Navier-Stokes equation in cylindrical coordinates for an unsteady one-dimensional motion of a viscous fluid flow in a given tube

Abstract

This paper proposed and applied a three-step computational algorithm to solve the time-fractional Navier-Stokes equation (FNS) in a given cylindrical coordinates for one-way unstable flow motion. The Caputo definition of fraction order was obtained using the Riemann Liouville fractional integral operator, which was coded with the MAPLE18 software command and applied to simulate the different fractional values ​​presented in 2D and 3D surface graphs for understanding better the operation of fractional Navier-Stokes equations over time in cylindrical coordinates. We considered different test cases to show the proposed algorithm's efficiency, robustness, and feasibility, which ultimately reduces the computational time and ease of implementation for the simulation of the fractional order of the fractional Navier-Stokes equation considered.