Impact of flexible walls of curved channel on biological flow of Reiner–Rivlin fluid

In this study, the Reiner–Rivlin fluid model is opted for examination as the complex dynamical fluid and is flowing on account of the waves travelling on the walls of flexible curved channel. The governing equations are solved analytically up to the first order to analyse the velocity profiles. As the governing equation is highly nonlinear, so the problem is solved by regular perturbation technique about small wave number. After the implication of regular perturbation, the second order Cauchy Euler ordinary differential equations are obtained for both the systems. A detailed analysis is conducted on the effects of diverse factors, such as the rheological properties of fluid, the curvature radius of the channel, the wave amplitude and the wall properties. The velocity of the fluid enhanced by increasing wall properties parameters, wave number, Reynolds number and the amplitude ratio parameter. It is also observed that the Reiner–Rivlin fluid flows slowly as compare to the Newtonian fluid, this type of findings can be helpful for the understanding of many physiological processes, like blood flow and food swallowing. This study enlightens the interaction between the curved nature of the channel and Reiner–Rivlin fluid flow in peristalsis that can be a great contribution for the designing of biomedical devices. Such types of problems have great significance in many physiological processes and engineering applications like microfluidic devices and drug delivery systems.