MHD effect on peristaltic motion of Williamson fluid via porous channel with suction and injection

Recent advancements in nanofluids (NFs) nanomaterials have led to diverse applications across multiple disciplines, enhancing heat transfer (HT) performance in clinical systems, engineering, cooling technologies, engine generators (EG), and more. These materials play a critical role in diagnosing underlying issues within human organs that rely on peristaltic pumping for fluid transfer, such as the stomach, intestines, and ureters. They are also integral to devices like flow meters, magnetohydrodynamic (MHD) generators and pumps, nuclear reactors using liquid metals, geothermal energy systems, and solar power absorbers. This research focuses on the influence of a magnetic field (MF) on peristaltic flow within a porous channel containing Williamson fluid (WF), driven by both injection and vertical pressure gradients. The objective is to analyze how peristaltic motion affects heat transfer efficiency in such systems. The fluid dynamics are modeled under the assumptions of long wavelengths and small Reynolds numbers. The study aims to evaluate key factors affecting pressure and frictional forces in the porous channel, including Hartmann number (HN), suction and injection parameters, and the rheological properties of Williamson fluid. Nonlinear differential equations governing the flow are solved analytically using perturbation techniques. The findings indicate that increasing the suction and injection parameters enhances volumetric flow rates, while the relationship between pressure rise and time-averaged volumetric flow rate is also explored. Results show that pressure rise decreases as the Hartmann number increases, consistent with the findings of Shapiro et al. The study concludes that the interaction between magnetic fields and peristaltic motion significantly influences fluid behavior, with potential applications in both biological and industrial systems.