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Math. Comput. Appl. 2010, 15(4), 742-761; doi:10.3390/mca15040742

Conservation Laws and Conserved Quantities for Laminar Radial Jets with Swirl

1,* , 2,* and 3,*
1
Centre for Mathematics and Statistical Sciences Lahore School of Economics, Lahore 53200, Pakistan
2
Department of Mathematics, School of Science and Engineering, LUMS, Lahore Cantt 54792, Pakistan
3
School of Computational and Applied Mathematics, Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, South Africa
*
Authors to whom correspondence should be addressed.
Published: 1 December 2010
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Abstract

Conserved quantities play a central role in the solution of jet flow problems. A systematic way of deriving conserved quantities for the radial jets with swirl is presented. The multiplier approach is used to derive the conservation laws for the system of three boundary layer equations for the velocity components and for the system of two partial differential equations for the stream function. When the swirl is zero or at a large distance from the orifice (at infinity), the boundary layer equations for the radial jets with swirl reduce to those of the purely radial jets. The conserved quantities for the radial liquid, free and wall jets with swirl are derived by integrating the conservation laws across the jets.
Keywords: Radial jets with swirl; conservation laws; conserved quantity Radial jets with swirl; conservation laws; conserved quantity
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Naz, R.; Naeem, I.; Mahomed, F. Conservation Laws and Conserved Quantities for Laminar Radial Jets with Swirl. Math. Comput. Appl. 2010, 15, 742-761.

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