Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids

Studies of multiple solutions on boundary layer flows have gained much attention in the field of fluid dynamics in the recent years. In this regard, stability analysis is also important to identify the stable and unstable solutions. In this thesis, the possibility of occurrence of multiple solutions...

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Main Author:	Dero, Sumera
Format:	Thesis
Language:	eng eng eng eng
Published:	2020
Subjects:	QA Mathematics
Online Access:	https://etd.uum.edu.my/8930/1/depositpermission-902590.pdf https://etd.uum.edu.my/8930/2/s902590_01.pdf https://etd.uum.edu.my/8930/3/s902590_02.pdf https://etd.uum.edu.my/8930/4/s902590_references.docx
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spelling	my-uum-etd.89302021-12-15T06:27:45Z Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids 2020 Dero, Sumera Mohd Rohni, Azizah Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts & Sciences QA Mathematics Studies of multiple solutions on boundary layer flows have gained much attention in the field of fluid dynamics in the recent years. In this regard, stability analysis is also important to identify the stable and unstable solutions. In this thesis, the possibility of occurrence of multiple solutions has been studied for boundary layer flows over stretching/shrinking sheet in nanofluids. Five different problems have been considered where two of the problems used nanofluid model proposed by Buongiomo and the remaining three problems used nanofluid model proposed by Tiwari and Das. The base fluids considered in this study are viscous fluid, Casson fluid and micropolar fluid. The mathematical models which govern the flows of five different problems have been constructed. Similarity transformations have been employed to transform the governing equations of partial differential equations to nonlinear ordinary differential equations. The resulting system is then solved numerically using shooting method with the aid of shootlib function in Maple software. To validate the results obtained in this study, comparison for specific cases have been done and in good agreement with existing solutions in literature. From this study, it is found that an increase of suction parameters will increase the rate of heat transfer in both stretching and shrinking cases. However, it causes the rate of skin friction to decrease for stretching case but to increase for shrinking case. Further, suction parameter, Casson parameter and Biot number decrease the temperature profiles but radiation, Brownian motion and thermophoresis parameters contribute towards the opposite. The results also displayed the occurrence of multiple solutions in all the problems considered. Therefore, the stability analysis has been performed to identify the stability of multiple solutions by using bvp4c solver in Matlab. The stability analysis indicates that the first solution is stable while the second and third solutions are unstable. 2020 Thesis https://etd.uum.edu.my/8930/ https://etd.uum.edu.my/8930/1/depositpermission-902590.pdf text eng staffonly https://etd.uum.edu.my/8930/2/s902590_01.pdf text eng 2023-12-23 staffonly https://etd.uum.edu.my/8930/3/s902590_02.pdf text eng public https://etd.uum.edu.my/8930/4/s902590_references.docx text eng public other doctoral Universiti Utara Malaysia
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng eng eng
advisor	Mohd Rohni, Azizah
topic	QA Mathematics
spellingShingle	QA Mathematics Dero, Sumera Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids
description	Studies of multiple solutions on boundary layer flows have gained much attention in the field of fluid dynamics in the recent years. In this regard, stability analysis is also important to identify the stable and unstable solutions. In this thesis, the possibility of occurrence of multiple solutions has been studied for boundary layer flows over stretching/shrinking sheet in nanofluids. Five different problems have been considered where two of the problems used nanofluid model proposed by Buongiomo and the remaining three problems used nanofluid model proposed by Tiwari and Das. The base fluids considered in this study are viscous fluid, Casson fluid and micropolar fluid. The mathematical models which govern the flows of five different problems have been constructed. Similarity transformations have been employed to transform the governing equations of partial differential equations to nonlinear ordinary differential equations. The resulting system is then solved numerically using shooting method with the aid of shootlib function in Maple software. To validate the results obtained in this study, comparison for specific cases have been done and in good agreement with existing solutions in literature. From this study, it is found that an increase of suction parameters will increase the rate of heat transfer in both stretching and shrinking cases. However, it causes the rate of skin friction to decrease for stretching case but to increase for shrinking case. Further, suction parameter, Casson parameter and Biot number decrease the temperature profiles but radiation, Brownian motion and thermophoresis parameters contribute towards the opposite. The results also displayed the occurrence of multiple solutions in all the problems considered. Therefore, the stability analysis has been performed to identify the stability of multiple solutions by using bvp4c solver in Matlab. The stability analysis indicates that the first solution is stable while the second and third solutions are unstable.
format	Thesis
qualification_name	other
qualification_level	Doctorate
author	Dero, Sumera
author_facet	Dero, Sumera
author_sort	Dero, Sumera
title	Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids
title_short	Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids
title_full	Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids
title_fullStr	Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids
title_full_unstemmed	Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids
title_sort	multiple solutions and stability analysis of boundary layer flows over a stretching/shrinking sheet in nanofluids
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2020
url	https://etd.uum.edu.my/8930/1/depositpermission-902590.pdf https://etd.uum.edu.my/8930/2/s902590_01.pdf https://etd.uum.edu.my/8930/3/s902590_02.pdf https://etd.uum.edu.my/8930/4/s902590_references.docx
_version_	1747828492159942656

Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids

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