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The present physical problem has a significant number of applications in intra-uterine fluid motion with tiny particles in a nonpregnant uterus, and this situation of fluid motion is very important in examining the embryo motion in a uterus. Due to these real-life applications, in the current investigation, a perturbation-oriented numerical investigation has been performed to describe the characteristics features of velocity, pressure rise, and trapping bolus through streamlines in a tapered channel under a porous medium. The present physical model results in the governing two-dimensional coupled nonlinear flow equations under low Reynolds number and long-wavelength approximations. A suitable equation for stream function is derived and a regular perturbation scheme is employed to produce the numerical solutions in terms of pressure rise, velocity, and streamlines for various values of physical parameters. The current investigation depicts that the enhancing Darcy parameter upsurged the pressure field, and the increasing power-law index suppressed the pressure field in the flow regime. The rincreasing channel width significantly diminished the velocity field at the central portion of the channel. The size of the trapping bolus suppressed for the enhancing values of Weissenberg number. In addition, the size of the trapping bolus increased for the magnifying values of wave amplitudes. Finally, current numerical solutions reasonably agree with the previously published results in the literature, and this fact confirms the accuracy of the present problem.

The aim of the present numerical investigation is to explore the impact of magnetic field on peristaltic flow of an incompressible tangent‐hyperbolic fluid in an asymmetric channel. The present physical model is developed based on the considered flow configuration and with the help of small Reynolds number approximations. The current flow problem is revealed under the influence of applied magnetic field. The asymmetric channel has been considered to narrate the present physical problem. Considered physical situation in the current investigation gives the unsteady coupled highly nonlinear system of partial differential equations. Also, the simplified equations for pressure, pressure gradient, and streamlines have been obtained with the help of suitable transformations. A regular perturbation scheme is employed to produce the semi‐analytical results of the present problem. The influence of various physical parameters on pressure, pressure gradient, and streamlines are illustrated with the help of graphs. From the present analysis, it is observed that the increasing magnetic number decreases the pressure and pressure gradient in the channel. Also, the size of trapping bolus increases with increasing values of Weissenberg number. [ABSTRACT FROM AUTHOR]