A Study of Fractional Relaxation Time Derivative on Blood Flow in Arteries with Magnetic and Thermal Radiation Effects

In this paper, a fractional relaxation model is studied to determine the effect of heat transfer and magnetic field on the blood flow. The flow is due to an oscillating periodic pressure gradient and body acceleration. We apply Laplace transform as well as finite Hankel transform to obtain the closed form solutions of the velocity and temperature distributions of the fractional time partial differential equations. Effect of the fluid flow parameters are shown graphically with changes in the ordinary model as well as the fractional parameters. The analysis shows that the fractional derivative is an excellent tool which gives remarkable change in controlling temperature and blood flow. The analysis depicts graphically, that in the presences of strong applied (exterior) magnetic field, reduces the temperature and blood flow velocities, which is appropriate to avoid tissues damage during treatment. In addition, it is seen that some of the aforementioned parameters influenced the fluid flow profiles in increasing and decreasing fashion which is interpreted as useful to the study.