Oscillatory free convection about a sphere in a porous medium

In the present study, the problem of oscillatory free convection about a sphere in a porous medium is considered. The surface temperature of the sphere oscillates harmonically about a mean surrounding temperature. The porous medium is assumed to be homogeneous, non-deformable and isotropic. The flow...

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Main Author:	Lai, Zhe Phooi
Format:	Thesis
Language:	English English
Published:	2012
Subjects:	SB183-317 Field crops Including cereals forage crops grasses legumes root crops sugar plants textile plants alkaloidal plants medicinal plants
Online Access:	https://eprints.ums.edu.my/id/eprint/41850/1/24%20PAGES.pdf https://eprints.ums.edu.my/id/eprint/41850/2/FULLTEXT.pdf
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spelling	my-ums-ep.418502024-12-09T07:33:52Z Oscillatory free convection about a sphere in a porous medium 2012 Lai, Zhe Phooi SB183-317 Field crops Including cereals, forage crops, grasses, legumes, root crops, sugar plants, textile plants, alkaloidal plants, medicinal plants In the present study, the problem of oscillatory free convection about a sphere in a porous medium is considered. The surface temperature of the sphere oscillates harmonically about a mean surrounding temperature. The porous medium is assumed to be homogeneous, non-deformable and isotropic. The flow is assumed to be incompressible and can be described by Darcy's law. The governing equations were derived from basic mass, momentum and energy equations In spherical coordinates. The method of matched asymptotic expansions used has divided the solution domain into an Inner region and an outer region. In the Inner region, the separation method was used to divide the second-order temperature and stream functions into steady and unsteady terms. The analytical solutions were obtained In the Inner region up to second-order steady term. In this outer region, a numerical computation was carried out by using a finite difference scheme and solved by Gauss-Seidel iterative method. It was found that a steady temperature and steady stream function exist at the outer edge of the inner region where the steady values depend on the dimensionless frequency. In addition, the steady stream function also depends on the Rayleigh number, Ra. The boundary condition near the outer edge of the inner region could not be satisfied, and these steady terms form the necessary Inner boundary conditions for the outer region. The temperature and flow patterns are compared and discussed. In various parameters including frequency of oscillation, a dimensionless parameter â‚¬ and Ra. It is found that, both the magnitudes of temperature and stream function decreases as frequency Increases or â‚¬ decreases. When Ra Increases, In the inner region the temperature tends to a steady value faster and the magnitude of stream function decreases. At the outer region, the frequency of oscillation has more significant effect than â‚¬ and Ra onto the temperature and stream function. The separation method used to obtain the solutions In Inner region Is found to simplify the analytical process. 2012 Thesis https://eprints.ums.edu.my/id/eprint/41850/ https://eprints.ums.edu.my/id/eprint/41850/1/24%20PAGES.pdf text en public https://eprints.ums.edu.my/id/eprint/41850/2/FULLTEXT.pdf text en validuser masters Universiti Malaysia Sabah School of Science and Technology
institution	Universiti Malaysia Sabah
collection	UMS Institutional Repository
language	English English
topic	SB183-317 Field crops Including cereals forage crops grasses legumes root crops sugar plants textile plants alkaloidal plants medicinal plants
spellingShingle	SB183-317 Field crops Including cereals forage crops grasses legumes root crops sugar plants textile plants alkaloidal plants medicinal plants Lai, Zhe Phooi Oscillatory free convection about a sphere in a porous medium
description	In the present study, the problem of oscillatory free convection about a sphere in a porous medium is considered. The surface temperature of the sphere oscillates harmonically about a mean surrounding temperature. The porous medium is assumed to be homogeneous, non-deformable and isotropic. The flow is assumed to be incompressible and can be described by Darcy's law. The governing equations were derived from basic mass, momentum and energy equations In spherical coordinates. The method of matched asymptotic expansions used has divided the solution domain into an Inner region and an outer region. In the Inner region, the separation method was used to divide the second-order temperature and stream functions into steady and unsteady terms. The analytical solutions were obtained In the Inner region up to second-order steady term. In this outer region, a numerical computation was carried out by using a finite difference scheme and solved by Gauss-Seidel iterative method. It was found that a steady temperature and steady stream function exist at the outer edge of the inner region where the steady values depend on the dimensionless frequency. In addition, the steady stream function also depends on the Rayleigh number, Ra. The boundary condition near the outer edge of the inner region could not be satisfied, and these steady terms form the necessary Inner boundary conditions for the outer region. The temperature and flow patterns are compared and discussed. In various parameters including frequency of oscillation, a dimensionless parameter â‚¬ and Ra. It is found that, both the magnitudes of temperature and stream function decreases as frequency Increases or â‚¬ decreases. When Ra Increases, In the inner region the temperature tends to a steady value faster and the magnitude of stream function decreases. At the outer region, the frequency of oscillation has more significant effect than â‚¬ and Ra onto the temperature and stream function. The separation method used to obtain the solutions In Inner region Is found to simplify the analytical process.
format	Thesis
qualification_level	Master's degree
author	Lai, Zhe Phooi
author_facet	Lai, Zhe Phooi
author_sort	Lai, Zhe Phooi
title	Oscillatory free convection about a sphere in a porous medium
title_short	Oscillatory free convection about a sphere in a porous medium
title_full	Oscillatory free convection about a sphere in a porous medium
title_fullStr	Oscillatory free convection about a sphere in a porous medium
title_full_unstemmed	Oscillatory free convection about a sphere in a porous medium
title_sort	oscillatory free convection about a sphere in a porous medium
granting_institution	Universiti Malaysia Sabah
granting_department	School of Science and Technology
publishDate	2012
url	https://eprints.ums.edu.my/id/eprint/41850/1/24%20PAGES.pdf https://eprints.ums.edu.my/id/eprint/41850/2/FULLTEXT.pdf
_version_	1818611436443664384

Oscillatory free convection about a sphere in a porous medium

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