Stability and Consistency Analysis of FTCS Scheme for Unsteady Magnetohydrodynamic Fluid Flow over a Vertical Stretching Sheet

A.O. Nyakebogo¹ , J.M. Kerongo² , R.K. Obogi³

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.4 , pp.38-43, Aug-2021

Online published on Aug 31, 2021

Copyright © A.O. Nyakebogo, J.M. Kerongo, R.K. Obogi . 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 analyzed the Forward Time Centered Space (FTCS) scheme for a two-dimensional fluid flow over a stretching surface. The fluid flow considered is unsteady, viscous and incompressible taking place under the influence of thermal radiation and variable viscosity in the presence of induced magnetic field. The partial differential equations considered, that is, the energy conservation and induction equations, cannot be solved using analytical methods. The finite difference numerical method has been used to discretize the partial differential equations to obtain a numerical scheme. The Forward Time and Central in Space (FTCS) scheme has been developed for the two governing equations. The Von-Neumann method is used to analyze for the stability of the FTCS scheme whereas the Taylor’s series expansion has been utilized in analyzing consistency. The energy conservation and the magnetic induction equations have been discretized to obtain the explicit scheme. It is observed that the FTCS scheme is conditionally stable for both equations while the consistency of both schemes is also confirmed from the analysis.

Key-Words / Index Term :
Viscous dissipation, Magnetohydrodynamics, induced magnetic field, Von-Neumann analysis, FTCS scheme, amplification factor.

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