Mathematical Computations for Peristaltic flow in a duct

Abstract

Peristalsis is the concept for the fluid movement that occurs within ducts possessing sinusoidally distorting walls. This peristaltic flow phenomenon has various uses in the treatment of physiological movement issues (i.e. transfer of urine to the bladder, transit of food through the digestive system, and blood flow across small blood arteries, among other functions.). Numerous engineering uses also exist, such as the conveyance of toxic and caustic fluids, potent chemicals, and slulT1es [1]. Numerous studies have been addressing the peristaltic flow issues for diverse geometries due to the broad range of applications (these geometrical models include asymmetric channels, tubes, rectangular ducts, etc.). A theoretical examination of two-dimensional fluid motion in a medium featuring sinusoidally distorting walls was offered by Pozrikidis [2]. A viscous Newtonian fluid's peristaltic flow inside cylindrical tubes had been studied by Yin and Fung [3). The combined impact of peristalsis and heat transmission inside an asymmetric geometry have been evaluated by Srinivas and Kothandapani [4). A mathematical assessment was presented by Nadeem and Akram [5] to examine the peristaltic flow inside a rectangular-cross-sectioned duct. There are also several recent research articles [6-9] that discuss the investigation of peristaltic flow inside complex geometries. Additionally, there is a vast body of literature on the investigation of peristaltic flow inside cylindrical, asymmetric, and rectangular ducts. Researchers' interest has recently increased in the analysis of fluid transport and heat transfer in ducts with elliptic cross sections and sinusoidally deformable walls. Similar to the peristaltic flow problems for rectangular and circular ducts, these elliptic duct problems have significant applications in the field. If a heat exchanger needs a better cooling effect than what a circular duct can provide and space is a key element in the design, an elliptic duct is more worth to consider. The elliptic duct has a longer circumferential length than the circular duct does, even if their cross sectional areas are equal [10].