Plane steady flows of a third grade fluid
type: Item
instance of: scholarly article
title: Plane steady flows of a third grade fluid
zbMATH Open document ID: 0615.76007
DOI: 10.1016/0020-7225(87)90004-8
author: Yanyan Li
published in: International Journal of Engineering Science
publication date: 1987-01-01T00:00:00Z
review text: This theoretical paper describes a different method to discuss steady two-dimensional flows of a non-Newtonian fluid, the model here used being a thermodynamically compatible four-constant third grade fluid. \textit{M. H. Martin's} approach [Arch. Ration. Mech. Anal. 41, 266-286 (1971; Zbl 0222.76023)] of introducing a curvilinear coordinate system (\(\phi\),\(\psi)\), in which coordinate lines \(\psi =cons\tan t\) are taken as streamlines whilst \(\phi =cons\tan t\) lines are initially chosen as arbitrary, is followed to study plane flows. Using the results from differential geometry and by assuming that coordinate lines \(\phi =cons\tan t\) are orthogonal trajectories of the streamlines, the original set of governing flow equations is shown to transform to a system of five equations in five unknowns in the new coordinate system. Next, possible flow patterns of the non-Newtonian fluid under consideration, are discussed when the streamlines are either straight lines or involutes of a curve. Some special flows, viz., radial flows, circular flows and flows with parallel streamlines are additionally considered to show the usefulness of the method, and the results in these cases are discussed in relation to predictions of Newtonian fluid and the second grade fluid.
Mathematics Subject Classification ID: 76A05
zbMATH DE Number: 3997351
zbMATH Keywords: coordinate transformation
zbMATH Keywords: steady two-dimensional flows
zbMATH Keywords: non-Newtonian fluid
zbMATH Keywords: thermodynamically compatible four-constant third grade fluid
zbMATH Keywords: curvilinear coordinate system
zbMATH Keywords: plane flows
zbMATH Keywords: streamlines
zbMATH Keywords: radial flows
zbMATH Keywords: circular flows
zbMATH Keywords: parallel streamlines
zbMATH Keywords: second grade fluid
MaRDI profile type: Publication
full work available at URL: 0020-7225(87)90004-8
OpenAlex ID: W2077695902
cites work: Q4023641
cites work: Q5848712
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cites work: Q5776708
description: scientific article; zbMATH DE number 3997351