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.
S. A., Mohammadein; A. Gad El-Rab, R.; and S. Ali, Maha
"The Simplest Analytical Solution of Navier-Stokes Equations,"
Information Sciences Letters: Vol. 10
, Article 1.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol10/iss2/1