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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 existence, uniqueness and boundedness of solutions to boundary value problems arising in fluid mechanics, and especially in boundary layer theory, are investigated. But the authors focus on the boundary value problem and do not consider the boundary layer problem.
Abstract: For given \({a \in \mathbb {R}}\) , c 0 such that fb exists on [0, + ∞) and is such that \({f'_b(t) \to 0}\) as t → + ∞, if and only if b ≥ b*. This allows to answer questions about existence, uniqueness and boundedness of solutions to a boundary value problem arising in fluid mechanics, and especially in boundary layer theory.

12 citations

Journal ArticleDOI
TL;DR: This paper uses perturbation theory to compute a first-order correction to the (steady-state) velocity resulting from a small change in hopper geometry, either distortion of the cross section or tilting away from vertical.
Abstract: Jenike's radial solution, widely used in the design of materials-handling equipment, is a similarity solution of steady-state continuum equations for the flow under gravity of granular material through an infinite, right-circular cone. In this paper we study how the geometry of the hopper influences this solution. Using perturbation theory, we compute a first-order correction to the (steady-state) velocity resulting from a small change in hopper geometry, either distortion of the cross section or tilting away from vertical. Unlike for the Jenike solution, all three components of the correction velocity are nonzero; i.e., there is secondary circulation in the perturbed flow.

12 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the Falkner-Skan flow of a viscoelastic fluid governed by the FENE-P model, and obtained a differential-algebraic system for the stream function and the stress.
Abstract: We study the Falkner–Skan flow of a viscoelastic fluid governed by the FENE-P model, as the Reynolds number Re → ∞ and the Weissenberg number We is such that WeRe 1 / 2 = O ( 1 ) . We obtain a differential–algebraic system for the stream function and the stress. We show that a similarity solution exists only for axisymmetric stagnation point flow which corresponds to an angle of attack m = 1 3 . The stream function is then governed by a generalized Falkner–Skan equation. The effect of extensibility on the skin friction and first normal stress coefficients are discussed.

12 citations


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