Stokes flow in a curved duct – A Ritz method

Fully-developed slow viscous flow in a curved duct of arbitrary curvature is solved by an efficient Ritz variational method. For a duct of rectangular cross section the Ritz results agrees well with those obtained by a Fourier–Bessel expansion. The Ritz method is then applied to the elliptic cross section. The fluid properties for Stokes flow in a curved duct are discussed.

► An efficient Ritz method is introduced to treat Stokes flow in highly curved tubes.
► The Ritz method is more advantageous to FEM in terms of memory space and ease in handling of curved boundaries.
► The flow rate in a curved tube may be larger than that in a straight tube.