Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Mechanical Engineering


Due to the apparent suppression of turbulent energy dissipation, viscoelastic materials make excellent drag reducing agents. The applications of viscoelastic fluids in this role have been multiplying rapidly since they can be used as drag reducing agents for the transporting and processing of most fluid substances without any ill effects. In the future it may even be possible to reduce the drag on a ship's hull or on a submarine by injecting a water soluble polymer into the boundary layer on the body. Since many of the phenomena exhibited by viscoelastic fluids, such as the swelling of a jet as it exits from a tube, the open channel siphon, and the Weisseriberg effect, are not predicted by the classical viscous flow theory for Newtonian fluids, more general rheological equations of state have had to be formulated. One of the simpler models proposed to describe the mechanical behavior of viscoelastic liquids was proposed by Oldroyd in 1958. This model exhibits the main non-Newtonian phenomena observable in the simple flow of a viscoelastic fluid. These phenomena are: a variation of apparent viscosity with rate of shear, a Weissenberg climbing effect, and a Robert-Weissenberg normal stress pattern. Oldroyd's model was used by Leslie to calculate the drag force induced by creeping flow past a sphere and by Williams and Bird to calculate flow rates through tubes. The results from both of these studies were in good agreement with experimental data. In this study Oldroyd's model will be used to describe the mechanical behavior of a viscoelastic fluid for the case of steady, two dimensional, incompressible flow past a semi-infinite flat plate coated with a viscoelastic material. For the purpose of analysis it will be assumed that the coating is soluble in the main flow and that the concentration of the coating in the main stream is small enough that the density and diffusivity will both be constants. The equations of motion and diffusion were obtained by boundary layer analysis. The set of partial differential equations was found to have a similarity solution only when the external stream velocity was proportional to the one third power of the distance along the plate. This is a Falkner-Skan type flow past a 90 degree wedge.




South Dakota State University