Analytical Solution of Hyperbolic Tangent Fluid's Peristaltic Flow in an Inclined Channel: Hall Effect's Impact

Aim: In our study, we investigated, based on the premise of a long wavelength, how Hall's theory affected the peristaltic pumping of a fluid with a hyperbolic tangent within an inclined planar channel, and how both affected each other.

Study Design: Abstract, introduction, Statement, Analytical Solution, Results and Discussion, and conclusion.

Methodology: The intra-uterine fluid motion with tiny particles in a non-pregnant uterus is one of the many applications of the current physical problem, and this fluid motion condition is crucial for analysing the motion of the embryo in a uterus. Perturbation-oriented numerical research has been carried out in the current study to characterise the properties of velocity and axial pressure gradient in an inclined channel under Hall effect on the peristaltic flow of a Hyperbolic tangent because of these real-world applications. Under low Reynolds number and long-wavelength approximations, the current physical model yields the governing two-dimensional coupled nonlinear flow equations. For different values of the physical parameters, a suitable equation for the stream function is derived, and a regular perturbation scheme is used to produce the numerical solutions in terms of pressure rise and velocity. Weissenberg number, power-law index, Hall parameter, Hartmann number, and amplitude ratio relationships are examined in graphs along with their effects on the axial pressure gradient and time-averaged volume flow rate. According to the findings of this study, whereas the axial pressure gradient and time-averaged flow rate in the pumping region enhance with rising values of the Weissenberg, Hartmann, Reynolds, angle of inclination, and amplitude ratio, they diminish with enhances in the power-law index, Hall parameter, and Froude number. Hyperbolic tangent fluid has been discovered to require less pumping than Newtonian fluid.