Numerical simulation of biomagnetic micropolar blood flow with the Rosensweig ferromagnetic formulation

Beg, OA; Beg, TA; Kadir, A; Leonard, HJ; Malysheva, LI; Khan, UF; El Gendy, M

Abstract

One of the most basic functions which magnetic fields exert on the human body is to increase circulation. When a cell (e.g. red blood cell) is damaged, it does not hold its ideal charge. This causes red cells to “stick” together, making circulation slow. When a magnetic field passes through the red cell, the membrane becomes properly charged, allowing the cell to repel itself and keep itself separate from other red cells, thereby increasing circulation. Magneto-physiological therapy also exploits the electrically conducting nature of streaming blood which is due to iron content in the haemoglobin molecule as well as ions suspended in plasma. The rotational motions of blood cells and the presence of proteins and other suspensions result in blood being rheological in nature. Therefore, to accurately simulate magnetic blood flow, a combined biomagnetic non-Newtonian formulation must be adopted. In this spirit, in the present work, we use a multii-physical biomagnetic micromorphic approach to achieve this. The Rosensweig ferromagnetic and Eringen micropolar models are combined to develop a mathematical model for two-dimensional fully developed steady, viscous hydrodynamic flow of deoxygenated blood, in an (X.Y) coordinate system. The momentum conservation equations are extended to incorporate the X- and Y-components of the biomagnetic body force term and micropolar coupling terms with appropriate boundary conditions. A separate angular momentum (micro-rotation) conservation equation is also featured. The transformed dimensionless transport equations are solved with a variational finite element method. A parametric investigation of the effects of Rosenseig biomagnetic number (NH), Eringen micropolar microinertia parameter (B) and Eringen micropolar viscosity ratio parameter (R) on the primary translational (U) and secondary translational (V) velocity profiles and micro-rotation i.e. angular velocity (N) is conducted. Translational velocities (U, V) are seen to be reduced with an increase in micropolar parameter (R) and also biomagnetic number (NH). Conversely the velocities are increased with a rise in microinertia parameter (B). Several special cases e.g. Newtonian biomagnetic and non-conducting micropolar physiological flow, are also discussed. The model finds applications in blood flow in biomedical device technology (e.g. oxygenators), hemodynamics under strong external magnetic fields, magnetic drug carrier analysis etc.

Citation

Beg, O., Beg, T., Kadir, A., Leonard, H., Malysheva, L., Khan, U., & El Gendy, M. Numerical simulation of biomagnetic micropolar blood flow with the Rosensweig ferromagnetic formulation. Presented at ICFMA 2022: 16th International Conference on Fluid Mechanics and Applications, Lisbon, Portugal

• Presentation Conference Type: Other
• Conference Name: ICFMA 2022: 16th International Conference on Fluid Mechanics and Applications
• Conference Location: Lisbon, Portugal
• End Date: Oct 29, 2022
• Acceptance Date: Dec 10, 2020
• Deposit Date: Jan 8, 2021
• Publisher URL: https://waset.org/fluid-mechanics-and-applications-conference-in-october-2022-in-lisbon
• Related Public URLs: https://waset.org/
• Additional Information: Event Type : Conference