On viscoelastic blood in a locally narrow artery with magnetic field: application of distributed-order time fractional Maxwell model

Abstract

Purpose. The study of hemorheology of heterogeneous vessels is of importance for the therapy of cardiovascular diseases. The present paper aims to investigate the effects of the height parameter of the stenosis, the Reynolds number, the relaxation time and the Hartmann number on the blood flow by applying distributed order time fractional Maxwell model. Methodology. Distributed order time fractional Maxwell constitutive fluid model is used to simulate viscoelastic blood flowing in a narrowing blood vessel with uniform magnetic field. The continuity and momentum equations are established in two-dimensional cylindrical coordinate system for calculation. With vorticity-stream function method, the finite difference technique, combined with the fractional derivative L1 interpolation approximation, is utilized to obtain numerical solutions of velocity and wall shear stress. The effectiveness of the numerical method is verified. Outcomes. It reveals the choice of relaxation time in the governing equation has an influence on the results. The numerical results show that an appropriate increase of Reynolds number can reduce the possibility of vessel damage. Furthermore, when the height parameter of the stenosis increases, the damage to the vessel wall is getting serious. Besides, the wall shear stress along the blood vessel increases with the increase of the magnetic field, but the wall shear stress in the narrowest part of the blood vessel changes little.