Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis

Over the last few years, non-Newtonian fluids have gained more attention due to their vast real-life applications, particularly in engineering and industries. Previous studies reveal that multiple solutions to these fluids problems occur due to the existence of nonlinearity nature in viscous shear...

Full description

Saved in:

Bibliographic Details
Main Author:	Lund, Liaquat Ali
Format:	Thesis
Language:	eng eng
Published:	2021
Subjects:	Q Science (General)
Online Access:	https://etd.uum.edu.my/9380/1/s902587_01.pdf https://etd.uum.edu.my/9380/2/s902587_02.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-uum-etd.9380
record_format	uketd_dc
spelling	my-uum-etd.93802022-06-09T03:03:52Z Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis 2021 Lund, Liaquat Ali Omar, Zurni Khan, Ilyas Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts & Sciences Q Science (General) Over the last few years, non-Newtonian fluids have gained more attention due to their vast real-life applications, particularly in engineering and industries. Previous studies reveal that multiple solutions to these fluids problems occur due to the existence of nonlinearity nature in viscous shear stress. However, these solutions are hard to detect experimentally as they are close to each other. Although from a mathematical point of view, all solutions should be considered since they satisfy all the conditions stipulated, only the stable one is meaningful and applicable. The main objective of this study is to find all possible solutions to six new problems and determine the solutions’ stability. Three of these problems use the Buongiorno nanofluid model while the remaining use viscous non-Newtonian fluids models proposed by Eringen and Casson. By using suitable similarity variables, the governing equations of each problem in partial differential equations have been transformed into boundary value problems (BVPs) of nonlinear ordinary differential equations (ODEs). The shooting method with the help of shootlib function in Maple software was employed to convert the resultant BVPs into initial value problems (IVPs) of first-order ODEs which were then solved using Runge- Kutta method of fourth-order. The numerical results for specific cases obtained in this study have been compared with the solutions in literature for validation purposes and found in excellent agreement. The effects of various involved physical parameters on the skin friction coefficient, heat and mass transfer rates, and profiles of velocity, angular velocity, temperature, and concentration have been investigated. Numerical results indicate that there are four and three solutions in nanofluid and Casson fluid problems, respectively, on the vertically exponential surface, while the dual solutions exist in the remaining problems. It is observed that there are different regions for multiple, unique, and no solutions for each considered problem. The stability analysis has been performed to determine the stability of multiple solutions and the results suggest that only the first solution is stable. This study has successfully discovered multiple solutions to the considered problems and contributed to the body of knowledge in fluid dynamics. The findings of this study can also be used as a reference to reduce the experimental cost in the applications of related areas. 2021 Thesis https://etd.uum.edu.my/9380/ https://etd.uum.edu.my/9380/1/s902587_01.pdf text eng 2024-05-20 staffonly https://etd.uum.edu.my/9380/2/s902587_02.pdf text eng public other doctoral Universiti Utara Malaysia
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Omar, Zurni Khan, Ilyas
topic	Q Science (General)
spellingShingle	Q Science (General) Lund, Liaquat Ali Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis
description	Over the last few years, non-Newtonian fluids have gained more attention due to their vast real-life applications, particularly in engineering and industries. Previous studies reveal that multiple solutions to these fluids problems occur due to the existence of nonlinearity nature in viscous shear stress. However, these solutions are hard to detect experimentally as they are close to each other. Although from a mathematical point of view, all solutions should be considered since they satisfy all the conditions stipulated, only the stable one is meaningful and applicable. The main objective of this study is to find all possible solutions to six new problems and determine the solutions’ stability. Three of these problems use the Buongiorno nanofluid model while the remaining use viscous non-Newtonian fluids models proposed by Eringen and Casson. By using suitable similarity variables, the governing equations of each problem in partial differential equations have been transformed into boundary value problems (BVPs) of nonlinear ordinary differential equations (ODEs). The shooting method with the help of shootlib function in Maple software was employed to convert the resultant BVPs into initial value problems (IVPs) of first-order ODEs which were then solved using Runge- Kutta method of fourth-order. The numerical results for specific cases obtained in this study have been compared with the solutions in literature for validation purposes and found in excellent agreement. The effects of various involved physical parameters on the skin friction coefficient, heat and mass transfer rates, and profiles of velocity, angular velocity, temperature, and concentration have been investigated. Numerical results indicate that there are four and three solutions in nanofluid and Casson fluid problems, respectively, on the vertically exponential surface, while the dual solutions exist in the remaining problems. It is observed that there are different regions for multiple, unique, and no solutions for each considered problem. The stability analysis has been performed to determine the stability of multiple solutions and the results suggest that only the first solution is stable. This study has successfully discovered multiple solutions to the considered problems and contributed to the body of knowledge in fluid dynamics. The findings of this study can also be used as a reference to reduce the experimental cost in the applications of related areas.
format	Thesis
qualification_name	other
qualification_level	Doctorate
author	Lund, Liaquat Ali
author_facet	Lund, Liaquat Ali
author_sort	Lund, Liaquat Ali
title	Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis
title_short	Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis
title_full	Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis
title_fullStr	Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis
title_full_unstemmed	Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis
title_sort	multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2021
url	https://etd.uum.edu.my/9380/1/s902587_01.pdf https://etd.uum.edu.my/9380/2/s902587_02.pdf
_version_	1747828585611132928

Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis

Similar Items