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On Hydromagnetic Channel Flow of an Oldroyd-B Fluid Induced by Tooth Pulses in a Rotating System | OMICS International | Abstract
ISSN: 2168-9679

Journal of Applied & Computational Mathematics
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Review Article

On Hydromagnetic Channel Flow of an Oldroyd-B Fluid Induced by Tooth Pulses in a Rotating System

Ghosh S*

Department of Computer Science, BIT Mesra, Kolkata Extension Centre, 1582 Rajdanga Main Road, Kolkata-700107, India

*Corresponding Author:
Ghosh S
Department of Computer Science
BIT Mesra, Kolkata Extension Centre
1582 Rajdanga Main Road, Kolkata-700107, India
Tel: 09885390953
E-mail: [email protected]

Received Date: March 13, 2015; Accepted Date: March 20, 2015; Published Date: April 20, 2015

Citation: Ghosh S (2015) On Hydromagnetic Channel Flow of an Oldroyd-B Fluid Induced by Tooth Pulses in a Rotating System. J Appl Computat Math 4:211. doi: 10.4172/2168-9679.1000211

Copyright: ©2015 Ghosh S. 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.

Abstract

An initial value problem concerning the motion of an incompressible electrically conducting viscoelastic Oldroyd-B fluid in a channel bounded by two infinite rigid non-conducting plates in presence of an external transverse magnetic field when both the fluid and the plates are in a state of solid body rotation with constant angular velocity about an axis normal to the plates is solved. The unsteady motion is generated impulsively from rest in such a fluid when the upper plate is subjected to velocity tooth pulses with the lower plate held fixed. It is assumed that no electric current exists in the basic state and the magnetic Reynolds number is very small. Exact solutions of the problem are obtained by utilizing two methods, of them, one is the method of Fourier analysis and the other is the method of Laplace transforms. The enquiries are made about the velocity field and the skin-friction on the walls. It is shown that both the methods give the same exact solution of the problem. The influence of rotation, the magnetic field and the elasticity of the fluid on the components of fluid velocity and the wall skin-frictions are examined quantitatively. Some known results are found to emerge as special cases of the present analysis.

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