The steady laminar flow of an elastico-viscous liquid in a curved pipe of varying elliptic cross-section (Q1381781)

We study a fully developed steady laminar flow of idealized elastico-viscous fluid through a curved tube with elliptic cross-section. The axes of the ellipse are placed in an arbitrary position with respect to the radius of curvature, and the cross-sectional area varies slowly with the longitudinal distance. A perturbation scheme in terms of Dean number and a nonuniform curvature parameter is applied to determine the effects of: (i) the nonuniformity of the curvature, (ii) the shape of the cross-section of the curved pipe, and (iii) the arbitrary positioning of the elliptic cross-section relative to the radius of curvature of the curved pipe.