Secondary flows of a viscoelastic fluid in pipes of complex cross-section shapes

The transversal flow field in pipes of non-circular cross-section shapes is determined for a Green-Rivlin fluid. An analytical approach is presented, which is applicable to unsteady flows driven by small amplitude pressure gradients. Both the longitudinal flow velocity and secondary velocity components are found by prescribing a pipe contour through a shape factor conveniently defined. Secondary flow patterns are computed for several pipe shapes. Results are presented herein for the specific cases where the shape factor prescribes tube cross-section of approximately triangular, square and pentagonal shapes.