A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach
In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equatio...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/109128 |
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| _version_ | 1832557072424632320 |
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| author | Taha Aziz F. M. Mahomed |
| author_facet | Taha Aziz F. M. Mahomed |
| author_sort | Taha Aziz |
| collection | DOAJ |
| description | In this communication, we utilize some basic symmetry
reductions to transform the governing nonlinear partial differential
equations arising in the study of third-grade fluid flows into ordinary
differential equations. We obtain some simple closed-form steady-state
solutions of these reduced equations. Our solutions are valid for the whole
domain [0,∞) and also satisfy the physical boundary conditions. We
also present the numerical solutions for some of the underlying equations.
The graphs corresponding to the essential physical parameters of the flow
are presented and discussed. |
| format | Article |
| id | doaj-art-0a0f218f87a24361a8b0d69ab977240b |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-0a0f218f87a24361a8b0d69ab977240b2025-02-03T05:43:40ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/109128109128A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact ApproachTaha Aziz0F. M. Mahomed1Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South AfricaDifferential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South AfricaIn this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.http://dx.doi.org/10.1155/2014/109128 |
| spellingShingle | Taha Aziz F. M. Mahomed A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach The Scientific World Journal |
| title | A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach |
| title_full | A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach |
| title_fullStr | A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach |
| title_full_unstemmed | A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach |
| title_short | A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach |
| title_sort | note on the solutions of some nonlinear equations arising in third grade fluid flows an exact approach |
| url | http://dx.doi.org/10.1155/2014/109128 |
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