The Sustainable Characteristic of Bio-Bi-Phase Flow of Peristaltic Transport of MHD Jeffrey Fluid in the Human Body

TLDR

The study examines peristaltic transport of a non‑Newtonian Jeffrey fluid containing uniformly distributed rigid particles in a rectangular duct, extending previous hydrodynamic, Newtonian, and single‑phase analyses by incorporating magnetic and bi‑phase effects. Using a long‑wavelength, low‑Reynolds approximation, the authors simplify the mass and momentum equations and obtain a closed‑form velocity solution via eigenfunction expansion, with pressure rise computed numerically. Graphical results illustrate how varying physical parameters influence the flow and confirm that the method reproduces known hydrodynamic, Newtonian, and single‑phase limits, demonstrating its suitability.

Abstract

This study deals with the peristaltic transport of non-Newtonian Jeffrey fluid with uniformly distributed identical rigid particles in a rectangular duct. The effects of a magnetohydrodynamics bio-bi-phase flow are taken into account. The governing equations for mass and momentum are simplified using the fact that wavelength is much greater than the amplitude and small Reynolds number. A closed-form solution for velocity is obtained by means of the eigenfunction expansion method whereby pressure rise is numerically calculated. The results are graphically presented to observe the effects of different physical parameters and the suitability of the method. The results for hydrodynamic, Newtonian fluid, and single-phase problems can be respectively obtained by taking the Hartmann number (M = 0), relaxation time (λ1=0), and volume fraction (C = 0) as special cases of this problem.