Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate

The second grade fluid is one of the most popular subclass of non-Newtonian fluids. Due to their importance in industry and engineering, most of researchers have concentrated on the flows dealing with these fluids. Therefore, the main purpose of this thesis is to obtain exact solutions for unsteady...

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Main Author:	Mohamad, Ahmad Qushairi
Format:	Thesis
Language:	English
Published:	2014
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/53466/1/AhmadQushairiMohamadMFS2014.pdf
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spelling	my-utm-ep.534662020-07-15T06:39:27Z Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate 2014-12 Mohamad, Ahmad Qushairi QA Mathematics The second grade fluid is one of the most popular subclass of non-Newtonian fluids. Due to their importance in industry and engineering, most of researchers have concentrated on the flows dealing with these fluids. Therefore, the main purpose of this thesis is to obtain exact solutions for unsteady free convection flows of rotating second grade fluid with the effects of isothermal and ramped wall temperatures. Specifically, a free convection flow is studied in the presence of magnetohydrodynamics and porosity. Using the constitutive equations, the governing equations are modeled. Some suitable non-dimensional variables are used to write these equations into non-dimensional form. Laplace transform method is used to solve these equation with imposed initial and boundary conditions. Solutions for velocity and temperature fields are obtained. Skin friction and Nusselt number are also evaluated. For the sake of physical understanding, analytical results for velocity are plotted graphically for the emerging flow parameters. As the velocity is a complex function, the graphs for both real and imaginary parts are shown separately. Both cases, isothermal and ramped wall temperatures, are discussed. It is observed that when the second grade parameter increases, the velocity shows an oscillating behavior which decreases and then increases, for both real and imaginary parts. For larger values of rotation parameter, the fluid velocity decreases for the real part whereas it increases for the imaginary part. It is further noted that velocity decreases when magnetic parameter increases for both real and imaginary parts. However, an opposite behavior is observed when the porosity parameter is increased. Both real and imaginary parts of the velocity are found to increase with increasing values of the porosity parameter. An interesting result for the velocity is observed from the comparison of ramped and isothermal temperatures. It is found that fluid moves slowly in case of ramped wall temperature compared to isothermal case. In limiting cases, the present solutions are found identical to published results. 2014-12 Thesis http://eprints.utm.my/id/eprint/53466/ http://eprints.utm.my/id/eprint/53466/1/AhmadQushairiMohamadMFS2014.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:86608 masters 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 Mohamad, Ahmad Qushairi Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate
description	The second grade fluid is one of the most popular subclass of non-Newtonian fluids. Due to their importance in industry and engineering, most of researchers have concentrated on the flows dealing with these fluids. Therefore, the main purpose of this thesis is to obtain exact solutions for unsteady free convection flows of rotating second grade fluid with the effects of isothermal and ramped wall temperatures. Specifically, a free convection flow is studied in the presence of magnetohydrodynamics and porosity. Using the constitutive equations, the governing equations are modeled. Some suitable non-dimensional variables are used to write these equations into non-dimensional form. Laplace transform method is used to solve these equation with imposed initial and boundary conditions. Solutions for velocity and temperature fields are obtained. Skin friction and Nusselt number are also evaluated. For the sake of physical understanding, analytical results for velocity are plotted graphically for the emerging flow parameters. As the velocity is a complex function, the graphs for both real and imaginary parts are shown separately. Both cases, isothermal and ramped wall temperatures, are discussed. It is observed that when the second grade parameter increases, the velocity shows an oscillating behavior which decreases and then increases, for both real and imaginary parts. For larger values of rotation parameter, the fluid velocity decreases for the real part whereas it increases for the imaginary part. It is further noted that velocity decreases when magnetic parameter increases for both real and imaginary parts. However, an opposite behavior is observed when the porosity parameter is increased. Both real and imaginary parts of the velocity are found to increase with increasing values of the porosity parameter. An interesting result for the velocity is observed from the comparison of ramped and isothermal temperatures. It is found that fluid moves slowly in case of ramped wall temperature compared to isothermal case. In limiting cases, the present solutions are found identical to published results.
format	Thesis
qualification_level	Master's degree
author	Mohamad, Ahmad Qushairi
author_facet	Mohamad, Ahmad Qushairi
author_sort	Mohamad, Ahmad Qushairi
title	Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate
title_short	Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate
title_full	Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate
title_fullStr	Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate
title_full_unstemmed	Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate
title_sort	exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2014
url	http://eprints.utm.my/id/eprint/53466/1/AhmadQushairiMohamadMFS2014.pdf
_version_	1747817562158137344

Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate

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