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Information Sciences Letters

Information Sciences Letters

Abstract

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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