Example of a solution for Dorodnitzyn’s limit formula
In the present paper, we show an example of a solution for Dorodnitzyn’s gaseous boundary layer limit formula. Oleinik’s no back-flow condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain R⊂R2. It also allowed us to find a limit formula for Dor...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-11-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X23000162 |
| _version_ | 1827917648021684224 |
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| author | C.V. Valencia-Negrete |
| author_facet | C.V. Valencia-Negrete |
| author_sort | C.V. Valencia-Negrete |
| collection | DOAJ |
| description | In the present paper, we show an example of a solution for Dorodnitzyn’s gaseous boundary layer limit formula. Oleinik’s no back-flow condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain R⊂R2. It also allowed us to find a limit formula for Dorodnitzyn’s stationary compressible boundary layer with constant total energy on a bounded convex domain in the plane R2. Under the same assumption, we can give an approximate solution u for the limit formula if |u|<<<1such that: u(z)≅δ∗c∗z+625⋅12i0⋅4U23z4+o(z5),that corresponds to an approximate horizontal velocity component when a small parameter ϵ given by the quotient of the maximum height of the domain divided by its length tends to zero. Here, c>0, δ is the boundary layer’s height in Dorodnitzyn’s coordinates, U is the free-stream velocity at the upper boundary of the domain, and T0is the absolute surface temperature. |
| first_indexed | 2024-03-13T03:31:24Z |
| format | Article |
| id | doaj.art-72565d8747494f5099bfb145ee5eadc5 |
| institution | Directory Open Access Journal |
| issn | 2666-657X |
| language | English |
| last_indexed | 2024-03-13T03:31:24Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj.art-72565d8747494f5099bfb145ee5eadc52023-06-24T05:19:37ZengElsevierExamples and Counterexamples2666-657X2023-11-013100114Example of a solution for Dorodnitzyn’s limit formulaC.V. Valencia-Negrete0Department of Physics and Mathematics, Universidad Iberoamericana Ciudad de Mexico, Prolongación Paseo de la Reforma 880, Mexico City, 01219, MexicoIn the present paper, we show an example of a solution for Dorodnitzyn’s gaseous boundary layer limit formula. Oleinik’s no back-flow condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain R⊂R2. It also allowed us to find a limit formula for Dorodnitzyn’s stationary compressible boundary layer with constant total energy on a bounded convex domain in the plane R2. Under the same assumption, we can give an approximate solution u for the limit formula if |u|<<<1such that: u(z)≅δ∗c∗z+625⋅12i0⋅4U23z4+o(z5),that corresponds to an approximate horizontal velocity component when a small parameter ϵ given by the quotient of the maximum height of the domain divided by its length tends to zero. Here, c>0, δ is the boundary layer’s height in Dorodnitzyn’s coordinates, U is the free-stream velocity at the upper boundary of the domain, and T0is the absolute surface temperature.http://www.sciencedirect.com/science/article/pii/S2666657X23000162Boundary-layer theoryGas dynamics |
| spellingShingle | C.V. Valencia-Negrete Example of a solution for Dorodnitzyn’s limit formula Examples and Counterexamples Boundary-layer theory Gas dynamics |
| title | Example of a solution for Dorodnitzyn’s limit formula |
| title_full | Example of a solution for Dorodnitzyn’s limit formula |
| title_fullStr | Example of a solution for Dorodnitzyn’s limit formula |
| title_full_unstemmed | Example of a solution for Dorodnitzyn’s limit formula |
| title_short | Example of a solution for Dorodnitzyn’s limit formula |
| title_sort | example of a solution for dorodnitzyn s limit formula |
| topic | Boundary-layer theory Gas dynamics |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X23000162 |
| work_keys_str_mv | AT cvvalencianegrete exampleofasolutionfordorodnitzynslimitformula |