Investigating Rheological Characteristics of Nonlinear Fluid Model in an Asymmetric Channel: A Peristaltic Pumping of Blood with Curvature and Hydrodynamic Impacts

Theoretical research is investigated for the steady rheology of incompressible blood from an asymmetric (penetrable) channel in the presence of curvature and non-linear hydrodynamic impacts. The motion takes place in an asymmetric channel due to a train of sinusoidal (complex nature) waves along the channel boundaries having different phases. The Casson fluid is used as blood in the present study. The governing equations are modeled in terms of Cartesian coordinates. The impacts of non-linear curvature become significant on the transportation of biological fluid in a complex domain such as the non-pregnant uterus at a higher Reynolds number. An approximate solution of flow models is obtained to the second order in the wavenumber (giving the curvature effect). A domain transformation is used to transform the variable cross-sectional of the flow regime into the uniform cross-section. This transformation helps find the closed-form solution of transformed rheological equations in higher order. The physical impacts of the curvature parameter, Casson parameter, phase difference, flow rate, Reynolds number, and permeability parameter on the axial velocity, pressure gradient, stress tensor, trapping phenomena, and pressure rise are investigated. The velocity of blood is smaller as it is associated with the viscous fluid. The number of boluses was reduced by increasing the Casson parameter and Reynolds number in the trapping phenomenon. The stressor tensor is an increasing function of the permeability parameter and Reynolds number. The pressure gradient is affected by the permeability parameter. The comparison between viscous fluid and blood is also addressed in the current study. The outcomes of current study arise in the medical domains, blood study, manufacturing of nano-blood pumps, bio-physical food processing, and chemical industry.