Novel study of inertial forces on MHD peristaltically driven micropolar fluid through porous-saturated asymmetric channel: Finite Galerkin approach

Abstract

This focused study investigates the peristaltic motion of a micropolar fluid within an uneven channel filled with a porous medium, incorporating an orthogonal magnetic field to the flow. This research diverges from the traditional assumptions of lubrication theory. The governing equations, encompassing the physical characteristics of micropolar fluid peristalsis, are transformed into nonlinear coupled partial differential equations. These equations are solved using the finite element method, considering inertial effects, such as non-zero wave and Reynolds numbers. This study delves into the influence of various crucial parameters on axial velocity, pressure gradient, microrotation, and stream function, presenting graphical representations. Notably, the incremental phase shift causes an intermingling of upper and lower streamlines within both halves of the channel. As the Reynolds number increases, there is an observed reduction in bolus size, particularly at maximum phase shifts, with a tendency to move toward the central region. An increase in Hartmann number leads the bolus formation to vanish in both channels, reduces microrotation, and leads to increased pressure. Vorticity lines intensify and incline toward the peristaltic walls. An increase in the permeability parameter amplifies velocity, microrotation, volume, and bolus formation regardless of phase differences while countering pressure elevation per wavelength. Reduced concavity is observed as vorticity lines disperse across the entire area.