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Investigation of the Incompressible Viscous Newtonian Fluids Flow using Three-Dimensions Linear Navier-Stokes Equations |
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PP: 125-132 |
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doi:10.18576/amis/170113
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Author(s) |
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Maha S. Ali,
Ali S. Ali,
Abdelrahman S. Ali,
S. A. Mohammadein,
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Abstract |
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| 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.
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