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