Impact of peristaltic inclined Tube of the Newtonian viscous fluid flow with different wavelengths described by linear Navier-Stokes equations

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Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

Abstract

On the basis of the physical concept for a linear velocity operator (  . ), the unstable and nonlinear Navier-Stokes equations in cartesian coordinates are transformed into the linear diffusion equations.  In this paper, the non-dimensional continuity and the linear Navier-Stokes' equations are used to explain the Newtonian viscous fluid flow in a two-dimensional peristaltic inclined tube with respect to the y-axis. The linear differential equations of the problem are solved analytically by using Picard method. The velocity and the stream function of the fluid are obtained as functions of the physical parameters like time, wavelengths, and Reynolds numbers for the first time. Several graphs for these results of physical interest are displayed and discussed in detail. The obtained analytical solutions satisfy the linear and nonlinear Navier-stokes and continuity equations for all values of physical parameters for a first time in the periodical journals up to date. The author considered this work as a millennium problem; which proposed by clay institute. 

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Sohag Journal of Sciences

Articles in Press, Accepted Manuscript
Available Online from 08 November 2024

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