Numerical Bifurcation Analysis of Carreau Fluid in Asymmetric Peristaltic Regime

This article provides numerical bifurcation analysis of the stagnation points in an asymmetric peristaltic flow of a Carreau fluid. A non-linear differential equation is obtained in terms of stream function after using the simplifying assumptions of long wavelength and negligible inertia. A numerical solution to this equation is obtained with the aid of Mathematica solver NDSolve which is based upon the shooting method and Runge-Kutta fourth-order technique. The obtained numerical solution is then utilized in conjunction with the qualitative theory of dynamical systems to identify and classify the stationary points. The impact of material parameter of Carreau model on emergence and evolution of stationary points is thoroughly examined through local and global bifurcation diagrams. This study examines the changes in flow topology through the channel when partial obstruction occurs. The results of this research could aid in maintaining smooth fluid flow through the pump, minimizing the risk of entrapment from inlet to outlet. Also, if eddying zone is occurring, these insights can be beneficial in detecting the specific location within the pump where the fluid is being trapped.