Non-Newtonian flow past curved external surfaces

The principle motivation of this research is the creation of a foundation for predicting resistance to motion of bodies in nonNewtonian fluids. A theoretical methodology is developed for the solution of two dimensional Navier-Stokes equations for incompressible nonNewtonian fluid flows past a range of elliptical surfaces. For the investigated flow conditions, methods of analysis involving asymptotic matching techniques of boundary layer equations are not appropriate. Such methods usually assume that the surface curvature effects and pressure difference across the boundary layer are negligible. Results of the presented research show that these two effects are significant for the flow conditions at hand. The variational formulation of the governing equations of motion and continuity and their discretization by the finite element method are developed. Solutions are implemented in a form suitable for efficient numerical computation. The effect of the nonNewtonian fluid on the pressure distribution along the external surface is analyzed. The presented results include velocity profiles and shear stresses along the external surfaces.