Hydrodynamics and Sensitivity Analysis of a Williamson Fluid in Porous-Walled Wavy Channel

In this work, a steady, incompressible Williamson fluid model is investigated in a porous wavy channel. This situation arises in the reabsorption of useful substances from the glomerular filtrate in the kidney. After 80% reabsorption, urine is left, which behaves like a thinning fluid. The laws of conservation of mass and momentum are used to model the physical problem. The analytical solution of the problem in terms of stream function is obtained by a regular perturbation expansion method. The asymptotic integration method for small wave amplitudes and the RK-Fehlberg method for pressure distribution has been used inside the channel. It is demonstrated that the forward flow becomes fast in the narrow region (at x = 0.75), which dominates the upward flow inside the channel. To study the impact of model parameters on outputs, we applied normalized local sensitivity analysis and noticed that the most influential parameter for the longitudinal velocity profile is the dimensionless wave amplitude. The reabsorption parameter is sensitive for transverse velocity in the narrow region, and the Weissenberg number has a strong effect on the pressure inside the channel. Further, the least sensitive parameters for the velocity components and pressure have been identified.