A study of full Navier-Stokes equations of peristaltic flow in a porous-saturated tube under the inducement of magnetic field: Finite element analysis

The core objective of this article is to investigate the full form of Navier-Stokes equations representing nonlinear peristaltic flow passing through the tube filled with homogeneous porous medium under the effect of the applied uniform magnetic field. The Galerkin's variational approach is used to apply the finite element method to find the numerical solution of the governing system of nonlinear partial differential equations. The results are obtained without imposing the assumptions of long wavelength with low Reynolds number on modeled differential equations. Consequently, we obtained the results which are valid for moderate values of wave number and Reynolds number. The effects of these parameters including Hartmann number, permeability parameter and time-mean flow rate on the longitudinal velocity distribution and pressure rise per wavelength are presented through graphs. Circulation of the trapped bolus is enhanced with the dominance of the inertial forces but an increase in magnetic field condenses the volume of the trapping bolus. Linear behavior of pressure is observed for small Reynolds number while for greater values of Reynolds number pressure rise per wavelength is perceived nonlinear behavior. The excellent agreement is observed in the comparison of the present numerical results with analytical results available in the literature in the limiting case.