The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

The study on the effects of biological fluids in the presence of magnetic field is known as biomagnetic fluid dynamics (BFD) and the most common biological fluid that exhibit such magnetic properties is blood. An extensive research work has been done in this area due to its applications in medical and bioengineering. Basically, it is essential for a study to be justified according to certain benchmark before progressing. Hence, biomagnetic fluid flow in a lid driven cavity is numerically investigated by utilizing two numerical schemes: finite difference and finite element methods. The formulation adopted is consistent with the principles of ferrohydrodynamics. The mathematical model describes Newtonian blood flow under the influence of a spatially varying magnetic field. The model considers the biofluid as non-conducting. The flow is assumed to be two-dimensional, steady, laminar and isothermal. The implementation of finite element method shows stability issue due to extremely steep magnetic field gradient while finite difference method shows no issue. Due to this, a solution is proposed to alleviate the problem and the result for various magnetic field intensity presented.