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Most pumping action s entail l a physical volume change of the duct, which is frequently achieved by having a compliant wall or membrane. To the best of our knowledge, the current study is the first report on a mathematical model developed to analyze the peristaltic transport of a Newtonian fluid in a curved duct with rectangular face and compliant walls. Such geometries are most commonly used in clinical and biological equipment, where the walls of the duct need to be flexible. Flexible ducts are more useful than rigid ones because they do not require any extra modifications or accessories. Here, we have used the conditions of lubrication theory to construct an accurate model, and a common perturbation technique was incorporated to handle the Navier-Stokes equations with emphasis on various aspect ratios and curvatures. A system of curvilinear coordinates operating according to the principles of the cylindrical system was employed to represent the mathematical problem. No-slip boundary limitations were considered at the walls along with the extra constraint of compliant walls showing damping force and stiffness. Comprehensive graphical representations were made to illustrate the effects of all emerging factors of the study in both two- and three-dimensional formats. We found that large curvatures and flexure rigidity decreased the fluid velocity uniformly, but the aspect ratio and amplitude parameters could promote fluid velocity. Validation of the results was performed through the generation of a residual error curve. The current readings were taken again with a straight duct to make a comparison with the existing literature. [ABSTRACT FROM AUTHOR]

The transport of complex rheological fluids in physiological ducts is often facilitated by the dynamic phenomenon of peristalsis. Additionally, peristaltic transport assisted by cilia plays a significant role in various natural processes such as respiration, circulation, locomotion, and reproduction. This study focuses on magnetically induced flow bounded by non-uniform curved walls, motivated by the importance of peristalsis and micro-organism motility. To characterize the complex rheology of the fluid liner, a viscoelastic model described by the constitutive equation of Jeffrey's fluid is employed. The flow problem is mathematically formulated using curvilinear coordinates. Subsequently, linear transformations and scaling factors are applied to convert the equations into dimensionless form, while considering biotic restrictions such as creeping transport and long wavelength to reduce dependent variables. By utilizing the stream function and cross-differentiation, a fourth-order equation is obtained and numerically approximated using the shooting method. The effects of various parameters on the flow are illustrated through graphs, and a physical interpretation of the graphical results is provided. It is observed that ciliated walls of the channel enhance the velocity and pumping, while trapping phenomena are more pronounced in a non-uniform channel compared to a uniform channel. [ABSTRACT FROM AUTHOR]