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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| Format: | Thesis |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://eprints.ums.edu.my/id/eprint/11550/1/mt0000000626.pdf |
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| Summary: | 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 € and Ra. It is found that, both the magnitudes of temperature and stream function decreases as frequency Increases or € 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 € 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. |
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