Implementing lubrication approximation to inspect magnetically influenced ciliated driven microflow and heat transfer in endoscopic coaxial cylinder

Abstract This study investigates the third-grade fluid movement across two coaxial cylinders. The inner tube represents an endoscope moving with constant velocity whereas the outer tube is flexible. The inner wall of the outer tube is lined with numerous cilia whose coordinated beating generate metachronal wave which helps in the movement of the fluid. Such geometries are useful in biomedical procedures involving endoscopic examinations, where the movement of the endoscope changes the surrounding fluid transport characteristics. The rheological behavior of several biological and industrial fluids cannot be accurately explained by the Newtonian model therefore the third-grade fluid model is used to study such behavior. Application of an external magnetic field in radial direction provides an effective mechanism for regulating fluid movement, which is helpful in targeted drug delivery, and medical treatments involving magnetic field. The heat source and viscous dissipation affect the temperature distribution especially in microscale devices where heat transfer effects are significant. The nonlinear partial differential equations are non-dimensionalized and solved under lubrication assumption. The resulting equations are nonlinear and involve a small third-grade parameter. Therefore, to simplify, regular perturbation method is applied for the third-grade parameter β $\\beta $ . This gives analytical solutions for radial velocity f $f$ , axial velocity g , $\\mathcal{g}\\text{,}$ temperature θ $\\theta $ and pressure P $P$ . The results indicate that ciliary activity and fluid rheology greatly affect the fluid transport. The axial velocity g $\\mathcal{g}$ , fluid temperature θ $\\theta $ and fluid pressure P $P$ rises with third-grade parameter β $\\beta $ whereas magnetic field decreases velocity, temperature and fluid pressure. The study concludes that fluid rheology, ciliary activity, and magnetic effects are key controlling parameters in endoscopic procedures. Employing these parameters appropriately can be helpful in regulating fluid transport, pumping performance, and heat transfer in biomedical systems. Cilia-driven movement has an important role in various physiological processes and is further affected by the presence of endoscope, non-Newtonian fluid properties, magnetic fields, and thermal effects. Motivated by these applications, the objective of the study is to investigate the combined effect of ciliary motion, endoscopic movement, third-grade fluid behavior, magnetic field effects, heat generation, and viscous dissipation on fluid transport within a coaxial cylindrical configuration. This study will help in better understanding of transport mechanisms relevant to biomedical devices, endoscopic technologies, and thermal-fluid systems.