Galerkin method study on flow of Oldroyd-B fluids in curved circular cross-section pipes

A Galerkin method was used to investigate steady, fully developed flow of Oldroyd-B fluids through curved pipes of circle cross-section. By using Galerkin method, large values of curvature ratio, Reynolds number and Weissenberg number can be discussed. The powers of the series of the Galerkin method in the present work are chosen carefully. Both effects of Reynolds number and Weissenberg number on axial velocity and stream function are discussed even for large values of the two non-dimensional parameters. It was discovered that the combined effect of large Reynolds number and Weissenberg number decreases the outward shifts of maximum axial velocity and maximum stream function. Axial normal stress of creeping flow is also studied here. The large Weissenberg number makes the stress concentration occur on the inner bend of the pipe.