Construction of the Exact Solution of Blood Flow of Oldroyd-B Fluids Through Arteries With Effects of Fractional Derivative Magnetic Field and Heat Transfer

Abstract

In this paper, we construct the exact solution of blood flow of Oldroyd-B fluids to represent the non-Newtonian characteristics of biofluids and to study the unsteady flow of blood and heat transfer through arterial segment with external magnetic field applied normal to the flow direction in the presence of thermal radiation and body acceleration. In the study, we investigate the influence of Caputo time-fractional parameter, heat transfer, external body acceleration, and magnetic field on the blood velocity and temperature distribution in a straight circular cylindrical vessel. The constitutive partial differential equation and temperature equation governing blood flow in the arterial wall are solved using Laplace and finite Hankel transforms. In addition, Gaver Stehfest’s algorithm is used for the inverse Laplace transform. The results obtained are interpreted graphically and discussed from the physiological point of view. The graphs show that the rate of heat transfer and blood velocity become less with the increase in the external magnetic field strength which is very good in regulating blood flow as well as temperature distribution during treatment. Based on the graphical representations, blood velocity and temperature distribution both decrease in ascending order of the fractional parameter as memory effect. Further, owing to the dissipation of energy caused by blood viscoelasticity and magnetic field effect, during pulsatile flow of blood, the heat transfer rate at the wall of the artery is enhanced. The significance of this study can be found in the application fields such as biomedical engineering, medicine and pathology.