Numerical study of pulsatile non-Newtonian blood flow and heat transfer in small vessels under a magnetic field

The purpose of this study is to analyze the impact of magnetic field on the unsteady blood flow pass a small vessel with a pulsatile pressure gradient by treating blood as a non-Newtonian fluid, which can be described by Maxwell fluid model with fractional derivative. Also the heat transfer characteristics of the flow arising out of radiative heat flux, viscous dissipation, and electromagnetic coupling is considered. We developed a finite difference algorithm to derive the numerical solutions of the nonlinear and coupled governing equations of velocity and temperature. The stability and convergence of the numerical algorithm are tested, and it is found to be stable and convergent. The influence of various significant dynamics parameters on velocity, flow rate and temperature are deeply discussed. It is indicated that, compared with the fractional Maxwell fluid model, Newtonian fluid dynamics underestimate the velocity and temperature of blood. Applying a magnetic field or increasing thermal radiation is conducive to give a higher temperature, but they have the opposite effect on velocity and flow rate, that is, the imposed magnetic field leads to a decrease of flow rate, while on the contrary, thermal radiation will enhance the flow rate.