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ISSN: 2090-0902

Journal of Physical Mathematics
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  • Research Article   
  • J Phys Math 2019, Vol 10(3): 307

Wave Perturbations for Linear Instability of Magneto Hydrodynamic Hartman Flow between Parallel Plates

Zakir Hussain1,2, Huisheng Zhang2 and Sergei Zuev3,4,5*
1Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan
2Department of Biomedical Engineering, School of Medicine, Shenzhen University, Shenzhen, P.R. China
3Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan
4Belgorod State Technological University, V.G. Shoukhov, Belgorod, Russia
5Crimean Federal University, Simferopol, Crimea
*Corresponding Author : Sergei Zuev, Belgorod State Technological University, V.G. Shoukhov, Belgorod, Russia, Tel: +7 477 2372742, Email: [email protected]

Received Date: Aug 28, 2019 / Accepted Date: Sep 28, 2019 / Published Date: Oct 15, 2019

Abstract

The Hartmann layers of conducting fluid between parallel plates under the influence of the transvers magnetic field are considered. The standard boundary conditions with zero velocities on the plates are used. The perturbations are used to obtain the exact solution for the given system. It is shown explicitly that no instability near the stationary solution can be found by perturbations in 2-dim cases. In 3-dim case the instability arises just when quaternionic perturbations applied. We use analytical solutions to obtain explicit results and wave perturbations for considered system. Our results are agreed with experimental facts which was solved by other authors and confirms the wellknown fact that traversal magnetic field overcomes the instability. Similarly we obtained the exact solution by using new quaternionic method and this way of nonlinear system consideration can deliver a variety of possibilities for finding new solutions.

Keywords: MHD; Conductive fluid; Hartmann layer instability; Hartmann flow; Exact solution; Quaternionic continuation

Citation: Hussain Z, Zhang H, Zuev S (2019) Wave Perturbations for Linear Instability of Magneto Hydrodynamic Hartman Flow between Parallel Plates. J Phys Math 10: 306.

Copyright: © 2019 Hussain Z, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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