Magnetohydrodynamic biorheological transport phenomena in a porous medium: A simulation of magnetic blood flow control and filtration

Application of magnetic fields to medical science is growing rapidly, with the development of novel magnetic pumps, hydromagnetic separation devices, etc. In this paper, we study the dual control mechanisms of transverse magnetic field and porous media filtration on viscous convection heat transfer in a buoyancy-driven blood flow regime in a vertical pipe, as a model of a blood separation configuration. Non-Newtonian characteristics of the blood are modeled with the well-tested, thermodynamically rigorous micropolar model introduced by Eringen. Porous media effects are simulated with a Darcy–Forchheimer drag force model. The two-point boundary value problem is normalized and the resulting dimensionless linear momentum, angular momentum (Eringen micro-rotation) and energy conservation equations are solved by the Differential Transform Method (DTM). The convergence analysis elucidates that the DTM yields exceedingly accurate results, which are validated with a comparison with optimized fourth-order Runge–Kutta numerical quadrature. The influence of micropolar vortex viscosity parameter (Eringen parameter (Er), Hartmann magnetohydrodynamic number (Ha), aspect ratio (A), Darcy number (Da), heat generation/absorption parameter () and Grashof number on the flow variables are studied in detail. The present study has important applications in magnetic field control of biotechnological (hemodynamic) processes, biomagnetic device technology, etc.

magnetohydrodynamic; biofluid; bio-rheology; convection; porous media; Differential transform method (DTM)