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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.534662020-07-15T06:39:27Z http://eprints.utm.my/id/eprint/53466/ Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate 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 NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/53466/1/AhmadQushairiMohamadMFS2014.pdf Mohamad, Ahmad Qushairi (2014) Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:86608
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/
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
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
publishDate 2014
url http://eprints.utm.my/id/eprint/53466/1/AhmadQushairiMohamadMFS2014.pdf
http://eprints.utm.my/id/eprint/53466/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:86608
_version_ 1674066169454133248
score 13.211869

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