Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel

<ns7:p>Background Peristaltic or undulating flow plays a significant role in various biomedical and industrial processes, where it provides an efficient mechanism for transporting fluids through flexible conduits such as catheters and endoscopic channels. Understanding such flow behavior is essential for improving medical devices and industrial applications involving non-Newtonian fluids. Methods This study investigates the peristaltic motion of a Carreau fluid whose viscosity varies with both temperature and concentration within a flexible, axisymmetric channel composed of two overlapping cylindrical tubes. The outer wall of the channel exhibits a sinusoidal wave pattern, simulating a realistic endoscopic configuration. The governing nonlinear, nonhomogeneous partial differential equations were formulated in cylindrical coordinates under the assumption of a long wavelength and low Reynolds number. The equations were transformed into a dimensionless form and solved using the uniform perturbation method. Graphical analyses were performed using Mathematica software. Results The results illustrate the combined effects of temperature-dependent and concentration-dependent viscosity on the velocity distribution and pressure gradient within the channel. Increasing temperature and solute concentration were found to enhance fluid velocity and reduce flow resistance. Conclusions The study provides a comprehensive understanding of peristaltic transport in variable-viscosity Carreau fluids under realistic physiological conditions. These findings may contribute to optimizing the design and performance of endoscopic and biomedical fluid transport systems.</ns7:p>