Effects of the fractional order and magnetic field on the blood flow in cylindrical domains

In this paper, based on the magnetohydrodynamics approach, the blood flow along with magnetic particles through a circular cylinder is studied. The fluid is acted by an oscillating pressure gradient and an external magnetic field. The study is based on a mathematical model with Caputo fractional derivatives. The model of ordinary fluid, corresponding to time-derivatives of integer order, is obtained as a particular case. Closed forms of the fluid velocity and magnetic particles velocity are obtained by means of the Laplace and finite Hankel transforms. Effects of the order of Caputo's time-fractional derivatives and of the external magnetic field on flow parameters of both blood and magnetic particles are studied. Numerical simulations and graphical illustrations are used in order to study the influence of the fractional parameter α, Reynolds number and Hartmann number on the fluid and particles velocity. The results highlights that, models with fractional derivatives bring significant differences compared to the ordinary model. This fact can be an important advantage for some practical problems. It also results that the blood velocity, as well as that of magnetic particles, is reduced under influence of the exterior magnetic field.