Peristaltic flow of a viscous fluid in a curved duct with a rectangular cross section - Riaz, Arshad; Ahammad, N. Ameer; Alqarni, M. M.; Hejazi, Hala A.; Tag-ElDin, ElSayed M. (Frontiers in Physics, 2022)
Most of the flow systems in human body are duct shaped like pancreatic duct, bile ducts, and gallbladder etc. Such flows are also common in industrial side like HVAC design system. In current investigation, a novel mathematical model has been introduced to analyze a peristaltic motion of a viscous fluid in a three dimensional curved duct with rectangular cross section for the first time in literature. Such geometries are more specifically used in industrial and medical applications. In current investigation, the constraints of lubrication theory have been incorporated. A perturbation technique has been utilized to solve the Navier-Stokes partial differential equations. A major focus is kept on aspect ratio of the duct and the curvature of the flow axis. Curvilinear coordinates followed by the cylindrical system are considered for the derivations coped with the curved geometry. Homogeneous no-slip boundary conditions are proposed at the flexible surfaces. Expression of pressure rise is found numerically by using NIntegrate tool on computing software Mathematica. Graphical discussion is comprehensively made to determine the impact of all considerable physical factors of the problem. It is found that large curvature and aspect ratio reduce the fluid speed gradually but flow rate promotes the fluid velocity. The pumping rate is a decreasing function of curvature and aspect ratio however a reverse pumping can occur for large curvature values. Streamlines suggest that larger wave amplitude raises the number of circulating boluses.