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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 steady two-dimensional incompressible flow of a conducting power-law fluid past a flat plate in the presence of a transverse magnetic field of the formH 0x(m−1)/2 and under the influence of a pressure gradient is considered.
Abstract: The steady two-dimensional incompressible flow of a conducting power-law fluid past a flat plate in the presence of a transverse magnetic field of the formH0x(m−1)/2 and under the influence of a pressure gradient is considered. The resulting similarity equation is first converted into a different form using Crocco variables and then solved by choosing a suitable profile for the dependent variable. The results are compared with those obtained by direct numerical integration of the original differential equation. The energy equation for a special case for which similarity solutions exist is also considered.

11 citations

Journal ArticleDOI
TL;DR: The second stage of oil spreading on water, in which gravity forces promote spreading against the resisting viscous effects, is investigated using a similarity solution in combination with the integral boundary layer approach in the case where oil is discharged at a constant rate as discussed by the authors.

11 citations

Journal ArticleDOI
TL;DR: In this article, the effects of viscous dissipation and compression work on mixed convection in a rotating solid-walled channel and the effect of compression work for a rotating semi-polygonal channel with transpiration flow and heat transfer characteristics were investigated.

11 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide a new formulation that enables all quantities of interest to be determined by a set of two-dimensional tables in which j8 and gw are the only entree parameters.
Abstract: T HE similar solutions of the compressible, laminar boundary-layer equations depend on a pressure gradient parameter |8 and on the wall-to-inviscid stagnation temperature ratio gw. However, derived quantities, such as various thicknesses, also depend on a speed parameter 5. A comprehensive table of results is therefore three-dimensional and, in fact, does not exist. One of the more extensive tabulations is due to Back. His three-dimensional table, however, is scanty, lacking results for negative /3 and for gw > 1 . Furthermore, the spacing on gw and S is nonuniform and inadequate for interpolation or extrapolation. These remarks are not criticisms, since a comprehensive three-dimensional table is a prohibitive undertaking and, even it is existed, would be difficult and awkard to use. We provide a new formulation that enables all quantities of interest to be determined by a set of two-dimensional tables in which j8 and gw are the only entree parameters. With such a set, accurate values can be found for the skin-friction coefficient, Stanton number, and the five most common viscous and thermal boundary-layer thicknesses for arbitrary values of S. We use the compressible similarity equations under the traditional assumptions of steady flow of a perfect gas with unity values for the Prandtl number and Chapman-Rubesin parameter. The bounding wall is assumed impermeable, and the flow is two-dimensional or axisymmetric. Our nomenclature is usually that of Ref. 1 or may be found in the full paper. For the subsequent derivation, we need the following collection of integrals, all of which are exact:

11 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the self-similarity of free-surface and submerged slot jet impingement in local heat transfer in laminar flow conditions and derived the scaling behavior for the wall-jet region.

11 citations


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