Numerical Solution of Time-Fractional Navier-Stokes Equation in Cylindrical Coordinates

S.S. Omorodion¹

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.5 , pp.21-26, Oct-2021

Online published on Oct 31, 2021

Copyright © S.S. Omorodion . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This paper presents the numerical solutions of the time-fractional Navier-Stokes equation (N-S equation) in cylindrical coordinates for unsteady one dimensional motion of a viscous fluid via a combination of Tarig transform and projected differential transform method (TPDTM). Two time-fractional N-S equations are solved to validate the effectiveness of the proposed method. The obtained results are presented by 2D plots and table and compared with the results of homotopy analysis method (HAM), fractional modified Laplace decomposition method (FMLDM), homotopy perturbation transform method (HPTM) and q-homotopy analysis transform method (q-HATM). The obtained results show that the TPDTM is an e?ective and straightforward tool for solving nonlinear fractional PDEs and it’s more adaptable than many numerical methods in the literature.

Key-Words / Index Term :
Time-Fractional Navier-Stokes Equation, Tarig Projected Differential Transform Method, Fractional Order Derivative

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