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The Simplest Analytical Solution of Navier-Stokes Equations |
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PP: 159-165 |
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doi:10.18576/isl/100201
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Author(s) |
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Mohammadein S. A.,
R. A. Gad El-Rab,
Maha S. Ali,
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Abstract |
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| The nonlinear convective acceleration term in fluids performs a strong obstacle against the analytical solutions of Navier-Stokes equations up to date. The obtained solutions are valid for long wave lengths only. In this paper, the nonlinear Navier-Stokes equations are converted to the linear diffusion equations based on the concept of linear velocity operator. The simplest analytical solutions of linear Navier-Stokes equations are obtained by using Picard method for a first time for different values of wave lengths and Reynolds number. As an application, the peristaltic incompressible viscous Newtonian fluid flow in a horizontal tube is described by the continuity and linear Navier-Stokes equations. The analytical solutions are obtained in terms of stream function and fluid velocity components. Moreover, the stream function is plotted in a laminar, transit and turbulent flows for different values of parameter δ.
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