Peristaltic flow of a viscous fluid in a curved duct with a rectangular cross section

Abstract

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Most flow systems in the human body are duct shaped, such as the pancreatic, bile, and gallbladder ducts. Such flow systems are also common in industrial applications like HVAC systems. This study presents a novel mathematical model to analyze the peristaltic motion of a viscous fluid in a three-dimensional curved duct with a rectangular cross section; specifically, such geometries are used more in industrial and medical applications. In the current investigation, the constraints of lubrication theory are considered, and a perturbation technique is used to solve the Navier–Stokes partial differential equations. The major focus of this work is on the aspect ratio of the duct and curvature of the flow axis. Curvilinear coordinates of cylindrical systems are considered for the derivations because of the curved geometry; homogeneous no-slip boundary conditions are proposed at the flexible surfaces, and the expression for pressure increase is found numerically using the NIntegrate tool of computing software Mathematica. A comprehensive graphical discussion is presented to determine the effects of all salient physical factors related to the problem. The results show that the large curvature and aspect ratio reduce the fluid speed gradually but that the flow rate promotes fluid velocity. The pumping rate is a decreasing function of the curvature and aspect ratio; however, reverse pumping can occur for large curvature values. Streamline evaluations suggest that large wave amplitudes increase the number of circulating boluses.

Keywords

• curved duct
• peristaltic flow
• homogeneous conditions
• Newtonian (viscous) fluid
• perturbation method
• curvilinear/cylindrical coordinates