New solutions of the Navier–Stokes equations associated with flow above moving boundaries
| Autor: | Patrick Weidman, Eugen Magyari |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mechanical Engineering
Computational Mechanics Geometry 02 engineering and technology Mechanics Lambda 01 natural sciences Omega 010305 fluids & plasmas Physics::Fluid Dynamics Transverse plane 020303 mechanical engineering & transports 0203 mechanical engineering Flow (mathematics) 0103 physical sciences Solid mechanics Shear stress Shear flow Navier–Stokes equations Mathematics |
| Zdroj: | Acta Mechanica. 228:3725-3733 |
| ISSN: | 1619-6937 0001-5970 |
| Popis: | Four problems are conceived which build on flows induced by moving boundaries. In the first problem, a stretching plate moves in the direction of stretching at speed $$u_0$$ and in the transverse direction at speed $$v_0$$ . The second problem superposes uniform shear flow of strength $$\omega _2$$ transverse to the stretching plate. The third problem superposes uniform shear flow of strength $$\omega _1$$ in the direction of stretching or opposite to it. For the second and third problems, we find a one-parameter family of wall shear stresses $$\lambda $$ that satisfy the plate and far-field conditions. For these cases, unique solutions are selected by the Glauert criterion which requires that the wall shear stress be that for which the solutions asymptotically match the far-field conditions of the flow displaced by the stretching sheet. The fourth problem is uniform shear flow above a radially stretching sheet. Here also a unique solution is selected by the Glauert criterion. |
| Databáze: | OpenAIRE |
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