A Novel Analytical Investigation of a Swirling Fluid Flow and a Rotating Disk in the Presence of Uniform Suction

This paper aims to find an exact solution for the von Karman swirling viscous fluid flow caused by the infinite radius rotating disk with uniform suction. The swirling flow occurred at infinity or far from the rotating disk, and two conditions were considered. The first condition is when the direction of swirling flow at infinity is the same as the direction of angular velocity that the rotating disk has. The second condition is when the direction of the rotating disk and that of the swirling flow are opposites. When there are no swirling flow at infinity and no suction on the surface of the rotating disk, the pressure distribution is just a function of distance above the disk. The similarity transformation converts the governing equations from partial differential equations into ordinary differential equations and then is solved analytically with the HAN method. In this study, three cases were considered. The first case is a swirling flow at infinity that has the opposite and same direction of the rotating disk when there is no suction on the disk's surface. The second case is no swirling flow at infinity, but the suction occurs on the rotating disk's surface. The third one is both suction on the rotating disk and swirling flow. In the first case, it was observed that when the angular velocity of the fluid at a distance away from the disk is insignificant compared to the angular velocity of the disk, the skin friction coefficient reaches the maximum value and vice versa when the angular velocity of the fluid increases at a distance away from the disk, the value of skin friction coefficient decreases. In the second case, it was observed that the more the surface suction increases, the more the skin friction coefficient increases. Hence, the skin friction coefficient on a porous disk on which suction occurs is higher than on a normal non-porous disk. The results demonstrate that when parameters such as s = a = 0, the pressure will be a distance function above the disk if we put r = 0.