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One-dimensional reductions and functional separable solutions to unsteady plane and axisymmetric boundary-layer equations for non-Newtonian fluids

Polyanin, Andrei D. and Zhurov, Alexei 2016. One-dimensional reductions and functional separable solutions to unsteady plane and axisymmetric boundary-layer equations for non-Newtonian fluids. International Journal of Non-Linear Mechanics 85 , pp. 70-80. 10.1016/j.ijnonlinmec.2016.05.005

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Abstract

The paper deals with equations describing the unsteady axisymmetric boundary layer of power-law non-Newtonian fluids on a body of revolution. The axisymmetric boundary-layer equation for the stream function is shown to reduce to a single third-order PDE of the form where n is a rheological parameter of the fluid; the function r(x), determining the shape of the body, is assumed arbitrary. For this non-linear PDE, we describe one-dimensional reductions as well as a number of new generalized and functional separable solutions, which depend on two to five arbitrary functions. The solutions are obtained with the direct method of functional separation of variables by using particular solutions to an auxiliary ODE and systems of first-order PDEs. Many of the solutions are expressed in terms of elementary functions, which, together with significant arbitrariness, makes them especially useful for solving certain model problems and testing numerical and approximate analytical methods in fluid dynamics. Apart from power-law fluids, the paper looks at three-parameter polynomial and generalized Sisko models of non-Newtonian fluids. The unsteady plane boundary-layer equations for the general non-Newtonian fluid model are shown to admit a reduction to an ODE. The paper presents new exact solutions to the plane boundary-layer equations for power-law fluids as well as some other rheologically complex fluids.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Dentistry
Medicine
Uncontrolled Keywords: Power-law non-Newtonian fluids; polynomial and generalized Sisko fluid models; unsteady axisymmetric boundary layer; generalized and functional separable solutions; one-dimensional reductions.
Publisher: Elsevier
ISSN: 0020-7462
Date of Acceptance: 20 May 2016
Last Modified: 11 Oct 2019 14:49
URI: http://orca.cf.ac.uk/id/eprint/103556

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