THE INFLUENCE OF FRACTIONAL ORDER AND MAGNETIC FIELD ON ELECTRO HYDRODYNAMIC FLOW OF JEFFREY FLUID ALONG WITH MAGNETIC NANOPARTICLES THROUGH ARTERIAL SEGMENT

Abstract

The study reports the influence of Caputo–Fabrizio fractional derivative and magnetic field on blood flow as an electrically conducting non-Newtonian fluid along with magnetic nanoparticles through circular cylindrical arterial segment, by assuming blood as Jeffrey fluid. The main structure of the governing fractional nonlinear partial differential equations was obtained from non-Newtonian fluid model in which convective derivative is considered instead of the time derivative which is capable of describing the phenomena of relaxation time and retardation time. The exact solutions of the governing fractional partial differential equations were obtained by the virtue of Laplace and Hankel transforms. Numerical simulations have been performed to analyze the behavior of the Jeffrey fluid flow using Mathcad software and the results are presented graphically for an explicit and detail discussion. We noticed from the graphical representation of results that the fractional derivative, particle concentration, electro-kinetic width, Jeffrey number and the applied magnetic field have profound influence on the magnitude of blood velocity along with magnetic nanoparticles. The effect of each of the influential parameters tremendously decelerates the fluid flow and thereby showing appreciable variation in the distribution of axial and radial velocities. Practically, increasing the applied magnetic field strength and the value of the Jeffrey number on the motion of fluid flow together with magnetic nanoparticles, vehemently decreases the velocities of blood along with magnetic nanoparticles, which helps to have effective control over the fluid networks. From the study, we conclude that the fractional model, Jeffrey number and the application of the external magnetic field on the fluid flow have extensive applications in the clinical and the medical sciences.