Plane steady flows of a third grade fluid
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.
thermodynamically compatible four-constant third grade fluid
scientific article; zbMATH DE number 3997351