The Effects of Fractional Relaxation Time and Magnetic Field on Blood Flow through Arteries along with Nanoparticles

Abstract

In this paper, we report the effects of fractional relaxation time on the parameters of blood flow together with magnetic particles through straight circular cylindrical arterial segment. A mathematical model of blood flow subject to pulsatile pressure gradient in the axial direction with external magnetic field applied normal to the direction of flow is presented. Combining the momentum equation together with the Maxwell model parameter appropriately, leads to the governing fractional partial differential equation which permits to obtain the velocity profile of blood along with magnetic particles. By adopting the non-dimensionalized form of the new version of the governing fractional partial differential equation allowed us to obtain the dimensionless relaxation time parameter λ1 which controls blood flow conditions. Solving the fractional partial differential equations using Laplace and finite Hankel transforms we found that the influence of the order of Caputo's fractional time-derivative and fractional relaxation time on the blood flow parameters with magnetic particles are enormous. The graphical results plotted of different influential parameters are presented and discussed in details. The velocities of blood flow and that of magnetic particles are reduced under the influence of the external magnetic field and the relaxation time parameter. The magnetic particles are assumed to be uniformly distributed within the blood, since they are flowing in the same axial direction designated by along a circular cylindrical coordinates of radius. This is a very good indication that blood velocity can be controlled by the application of external magnetic field as well as the relaxation time parameter during treatment to avoid tissues damage. The present study has important applications in magnetic field control of biotechnological processes, bio magnetic device technology, biomedical engineering and pathology. Keywords: Arterial segment, Blood flow, Relaxation time, Magnetic field, Magnetic particles