FINITE ELEMENT STUDY OF TRANSIENT PULSATILE MAGNETO-HEMODYNAMIC NON-NEWTONIAN FLOW AND DRUG DIFFUSION IN A POROUS MEDIUM CHANNEL

Abstract

A numerical study of pulsatile hydromagnetic flow and mass transfer of a non-Newtonian biofluid through a porous channel containing a non-Darcian porous material is undertaken. An extensively-validated biofluid dynamics variational finite element code, BIOFLOW, is employed to obtain comprehensive computational solutions for the flow regime which is described using a spatially two-dimensional momentum equation and a spatially one-dimensional mass transport equation, under appropriate boundary conditions. The Nakamura-Sawada rheological model is employed which provides a higher yield stress than the Casson model. A non-Newtonian model is justified on the basis that blood exhibits deviation from Newtonian behavior at low shear rates. The conduit considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. One hundred two-noded line elements have been employed in the computations. The influence of magnetic field on the flow is studied via the magnetohydrodynamic body force parameter (Nm), which defines the ratio of magnetic (Lorentz) retarding force to the viscous hydrodynamic force. Blood vessel blockage effects are simulated with a Darcy-Forchheimer nonlinear drag force model incorporating a Darcian linear impedance for low Reynolds numbers and a Forchheimer quadratic drag for higher Reynolds numbers. Transformed velocity and concentration profiles are plotted for the influence of Reynolds number (Re), Darcy parameter (λ), Forchheimer inertial drag parameter (NF), non-Newtonian parameter (β), and Schmidt number (Sc) and at various times (T). Three-dimensional profiles of velocity varying in space and time are also provided. Applications of the model include magnetic therapy, biomagnetic pharmaco-dynamics and the simulation of diseased arteries.