The paper reports on a comprehensive mathematical model for simulations of blood flow under the presence of strong non-uniform magnetic fields. The model consists of a set of Navier–Stokes equations accounting for the Lorentz and magnetisation forces, and a simplified set of Maxwell’s equations (Biot–Savart/Ampere’s law) for treating the imposed magnetic fields. The relevant hydrodynamic and electromagnetic properties of human blood were taken from the literature. The model is then validated for different test cases ranging from a simple cylindrical geometry to real-life right-coronary arteries in humans. The time-dependency of the wall-shear-stress for different stenosis growth rates and the effects of the imposed strong non-uniform magnetic fields on the blood flow pattern are presented and analysed. It is concluded that an imposed non-uniform magnetic field can create significant changes in the secondary flow patterns, thus making it possible to use this technique for optimisations of targeted drug delivery.
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