On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

Rao, Adabala Ramachandra and Kasiviswanathan, Sethupathy R (1987) On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis. In: International Journal of Engineering Science, 25 (3). pp. 337-349.

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Abstract

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

Item Type:	Journal Article
Publication:	International Journal of Engineering Science
Publisher:	Elsevier Science
Additional Information:	Copy right of this article belongs to Elsevier Science.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	07 Jan 2010 07:14
Last Modified:	19 Sep 2010 05:36
URI:	http://eprints.iisc.ac.in/id/eprint/21300

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