Mathematical modeling of magneto-peristaltic propulsion of a viscoelastic fluid through a complex wavy non-uniform channel: an application of hall device in bio-engineering domains

Abstract

Applications of the Hall device into both the biological and engineering domains have been investigated in the current study. A complex peristaltic driven flow of a viscoelastic fluid is considered through a non-uniform regime having wavy walls under the magnetic and Hall effects. The physical influences of magnetic and Hall parameters on different rheological features of biomimetic propulsion in the wave frame are highlighted in details. Due to the complex nature of the flow regime, the curvilinear coordinates are used in the derivation of continuity and momentum equations. The flow analysis is based on creeping phenomena and long wavelength approximations. Analytical solutions of the governing equations are difficult to obtain due to complicated and complex mathematical form of partial differential equations. Numerical solutions of the governing equations are obtained with the help of the versatile BVP4C command in MATLAB software. The main objective of the current study is to observe the physical behavior of embedded parameters such as dimensionless radius of curvature, Hartmann number (magnetic parameter), Hall parameter, phase difference, non-uniform parameter, and viscoelastic (time relaxation and retardation) parameters on the axial velocity, stream function, pressure gradient, pumping, and trapping phenomena. Moreover, the comparison between viscous and viscoelastic fluids has been argued in detail through graphs. This research work provides comprehensive information about the magnetic and Hall devices, respectively, that are more productive to control the flow of biological fluids through the non-uniform nature of vessels. This study has numerous applications in micro-scale devices of biomedical and industrial domains, cooling systems in nuclear power stations, magnetic therapy, hydrology, physiological drug delivery systems, blood pumping, and micro devices used during surgical treatments.