On the viscous flow through a porous-walled pipe: asymptotic MHD effects

Abstract

This study explores the filtration problem of Newtonian, incompressible, and viscous two-dimensional fluid flow through a permeable-walled tube. The generated pressure-driven flow incorporates Darcy’s law at the circular pipe wall. We then apply a transverse magnetic field of uniform strength to control the fluid filtration. Subsequently, we analytically examine the potential impacts of the magnetic field on the magnetohydrodynamic behavior of the fluid particles and the axial pressure field using perturbation analysis. Our results delineate the characteristics of the Lorentz force on the flow and pressure field within the porous-walled pipe. Notably, the magnetically affected pressure changes sign at a specific downstream location within the pipe, while the axial velocity flattens with increasing Hartman number at the inlet. Although the inlet regime is under the well-recognized damping dominance of the magnetic field, the filtration process downstream is accelerated with the assist of it.