Free Convection Caputo-Fabrizio Casson Blood Flow in the Cylinder with Slip Velocity

Recently, fluid with fractional-order derivative model attracted many researchers to further study compared with the classical fluid mode since it is more precise and realistic. To imitate the applications of blood flow in narrow arteries, researchers focused on the fractional Casson fluid flow in the cylinder. However, most researchers solved the problems numerically and without considering the slip effect at the boundary. Thus, obtaining solutions analytically to the unsteady fractional Casson fluid flow in the slip cylinder with free convection is the goal of this study. The Caputo-Fabrizio fractional derivative approach is utilized to model this problem. By joining the approach of the Laplace transform and finite Hankel transform, the fractional governing equations are solved, and analytical solutions to the velocity and temperature profiles are gained. The fluid velocity rises as the slip velocity and Grashof number increase and it declines with the increment of the Casson parameter and Prandtl number. Increasing the fractional parameter will result in an increase in fluid velocity and temperature for a large time interval. The slip velocity effect influenced fluid flow, especially at the cylinder’s wall. These findings are beneficial to explore the more fractional-order derivative model and for studying the problems in biomedical engineering.