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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 615612, 12 pages
http://dx.doi.org/10.1155/2011/615612
Research Article

Group-Invariant Solutions for Two-Dimensional Free, Wall, and Liquid Jets Having Finite Fluid Velocity at Orifice

Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan

Received 28 January 2011; Accepted 22 June 2011

Academic Editor: Furong Gao

Copyright © 2011 R. Naz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The group-invariant solutions for nonlinear third-order partial differential equation (PDE) governing flow in two-dimensional jets (free, wall, and liquid) having finite fluid velocity at orifice are constructed. The symmetry associated with the conserved vector that was used to derive the conserved quantity for the jets (free, wall, and liquid) generated the group invariant solution for the nonlinear third-order PDE for the stream function. The comparison between results for two-dimensional jet flows having finite and infinite fluid velocity at orifice is presented. The general form of the group invariant solution for two-dimensional jets is given explicitly.