Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection

The problem of thermal convection in a fluid layer driven by either buoyancy (Bénard) or thermocapillary (Marangoni) effects has recently been assumed importance in material processing. In this study, the problems of Marangoni and Bénard-Marangoni convection in a horizontal fluid layer are theore...

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Main Author:	Mohamed Isa, Siti Suzilliana Putri
Format:	Thesis
Language:	English English
Published:	2010
Subjects:	Marangoni effect Benard cells Galerkin methods
Online Access:	http://psasir.upm.edu.my/id/eprint/10087/1/IPM_2010_1_A.pdf
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id	my-upm-ir.10087
record_format	uketd_dc
spelling	my-upm-ir.100872013-05-27T07:44:57Z Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection 2010 Mohamed Isa, Siti Suzilliana Putri The problem of thermal convection in a fluid layer driven by either buoyancy (Bénard) or thermocapillary (Marangoni) effects has recently been assumed importance in material processing. In this study, the problems of Marangoni and Bénard-Marangoni convection in a horizontal fluid layer are theoretically considered. The fluid layer is bounded from below by a rigid boundary and above by a non-deformable free surface. A linear stability analysis is applied to the problem, and the effect of non-uniform temperature profiles and magnetic field are examined. The critical Marangoni numbers are obtained for free-slip and isothermal, and no-slip and adiabatic lower boundary with adiabatic temperature on upper free surface. Six non-uniform basic temperature profiles which are linear, inverted parabola, parabola, step function (superposed two-fluid layer), piecewise linear (heated from below) and piecewise linear (cooled from above) are considered. The eigenvalues are obtained and solved using single-term Galerkin expansion procedure. The influence of various parameters such as Chandrasekhar number and thermal depth on the convection has been analysed. Finally, we showed that the inverted parabola is most stabilizing basic temperature distribution, and the step function is the most destabilizing basic temperature distribution. We have also proved that magnetic field suppressed Marangoni and Bénard-Marangoni convection. Marangoni effect Benard cells Galerkin methods 2010 Thesis http://psasir.upm.edu.my/id/eprint/10087/ http://psasir.upm.edu.my/id/eprint/10087/1/IPM_2010_1_A.pdf application/pdf en public masters Universiti Putra Malaysia Marangoni effect Benard cells Galerkin methods Institute for Mathematical Research English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Marangoni effect Benard cells Galerkin methods
spellingShingle	Marangoni effect Benard cells Galerkin methods Mohamed Isa, Siti Suzilliana Putri Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection
description	The problem of thermal convection in a fluid layer driven by either buoyancy (Bénard) or thermocapillary (Marangoni) effects has recently been assumed importance in material processing. In this study, the problems of Marangoni and Bénard-Marangoni convection in a horizontal fluid layer are theoretically considered. The fluid layer is bounded from below by a rigid boundary and above by a non-deformable free surface. A linear stability analysis is applied to the problem, and the effect of non-uniform temperature profiles and magnetic field are examined. The critical Marangoni numbers are obtained for free-slip and isothermal, and no-slip and adiabatic lower boundary with adiabatic temperature on upper free surface. Six non-uniform basic temperature profiles which are linear, inverted parabola, parabola, step function (superposed two-fluid layer), piecewise linear (heated from below) and piecewise linear (cooled from above) are considered. The eigenvalues are obtained and solved using single-term Galerkin expansion procedure. The influence of various parameters such as Chandrasekhar number and thermal depth on the convection has been analysed. Finally, we showed that the inverted parabola is most stabilizing basic temperature distribution, and the step function is the most destabilizing basic temperature distribution. We have also proved that magnetic field suppressed Marangoni and Bénard-Marangoni convection.
format	Thesis
qualification_level	Master's degree
author	Mohamed Isa, Siti Suzilliana Putri
author_facet	Mohamed Isa, Siti Suzilliana Putri
author_sort	Mohamed Isa, Siti Suzilliana Putri
title	Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection
title_short	Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection
title_full	Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection
title_fullStr	Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection
title_full_unstemmed	Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection
title_sort	effect of non-uniform temperature gradient and magnetic field on marangoni and benard-marangoni convection
granting_institution	Universiti Putra Malaysia
granting_department	Institute for Mathematical Research
publishDate	2010
url	http://psasir.upm.edu.my/id/eprint/10087/1/IPM_2010_1_A.pdf
_version_	1747811045117788160

Effect of Non-Uniform Temperature Gradient and Magnetic Field on Marangoni and Benard-Marangoni Convection

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