title: |
Symmetry Solutions of a Third-Order Ordinary Differential Equation which Arises from Prandtl Boundary Layer Equations |
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publication: |
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| volume-issue: | 15 - Supplement 1 | |
| pages: | 179 - 191 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2008.15.s1.16 (how to use a DOI) | |
author(s): |
R. Naz, Fazal M. Mahomed, David P. Mason |
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publication date: |
August 2008 |
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abstract: |
The similarity solution to Prandtl’s boundary layer equations for two-dimensional and radial flows with vanishing or constant mainstream velocity gives rise to a third-order ordinary differential equation which depends on a parameter ?. For special values of ? the third-order ordinary differential equation admits a three-dimensional symmetry Lie algebra L3. For solvable L3 the equation is integrated by quadrature. For non-solvable L3 the equation reduces to the Chazy equation. The Chazy equation is reduced to a first-order differential equation in terms of differential invariants which is transformed to a Riccati equation. In general the third-order ordinary differential equation admits a two-dimensional symmetry Lie algebra L2. For L2 the differential equation can only be reduced to a first-order equation. The invariant solutions of the third-order ordinary differential equation are also derived.
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |