Semi-analytical solution for nonlinear Von Kármán swirling fluid flow via the hybrid analytical and numerical method

Ali  Ahmadi Azar

doi:10.59400/mea2878

Semi-analytical solution for nonlinear Von Kármán swirling fluid flow via the hybrid analytical and numerical method

Ali Ahmadi Azar Department of Mechanical Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran

Article ID: 2878

Keywords: Von Kármán swirling viscous flow; semi-analytical solution; the Hybrid Analytical and Numerical Method; the HAN-method

Abstract

This study investigates the nonlinear and classical problem of Von Kármán’s viscous swirling fluid flow caused by a single rotating disk. Despite over a century since this problem was first introduced, recent advancements enable more accurate calculations and practical results than previously possible. The core innovation of this paper lies in the application of the Hybrid Analytical and Numerical method (HAN method), which facilitates the derivation of a semi-analytical solution to complex nonlinear differential equations. The HAN method combines numerical and analytical approaches to solve nonlinear problems. Initially, the system of nonlinear differential equations is solved using an arbitrary numerical method. The numerical solution then aids in extracting the analytical solution, which can take forms such as polynomial solutions with constant and unknown coefficients. Since boundary conditions lack the capacity to generate a sufficient number of algebraic equations, the numerical solution provides the additional required equations. The flexibility of the HAN method stems from its ability to leverage various numerical methods, making it a robust approach for solving nonlinear differential equations. Using this methodology, the Von Kármán problem is analytically calculated with remarkable accuracy. Furthermore, this study provides highly precise calculations of several physical and practical outputs, including the thickness of the layer, the slope of flow lines at the wall in the peripheral direction, the peripheral component of wall shear stress, the moment on one side of the wetted disk, the dimensionless moment coefficient for both sides of the disk, Reynolds number as a function of the disk’s finite radius, volume flux, and mechanical power. This research contributes to two main perspectives: first, the mathematical aspect, which demonstrates the ability of the HAN method to solve various nonlinear problems; second, the practical-physical perspective, showcasing the enhanced accuracy and reliability of the obtained results in analyzing fluid flow mechanics.

Published

2025-04-10

How to Cite

Ahmadi Azar, A. (2025). Semi-analytical solution for nonlinear Von Kármán swirling fluid flow via the hybrid analytical and numerical method. Mechanical Engineering Advances, 3(2), 2878. https://doi.org/10.59400/mea2878

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Vol. 3 No. 2 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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