HAM Solution of an Unsteady Three Dimensional Navier-Stokes Equations of Flow between Two Parallel Disks

[摘要] Purpose: The paper aims to find an analytic solution of an unsteady three dimensional Navier-Stokes equations of flow between two parallel disks by using von Karman type similarity transformation. Methodology: In this paper, the Homotopy Analysis Method (HAM) with the value of unknown convergence control parameter has been used to derive accurate analytic solution for an unsteady three dimensional Navier- Stokes equations of flow between two parallel disks. The possible optimal value of the convergence control parameter determined by increasing the order of HAM. Findings: The results obtained from HAM are compared with numerical results. The result shows that this method gives an analytic solution with high order of accuracy with a few iterations.

[关键词] 3D Navier-Stokes equation;Homotopy analysis method;Convergence;System of nonlinear differential equations