Non-uniform pumping flow model for the couple stress particle-fluid under magnetic effects

In this article, peristaltically induced motion of couple stress fluid under the suspension of small particles have been studied. A peristaltic wave with non-uniform motion is traveling with a constant wave celerity. An extrinsic magnetic field is applied to an electrically conducting incompressible fluid with irrotational motion. Lubrication theory is applied for the mathematical formulation of both fluid- and particle-phase equations. Analytically and numerically, the formulated equations are solved using computational software Mathematica. The exact solutions are determined against the velocity profile for both fluid- and particulate-phases. The volumetric flow rate is also presented and calculated numerically to examine the pumping characteristics. Trapping mechanisms via streamlines are plotted and discussed against all the leading parameters. The present results are also beneficial to observe the Newtonian behavior and single phase fluid model. It is also observed that magnetic field opposes the fluid movement in the middle of the channel, while the presence of small particles tends to resist the fluid motion along the whole channel. A significant reduction in the pumping rate was observed due to the rise in the couple stress fluid parameter, the fraction of the particle volume, and the average volume flow rate, but a dual behavior is observed against the magnetic parameter. The fluid bolus diminishes in magnitude and reduces in quantity against the higher values of Hartmann number.