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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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Journal ArticleDOI
TL;DR: In this article, the boundary layer analysis of an unsteady separated stagnation-point (USSP) flow of an incompressible viscous fluid over a flat plate, moving in its own plane with a given speed, is explored numerically.

20 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed embedded converging surface microchannels as effective new ways of reducing entropy production in boundary layer flow with convective heat transfer, where a similarity solution with slip-flow boundary conditions is developed to find the spatial distributions of velocity, temperature, wall shear stress and wall heat flux.

20 citations

Journal ArticleDOI
TL;DR: In this article, an analytical solution in a closed form for the boundary layer flow over a shrinking sheet is presented when arbitrary velocity distributions are applied on the shrinking sheet, and the results demonstrate distinctive momentum and energy transport characteristics.

20 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the linear stability properties of the Barenblatt-Pattle (B-P) self-similar solutions of the porous medium equation which models flow including viscous and porous media gravity currents and established that the axisymmetric B-P solution is linearly stable to asymmetric perturbations.
Abstract: We study the linear stability properties of the Barenblatt–Pattle (B–P) self-similar solutions of the porous medium equation which models flow including viscous and porous media gravity currents Grundy and McLaughlin [RE Grundy, R McLaughlin, Eigenvalues of the Barenblatt–Pattle similarity solution in nonlinear diffusion, Proc Roy Soc London Ser A 383 (1982) 89–100] have shown that, in both planar and axisymmetric geometries, the B–P solutions are linearly stable to symmetric perturbations Using a new technique that eliminates singularities in the linear stability analysis, we extend their result and establish that the axisymmetric B–P solution is linearly stable to asymmetric perturbations This suggests that the axisymmetric B–P solution provides the intermediate asymptotics of gravity currents that evolve from a wide range of initial distributions including those that are not axisymmetric We use the connection between the perturbation eigenfunctions and the symmetry transformations of the B–P solution to demonstrate that the leading order rate of decay of the perturbations can be maximised by redefining the volume, time and space variables We show that, in general, radially symmetric perturbations decay faster than asymmetric perturbations of equal amplitude These theoretical predictions are confirmed by numerical results

20 citations

Journal ArticleDOI
TL;DR: In this article, the authors show that the generic blowup in this fourth-order problem is described by a similarity solution u∗(x, t )= − ln(T − t )+ f1(x/(T −t) 1/4 )( T> 0 is the blowup time), with a non-trivial profile f1 0.
Abstract: with a parameter β 0, which is a model equation from explosion-convection theory Unlike the classical Frank-Kamenetskii equation ut = uxx +e u (a solid fuel model), by using analytical and numerical evidence, we show that the generic blow-up in this fourth-order problem is described by a similarity solution u∗(x, t )= − ln(T − t )+ f1(x/(T − t) 1/4 )( T> 0 is the blowup time), with a non-trivial profile f1 0 Numerical solution of the PDE shows convergence to the self-similar solution with the profile f1 from a wide variety of initial data We also construct a countable subset of other, not self-similar, blow-up patterns by using a spectral analysis of an associated linearized operator and matching with similarity solutions of a first-order Hamilton–Jacobi equation

20 citations


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