Steady laminar flow of viscoelastic fluid in a curved pipe of circular cross-section with varying curvature

Abstract

The steady laminar flow of viscoelastic fluid through pipes of circular cross-section, whose center-line curvature varies locally, is analyzed theoretically. The flows in three kinds of pipes whose center-lines are specified by ▪ as the examples of once, twice, and periodically curved pipes, respectively, are discussed in comparison with purely viscous flow. The analysis is valid for any other two-dimensionally curved pipes, when the center-line curvature is small. In addition, the reason why the secondary flow of a viscoelastic fluid in a curved pipe of circular cross-section is stronger than that of a purely viscous fluid is explained. In the present paper, the White—Metzner model is employed as the constitutive equation.