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Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4

The present work is concerned with exact solutions of Stokes second problem for magnetohydrodynamics (MHD) flow of a Burgers' fluid. The fluid over a flat plate is assumed to be electrically conducting in the presence of a uniform magnetic field applied in outward transverse direction to the fl...

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Main Authors: Khan, Ilyas, Ali, Farhad, Shafie, Sharidan
Format: Article
Published: 2013
Subjects:
Q Science
Online Access:http://eprints.utm.my/id/eprint/40893/
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spelling my.utm.408932017-08-17T06:37:04Z http://eprints.utm.my/id/eprint/40893/ Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4 Khan, Ilyas Ali, Farhad Shafie, Sharidan Q Science The present work is concerned with exact solutions of Stokes second problem for magnetohydrodynamics (MHD) flow of a Burgers' fluid. The fluid over a flat plate is assumed to be electrically conducting in the presence of a uniform magnetic field applied in outward transverse direction to the flow. The equations governing the flow are modeled and then solved using the Laplace transform technique. The expressions of velocity field and tangential stress are developed when the relaxation time satisfies the condition ??=??2/4 or ?>?2/4. The obtained closed form solutions are presented in the form of simple or multiple integrals in terms of Bessel functions and terms with only Bessel functions. The numerical integration is performed and the graphical results are displayed for the involved flow parameters. It is found that the velocity decreases whereas the shear stress increases when the Hartmann number is increased. The solutions corresponding to the Stokes' first problem for hydrodynamic Burgers' fluids are obtained as limiting cases of the present solutions. Similar solutions for Stokes' second problem of hydrodynamic Burgers' fluids and those for Newtonian and Oldroyd-B fluids can also be obtained as limiting cases of these solutions. 2013 Article PeerReviewed Khan, Ilyas and Ali, Farhad and Shafie, Sharidan (2013) Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4. PloS One, 8 (5). pp. 1-18. ISSN 1932-6203
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic Q Science
spellingShingle Q Science
Khan, Ilyas
Ali, Farhad
Shafie, Sharidan
Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4
description The present work is concerned with exact solutions of Stokes second problem for magnetohydrodynamics (MHD) flow of a Burgers' fluid. The fluid over a flat plate is assumed to be electrically conducting in the presence of a uniform magnetic field applied in outward transverse direction to the flow. The equations governing the flow are modeled and then solved using the Laplace transform technique. The expressions of velocity field and tangential stress are developed when the relaxation time satisfies the condition ??=??2/4 or ?>?2/4. The obtained closed form solutions are presented in the form of simple or multiple integrals in terms of Bessel functions and terms with only Bessel functions. The numerical integration is performed and the graphical results are displayed for the involved flow parameters. It is found that the velocity decreases whereas the shear stress increases when the Hartmann number is increased. The solutions corresponding to the Stokes' first problem for hydrodynamic Burgers' fluids are obtained as limiting cases of the present solutions. Similar solutions for Stokes' second problem of hydrodynamic Burgers' fluids and those for Newtonian and Oldroyd-B fluids can also be obtained as limiting cases of these solutions.
format Article
author Khan, Ilyas
Ali, Farhad
Shafie, Sharidan
author_facet Khan, Ilyas
Ali, Farhad
Shafie, Sharidan
author_sort Khan, Ilyas
title Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4
title_short Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4
title_full Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4
title_fullStr Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4
title_full_unstemmed Stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4
title_sort stokes' second problem for magnetohydrodynamics flow in a burgers' fluid: the cases ?= ?2/4 and ?> ?2/4
publishDate 2013
url http://eprints.utm.my/id/eprint/40893/
_version_ 1643650586849050624
score 13.211869

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