Nonlinear Bifurcation and Numerical Analysis of Equilibria in Heated Curved Endoscopic Peristaltic Flow

Bifurcation analysis constitutes a powerful tool for understanding transport flow phenomena arising from peristaltic motion in a curved heated endoscope. This approach is useful for assessing a peristaltic endoscope model in a curved tube. Bifurcation and dynamical analyses reveal heat transfer and entropy behavior at critical points. The stream function has been determined through an exact analytical approach, incorporating the coupled wave velocities in curvilinear coordinates that characterize the peristaltic motion of the endoscope. Endoscopic peristaltic motion is analyzed by determining and classifying equilibrium points analytically and through a homotopy continuation–based numerical framework, enabling comprehensive exploration of bifurcations and topological transitions in the curved bounded channel. The identification of saddle-node, periodic, and heteroclinic orbits in the endoscopic peristaltic flow indicates qualitative transitions within the attraction basin, leading to the appearance or disappearance of partial and complete trapping zones. The results reveal that the catheter radius ratio, amplitude ratio, and flow rate significantly influence the streamline bifurcation structure. An increase in the catheter radius ratio stabilizes the flow and suppresses bifurcation, while higher amplitude ratios and flow rates promote stronger vortical motion, enhancing heat transfer and entropy generation within the endoscopic peristaltic channel.