Slip velocity effect on unsteady free convection flow of Casson fluid in a vertical cylinder

Abstract

Many researchers study the Casson fluid flow in the cylinder since it imitates human blood flow in the small arteries. However, only a few researchers considered slip velocity at the boundary. The slip velocity is crucial in blood flow study due to naturally occurs during stretchable movement of the arteries. Hence, the study aims to obtain analytical solutions and understand the fluid flow behaviour with the slip velocity effect for the unsteady free convection flow of Casson fluid in a cylinder. The analytical solutions are obtained by using the joint methods of the finite Hankel transform and the Laplace transform. All initial and boundary conditions are satisfied by the analytical solutions that were obtained. The behaviour of velocity and temperature profiles are plotted and discussed graphically. It is evident from the results that increasing the slip velocity, Grashof number and time will enhance blood velocity while increasing the Casson parameter causes a decrement of blood velocity. Besides, the Prandtl number increases resulting in blood velocity and the blood temperature falling. Lastly, the obtained analytical solution is validated by comparing it with the previ ous study and found to be in good mutual agreement. The obtained analytical solution is significant to check the accuracy of the numerical solutions.