Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate

Fluid-mechanics is an ancient science that is incredibly alive today. Therefore, the modern technologies require a deeper understanding of the behaviour of real fluids. Based on the relationship between shear stress and the rate of strain, fluids can be categorized as Newtonian fluids and non-Newton...

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Main Author:	Khalid, Asma
Format:	Thesis
Language:	English
Published:	2017
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/78487/1/AsmaKhalidPFS2017.pdf
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spelling	my-utm-ep.784872018-08-26T11:56:32Z Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate 2017-01 Khalid, Asma QA Mathematics Fluid-mechanics is an ancient science that is incredibly alive today. Therefore, the modern technologies require a deeper understanding of the behaviour of real fluids. Based on the relationship between shear stress and the rate of strain, fluids can be categorized as Newtonian fluids and non-Newtonian fluids. Various non- Newtonian fluid models have been used to investigate the behaviour of fluid motion, because of their universal nature. Solution corresponding to Newtonian and non- Newtonian fluids problem have received considerable attention due to their numerous applications in industries. This thesis is devoted to study the unsteady free convection flow of Newtonian fluid (nanofluids) and non-Newtonian fluids (Casson and micropolar fluids) over an oscillating vertical plate. Specifically, free convection flows of Casson fluids and micropolar fluids were studied with and without magnetohydrodynamic and porosity effects. Whereas studied in nanofluids also considered ramped wall temperature. Laplace transform was used to solve the partial differential equations governing the motion. The expressions of the obtained solutions for velocity, temperature and concentration were presented in simple forms. Skin friction, Nusselt number and Sherwood number were also calculated. The analytical results were plotted and discussed for magnetic, porosity, radiation, nanoparticle volume friction, Casson and microrotation parameters as well as Prandtl, Grashof and modified Grashof numbers. For Casson fluid, it was observed that velocity decreases with increasing values of Casson parameter as Casson fluid exhibits yield stress. In case of nanofluids, it was found that fluid velocity was greater for isothermal temperature as compared to ramped wall temperature of the plate. However, for micropolar fluid, microrotations increases near the plate and decreases far away from the plate due to an increase in viscosity parameter. The results showed that for long time interval, the oscillations have similar amplitudes and phase shift that persists for all times. For verification, the obtained solutions were recovered as special cases. The existing solutions in the literature were also reduced to their limiting cases of the present results. The exact solutions obtained in this thesis serve as a benchmark to verify approximate methods, whether asymptotic, experimental or numerical. 2017-01 Thesis http://eprints.utm.my/id/eprint/78487/ http://eprints.utm.my/id/eprint/78487/1/AsmaKhalidPFS2017.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:106960 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 Khalid, Asma Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate
description	Fluid-mechanics is an ancient science that is incredibly alive today. Therefore, the modern technologies require a deeper understanding of the behaviour of real fluids. Based on the relationship between shear stress and the rate of strain, fluids can be categorized as Newtonian fluids and non-Newtonian fluids. Various non- Newtonian fluid models have been used to investigate the behaviour of fluid motion, because of their universal nature. Solution corresponding to Newtonian and non- Newtonian fluids problem have received considerable attention due to their numerous applications in industries. This thesis is devoted to study the unsteady free convection flow of Newtonian fluid (nanofluids) and non-Newtonian fluids (Casson and micropolar fluids) over an oscillating vertical plate. Specifically, free convection flows of Casson fluids and micropolar fluids were studied with and without magnetohydrodynamic and porosity effects. Whereas studied in nanofluids also considered ramped wall temperature. Laplace transform was used to solve the partial differential equations governing the motion. The expressions of the obtained solutions for velocity, temperature and concentration were presented in simple forms. Skin friction, Nusselt number and Sherwood number were also calculated. The analytical results were plotted and discussed for magnetic, porosity, radiation, nanoparticle volume friction, Casson and microrotation parameters as well as Prandtl, Grashof and modified Grashof numbers. For Casson fluid, it was observed that velocity decreases with increasing values of Casson parameter as Casson fluid exhibits yield stress. In case of nanofluids, it was found that fluid velocity was greater for isothermal temperature as compared to ramped wall temperature of the plate. However, for micropolar fluid, microrotations increases near the plate and decreases far away from the plate due to an increase in viscosity parameter. The results showed that for long time interval, the oscillations have similar amplitudes and phase shift that persists for all times. For verification, the obtained solutions were recovered as special cases. The existing solutions in the literature were also reduced to their limiting cases of the present results. The exact solutions obtained in this thesis serve as a benchmark to verify approximate methods, whether asymptotic, experimental or numerical.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Khalid, Asma
author_facet	Khalid, Asma
author_sort	Khalid, Asma
title	Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate
title_short	Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate
title_full	Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate
title_fullStr	Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate
title_full_unstemmed	Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate
title_sort	exact solutions of unsteady free convection flow of casson, nano, and micropolar fluids over an oscillating vertical plate
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2017
url	http://eprints.utm.my/id/eprint/78487/1/AsmaKhalidPFS2017.pdf
_version_	1747817996836929536

Exact solutions of unsteady free convection flow of Casson, nano, and micropolar fluids over an oscillating vertical plate

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