Mathematical modeling and analysis of non-Newtonian Rabinowitsch fluid flow in an elliptical duct: Insights into pseudoplastic and dilatant behaviors

This research introduces a novel mathematical model for the peristaltic flow of non-Newtonian Rabinowitsch fluid within an elliptical duct, uniquely capturing both pseudoplastic and dilatant behaviors. By employing Cartesian coordinates with elliptical boundary conditions, the model preserves the duct’s geometric integrity. The resulting complex partial differential equations, though challenging, were solved exactly using dimensional analysis and scaling methods. Additionally, perturbation techniques were utilized to thoroughly analyze the flow dynamics. Comprehensive graphical analyses depict key characteristics such as dimensionless velocity, axial pressure gradient, and pressure rise, offering fresh insights into Rabinowitsch fluid behavior in elliptical geometries. The findings reveal that an increase in volumetric flow rate significantly enhances central velocity in the duct, particularly for pseudoplastic fluids, while dilatant fluids exhibit reduced velocity under similar conditions. Notably, the pressure gradient demonstrates distinct patterns, with dilatant fluids showing oscillatory fluctuations, underscoring the limitations of Newtonian models in accurately representing these complex fluid dynamics.