Mathematical Modeling of a Complex System for MHD Flow in Hemodynamics

Many physiological system in humans and animals are complex systems. Hemodynamic is a branch of physiology and is a complex system which deals with the study of blood flow in arteries. We study the complex physical system of blood flow in a narrow artery with asymmetric stenos is in the presence of external magnetic field, treating blood as Herschel-Bulkey fluid model. Finite difference scheme is applied to solve the resulting system of nonlinear partial differential equations with appropriate initial and boundary conditions. The finite difference schemes for the velocity distribution, skin friction, flow rate and longitudinal impedance to flow are obtained. It is found that the velocity decreases with the increase of the magnetic field and pressure gradient reverse behavior is noticed when the yield stress and depth of the stenos is increase. It is also observed that the flow rate decreases with the increase of the stenos is shape parameter, power law index and yield stress. Also, it is noted that the presence of external magnetic field influences the mean velocity by increasing its magnitude significantly in arteries of different radii.