Magneto hydrodynamic (MHD) pulsatile motion of blood with wall slip velocity and periodic body acceleration

Abstract

Background: The present investigation is concerned with the theory of a model of the pulsatile motion of blood through a mild stenosedlong tube under the influence of a uniform transverse magnetic field and periodic body acceleration. Methods: In the present investigation,a mathematical model has been developed to study the effect of externally applied uniform transverse magnetic field on blood motionthrough stenosed vessels, considering slip velocity at the vessel’s endothelium. Results: To analyze the problem, blood is assumed tobe incompressible and Newtonian homogeneous fluid as far as large arteries’ shear rate is high. Noting the behavior of red cells in thearteries, the possibility of the role of slip velocity at the wall under certain conditions has been considered. Also, since for biologicalsystems, blood is conducted with a low magnetic Reynolds number, the flow is supposed to be under the action of a uniform magneticfield for which the induced magnetic field can be neglected. Moreover, the pulsatile motion is generated by sinusoidal behavior andis affected by periodic body acceleration. Exact solutions of the relevant equations are obtained using Laplace and Hankel integraltransforms. Conclusion: The expressions for axial velocity, flow rate, fluid acceleration, and shear stress are given in analytical for us. Theeffects of magnetic field and body acceleration on the solutions have been discussed graphically. The present study seems to immerseimportance in diversified fields of biomedical engineering.