Abstract
In this paper, homotopy analysis method (HAM) and Padé approximant will be considered for finding analytical solution of three-dimensional viscous flow near an infinite rotating disk which is a well-known classical problem in fluid mechanics. The solution is compared to the numerical (fourth-order Runge-Kutta) solution and the convergence of the obtained series solution is carefully analyzed. The results illustrate that HAM-Padé is an appropriate method in solving the systems of nonlinear equations.
Highlights
Von Karman swirling viscous flow [1] is a well-known classical problem in fluid mechanics
The original problem raised by Von Karman is about the viscous flow induced by an infinite rotating disk where the fluid, far from the disk, is at rest
The purpose of this paper is to extend homotopy analysis method and Padé approximant to solve three-dimensional Navier-Stokes equations for the viscous flow near an infinite rotating disk
Summary
Von Karman swirling viscous flow [1] is a well-known classical problem in fluid mechanics. The problem is generalized in considering the case where the fluid itself is rotating as a solid body far from the disk with suction or injection at the disk surface [2]. This generates a parameter, i.e. the ratio of the angular velocity of the fluid at infinity to the angular velocity of the disk. Another generalization is to consider the viscous flow between two infinite coaxial rotating disks with suction or injection at both disks and this reveals another parameter, i.e. the Reynolds number determined by the distance of the two disks.
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