Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation

In this work, the physical problems dealing with unidirectional magnetohydrodynamic (MHD) flows of some viscoelastic fluids in a porous medium and rotating frame are investigated. By using modified Darcy’s law, the corresponding equations governing the flow are modelled. Employing Fourier sine trans...

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Main Author:	Yousif Rasheed, Faisal Salah
Format:	Thesis
Language:	English
Published:	2012
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/30787/1/FaisalSalahYousifPFS2012.pdf
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spelling	my-utm-ep.307872018-04-27T01:15:27Z Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation 2012-03 Yousif Rasheed, Faisal Salah QA Mathematics In this work, the physical problems dealing with unidirectional magnetohydrodynamic (MHD) flows of some viscoelastic fluids in a porous medium and rotating frame are investigated. By using modified Darcy’s law, the corresponding equations governing the flow are modelled. Employing Fourier sine transform, new results in terms of the exact solutions of the modelled equations are generated for the problems of constantly accelerating and oscillatory MHD flows of second grade fluid in a porous space, accelerated MHD flows of an Oldroyd–B fluid in a porous medium and rotating frame, accelerating rotating MHD flow of second grade fluid in a porous space, accelerated MHD flow of Maxwell fluid in a porous medium and rotating frame, accelerated rotating MHD flow of generalized Burgers’ fluid in a porous medium. The Fourier sine and Laplace transforms are then utilized to obtain new exact solutions by solving analytically the Stokes’ first problem for two types of MHD fluids, namely the second grade fluid and Maxwell fluid in a porous medium and rotating frame. The new explicit solutions for the corresponding velocity fields are obtained for constant accelerated, variable accelerated and constant velocity flows for each problem mentioned above. The well – known solutions for Newtonian fluid in a porous medium in the cases mentioned above, are significantly shown to appear as the limiting cases of the present analysis. Finally, the effects of the material parameters (i.e. rotation, MHD and porous) on the velocity fields are demonstrated via graphical illustrations. These graphs generally show that: (i) by increasing the rotation parameter, this would lead to a decrease in the real part of the velocity profile; however for the magnitude of imaginary part of the velocity profile, it is found to be quite the opposite, (ii) when MHD parameter increases, the real and imaginary parts of the velocity profile decrease, and (iii) by increasing the porous parameter, both parts of the velocity profile increase 2012-03 Thesis http://eprints.utm.my/id/eprint/30787/ http://eprints.utm.my/id/eprint/30787/1/FaisalSalahYousifPFS2012.pdf application/pdf en public phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Yousif Rasheed, Faisal Salah Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation
description	In this work, the physical problems dealing with unidirectional magnetohydrodynamic (MHD) flows of some viscoelastic fluids in a porous medium and rotating frame are investigated. By using modified Darcy’s law, the corresponding equations governing the flow are modelled. Employing Fourier sine transform, new results in terms of the exact solutions of the modelled equations are generated for the problems of constantly accelerating and oscillatory MHD flows of second grade fluid in a porous space, accelerated MHD flows of an Oldroyd–B fluid in a porous medium and rotating frame, accelerating rotating MHD flow of second grade fluid in a porous space, accelerated MHD flow of Maxwell fluid in a porous medium and rotating frame, accelerated rotating MHD flow of generalized Burgers’ fluid in a porous medium. The Fourier sine and Laplace transforms are then utilized to obtain new exact solutions by solving analytically the Stokes’ first problem for two types of MHD fluids, namely the second grade fluid and Maxwell fluid in a porous medium and rotating frame. The new explicit solutions for the corresponding velocity fields are obtained for constant accelerated, variable accelerated and constant velocity flows for each problem mentioned above. The well – known solutions for Newtonian fluid in a porous medium in the cases mentioned above, are significantly shown to appear as the limiting cases of the present analysis. Finally, the effects of the material parameters (i.e. rotation, MHD and porous) on the velocity fields are demonstrated via graphical illustrations. These graphs generally show that: (i) by increasing the rotation parameter, this would lead to a decrease in the real part of the velocity profile; however for the magnitude of imaginary part of the velocity profile, it is found to be quite the opposite, (ii) when MHD parameter increases, the real and imaginary parts of the velocity profile decrease, and (iii) by increasing the porous parameter, both parts of the velocity profile increase
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Yousif Rasheed, Faisal Salah
author_facet	Yousif Rasheed, Faisal Salah
author_sort	Yousif Rasheed, Faisal Salah
title	Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation
title_short	Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation
title_full	Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation
title_fullStr	Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation
title_full_unstemmed	Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation
title_sort	exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2012
url	http://eprints.utm.my/id/eprint/30787/1/FaisalSalahYousifPFS2012.pdf
_version_	1747815748253777920

Exact solutions for unidirectional magnetohydrodynamics flow of non-newtonian fluid in a porous medium with and without rotation

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