper presents an analytical model for laminar pressure-driven axial flow along a circular pipe containing an internal concentric circular grating of no-slip fins. Explicit expressions for the velocity field are derived using complex analysis techniques and conformal mappings. From these solutions, formulas for the Fanning friction factor associated with axial flow in such finned pipes are derived and, using these, the drag properties of the pipes are examined. The results offer valuable insights for optimising finned duct designs in applications involving heat transfer, fluid flow, and biofilm cultivation.