Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties
We consider a system of coupled partial differential equations describing transient fluid flow and heat transfer with variable flow properties. Classical Lie point symmetry analysis of this system resulted in admitted large Lie algebras for some special cases of the arbitrary constants and the sourc...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2013-01-01
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| Series: | Advances in Mechanical Engineering |
| Online Access: | https://doi.org/10.1155/2013/983962 |
| _version_ | 1819006696225243136 |
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| author | R. J. Moitsheki O. D. Makinde |
| author_facet | R. J. Moitsheki O. D. Makinde |
| author_sort | R. J. Moitsheki |
| collection | DOAJ |
| description | We consider a system of coupled partial differential equations describing transient fluid flow and heat transfer with variable flow properties. Classical Lie point symmetry analysis of this system resulted in admitted large Lie algebras for some special cases of the arbitrary constants and the source term. Symmetry reductions are performed and as such the system of partial differential equations is reduced to the system of ordinary differential equations. Some reduced ordinary differential equation could be solved exactly with restrictions on the parameters appearing in it. In addition, shooting quadrature is employed to numerically tackle the nonlinear model boundary value problem and pertinent results are presented graphically and discussed quantitatively. |
| first_indexed | 2024-12-21T00:12:47Z |
| format | Article |
| id | doaj.art-e08a2371c1d3442ba7cd4bb589e2965b |
| institution | Directory Open Access Journal |
| issn | 1687-8132 |
| language | English |
| last_indexed | 2024-12-21T00:12:47Z |
| publishDate | 2013-01-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Advances in Mechanical Engineering |
| spelling | doaj.art-e08a2371c1d3442ba7cd4bb589e2965b2022-12-21T19:22:19ZengSAGE PublishingAdvances in Mechanical Engineering1687-81322013-01-01510.1155/2013/98396210.1155_2013/983962Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable PropertiesR. J. Moitsheki0O. D. Makinde1 Center for Differential Equations and Continuum Mechanics, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South AfricaWe consider a system of coupled partial differential equations describing transient fluid flow and heat transfer with variable flow properties. Classical Lie point symmetry analysis of this system resulted in admitted large Lie algebras for some special cases of the arbitrary constants and the source term. Symmetry reductions are performed and as such the system of partial differential equations is reduced to the system of ordinary differential equations. Some reduced ordinary differential equation could be solved exactly with restrictions on the parameters appearing in it. In addition, shooting quadrature is employed to numerically tackle the nonlinear model boundary value problem and pertinent results are presented graphically and discussed quantitatively.https://doi.org/10.1155/2013/983962 |
| spellingShingle | R. J. Moitsheki O. D. Makinde Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties Advances in Mechanical Engineering |
| title | Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties |
| title_full | Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties |
| title_fullStr | Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties |
| title_full_unstemmed | Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties |
| title_short | Computational Modelling and Similarity Reduction of Equations for Transient Fluid Flow and Heat Transfer with Variable Properties |
| title_sort | computational modelling and similarity reduction of equations for transient fluid flow and heat transfer with variable properties |
| url | https://doi.org/10.1155/2013/983962 |
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