Mathematical study of peristaltic propulsion of solid-liquid multiphase flow with a biorheological fluid as the base fluid in a duct

In this paper, the peristaltic transport of a MHD dusty three-dimensional biorheological (Casson) fluid in a duct is investigated. The governing flow problem is based on the continuity and momentum equations. These equations are modeled for both the fluid phase and particle phase by means of a creeping flow regime and long wavelength assumption. The exact solution has been obtained for the resulting partial differential equation by means of the eigenfunction expansion method. Graphical results are discussed against all the emerging parameters such as the Hartmann number, particle volume fraction, Casson fluid parameter etc. Numerical integration has been used to determine the pumping characteristics. Trapping phenomena are also discussed and sketched by drawing streamlines for all the physical parameters. A graphical comparison is also presented with the previously published data and it is found that the present results are in excellent agreement, which assures that the current methodology and results are correct. It is observed that the velocity profile diminishes due to a greater influence of the particle volume fraction and Hartmann number. Moreover, it is found that the Casson fluid parameter enhances the fluid velocity near the walls of the duct and opposes the flow in the middle of the duct.