Fluids dynamics of non-Newtonian power-law fluids: Investigating separation points on cylindrical shapes

The theoretical investigation of flow separation in non-Newtonian fluids characterized by power-law behavior remains unexplored in the existing literature, particularly concerning axisymmetric surfaces that exhibit surface curvature. This study aims to analyze flow separation in a non-Newtonian context, extending insights from Newtonian fluids to a range of cylindrical geometries, from uniform circular cylinders to more streamlined shapes. We enhanced current transformation methods for variable radius cylinders with transverse curvature applicable to inelastic fluids. By applying Howarth's retarded flow model, characterized by a decrease in longitudinal flow, we introduced a variable radius and specific free-stream conditions, resulting in a non-similar problem that influences flow characteristics. The Keller-box method was employed to obtain solutions to the governing equations, with validation against known Newtonian cases. Our results demonstrate that the separation length increases with a power-law index of 0.9 x 6.11%, 6.54%, 6.68%, 4.84%, and 4.98% across body contour parameters from 0.0 to 1.0, compared to the Newtonian case. At a power-law index of 0.4, the increases are significantly higher at 45.38%, 40.47%, 44.89%, 38.91%, and 36.16%. Additionally, for a transverse curvature parameter of 5, the increases compared to Newtonian fluids are 9.72%, 8.59%, 9.68%, 9.54%, and 10.40%. These findings highlight the unique flow dynamics associated with non-Newtonian fluids.