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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.

A two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with variable thermal conductivity and exterior squeezing with viscous dissipation effect is investigated, numerically. Present flow model is developed based on the considered flow geometry. Effect of Lorentz forces on flow behaviour is described in terms of magnetic field and which is accounted in momentum equation. Influence of variable thermal conductivity on heat transfer is considered in the energy equation. Present investigated problem gives the highly complicated nonlinear, unsteady governing flow equations and which are coupled in nature. Owing to the failure of analytical/direct techniques, the considered physical problem is solved by using Runge-Kutta scheme (RK-4) via similarity transformations approach. Graphs and tables are presented to describe the physical behaviour of various control parameters on flow phenomenon. Temperature boundary layer thickens for the amplifying value of Weissenberg parameter and permeable velocity parameter. Velocity profile decreased for the increasing squeezed flow index and permeable velocity parameter. Increasing magnetic number increases the velocity profile. Magnifying squeezed flow index magnifies the magnitude of Nusselt number. Also, RK-4 efficiently solves the highly complicated nonlinear complex equations that are arising in the fluid flow problems. The present results in this article are significantly matching with the published results in the literature.

Present research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.

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]