Investigation of the Incompressible Viscous Newtonian Fluids Flow using Three-Dimensions Linear Navier-Stokes Equations

Authors

Maha S. Ali, Department of Mathematics, Faculty of Science, Tanta University, Tanta, EgyptFollow
Ali S. Ali, Department of Mathematics Department, Faculty of Science, Aswan University, Aswan, EgyptFollow
Abdelrahman S. Ali, Department of Mechanics, Faculty of Engineering, Tanta University, Tanta, EgyptFollow
S. A. Mohammadein, Department of Mathematics, Faculty of Science, Tanta University, Tanta, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this paper, the unsteady and nonlinear Navier-Stokes equations in three Cartesian coordinates are converted to the linear diffusion equations based on the concept of linear velocity operator (▁(v ̂ ) . ▁∇). The stream function Ψ(x, y, z, t) represents the analytical solutions of dimensional continuity and linear Navier-Stokes equations. As a physical application, the viscous Newtonian fluid flow in a 3D peristaltic horizontal tube is described by non-dimensional continuity and linear Navier-Stokess equations. The analytical solution in terms of stream function is obtained for different values of time, wavelengths, and Reynolds numbers for a first time. Moreover, the streamlines change from laminar, to transit, and then to turbulent flow with increasing time interval. Authors introduced the 3D analytical solutions of linear and nonlinear Navier-Stokes equations as a millennium problem.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/170113

Recommended Citation

S. Ali, Maha; S. Ali, Ali; S. Ali, Abdelrahman; and A. Mohammadein, S. (2023) "Investigation of the Incompressible Viscous Newtonian Fluids Flow using Three-Dimensions Linear Navier-Stokes Equations," Applied Mathematics & Information Sciences: Vol. 17: Iss. 1, Article 13.
DOI: http://dx.doi.org/10.18576/amis/170113
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss1/13