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Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.


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TL;DR: In this paper, the DTM-Pade technique is extended to give solutions for nonlinear differential equations with boundary conditions at infinity, where the similarity solution for the steady stagnation flow toward an off-centered rotating disc gives a system of nonlinear partial differential equations.
Abstract: The similarity solution for the steady stagnation flow toward an off-centered rotating disc gives a system of nonlinear partial differential equations. These nonlinear differential equations are analytically solved by applying a newly developed method called DTM–Pade technique (the combination of the differential transform method (DTM) and the Pade approximation). This technique is extended to give solutions for nonlinear differential equations with boundary conditions at infinity. Graphical results are presented to investigate influence of the rotation ratio α on the radial velocity, azimuthal velocity, and the induced velocity. In order to show the effectiveness of the DTM–Pade technique, the results obtained from the DTM–Pade technique are compared with available solutions obtained using shooting method to generate the numerical solution. The obtained results demonstrate the reliability of the algorithm and the DTM–Pade technique is an attractive method in solving the systems of nonlinear partial differential equations.

44 citations

Journal ArticleDOI
TL;DR: In this article, the authors derived an equation for the structure of a two-dimensional non-Hugoniot shock in the case of weak shocks with Mach numbers close to one, based on the assumption that the vertical velocity is of order (M1* − 1)3/2 and that the flow within the shock is irrotational.
Abstract: As the curvature of shock waves increases, the shock structure becomes two dimensional, and the usual Hugoniot jump conditions no longer hold. An equation has been derived for the structure of such a two‐dimensional non‐Hugoniot shock in the case of weak shocks with Mach numbers close to one. The development of this equation from the Navier‐Stokes equations is based on the assumptions that the vertical velocity is of order (M1* − 1)3/2 and that the flow within the shock is irrotational. From the derivation it appears that the non‐Hugoniot region behaves as an acoustic wave driven by higher‐order viscous effects. The properties of the above equation, which has been called the viscous‐transonic or V‐T equation have been investigated. The V‐T equation appears to be a combination of Burgers' equation for weak normal shock structure and the transonic equation. It is shown that the structure of oblique shocks is a similarity solution of the V‐T equation. Proper formulation of boundary conditions is considered a...

44 citations

Journal ArticleDOI
TL;DR: In this paper, a set of slip-flow boundary conditions for the flow due to a lubricated disk rotating in a Newtonian fluid is derived, and numerical solutions are presented for this case, showing that the three-dimensional flow field is dramatically affected by accentuated velocity slip.

44 citations

Journal ArticleDOI
TL;DR: In this article, the scaling laws for flexible marine rotors that are designed to interact with the surrounding flow have been established, along with scaling factors for the various fluid and structural parameters that control the dynamic interactions between the flexible rotor and the surrounding fluid.

43 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850