Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 938604, 7 pages
http://dx.doi.org/10.1155/2012/938604
Research Article

Nonclassical Symmetry Analysis of Boundary Layer Equations

1Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan
2Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Lahore Cantt 54792, Pakistan

Received 11 August 2012; Accepted 1 October 2012

Academic Editor: Fazal M. Mahomed

Copyright © 2012 Rehana Naz et al. 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.

Linked References

  1. L. Prandt, “Uber Flussigkeitsbewegungen bei sehr kleiner Reibung,” in 3 Internationalen Mathematischen Kongress, pp. 484–491, Heidelberg, Germany, 1904.
  2. H. Schlichting, “Laminare strahlausbreitung,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 13, pp. 260–263, 1933. View at Publisher · View at Google Scholar
  3. H. Schlichting, Boundary Layer Theory, McGraw-Hill, New York, NY, USA, 1955.
  4. R. Naz, D. P. Mason, and F. M. Mahomed, “Conservation laws and conserved quantities for laminar two-dimensional and radial jets,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 2641–2651, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. D. P. Mason, “Group invariant solution and conservation law for a free laminar two-dimensional jet,” Journal of Nonlinear Mathematical Physics, vol. 9, supplement 2, pp. 92–101, 2002. View at Publisher · View at Google Scholar
  6. R. Naz, F. M. Mahomed, and D. P. Mason, “Conservation laws via the partial Lagrangian and group invariant solutions for radial and two-dimensional free jets,” Nonlinear Analysis: Real World Applications, vol. 10, no. 6, pp. 3457–3465, 2009. View at Publisher · View at Google Scholar
  7. M. B. Glauert, “The wall jet,” Journal of Fluid Mechanics, vol. 1, pp. 625–643, 1956. View at Publisher · View at Google Scholar
  8. E. J. Watson, “The radial spread of a liquid jet over a horizontal plane,” Journal of Fluid Mechanics, vol. 20, pp. 481–499, 1964. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. H. B. Squire, 50 Jahre Grenzschichtforschung. Eine Festschrift in Originalbeiträgen, Friedrich Vieweg & Sohn, Braunschweig, Germany, 1955, Edited by H. Gorter, W. Tollmien.
  10. N. Riley, “Radial jets with swirl. I. Incompressible flow,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 15, pp. 435–458, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. W. H. Schwarz, “The radial free jet,” Chemical Engineering Science, vol. 18, pp. 779–786, 1963. View at Publisher · View at Google Scholar
  12. G. W. Bluman and J. D. Cole, “The general similarity solution of the heat equation,” vol. 18, pp. 1025–1042, 1968. View at Google Scholar
  13. P. A. Clarkson and M. D. Kruskal, “New similarity reductions of the Boussinesq equation,” Journal of Mathematical Physics, vol. 30, no. 10, pp. 2201–2213, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. P. J. Olver, “Direct reduction and differential constraints,” Proceedings of the Royal Society. London A, vol. 444, no. 1922, pp. 509–523, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. P. A. Clarkson and E. L. Mansfield, “Algorithms for the nonclassical method of symmetry reductions,” SIAM Journal on Applied Mathematics, vol. 54, no. 6, pp. 1693–1719, 1994. View at Publisher · View at Google Scholar
  16. N. Bîlă and J. Niesen, “On a new procedure for finding nonclassical symmetries,” Journal of Symbolic Computation, vol. 38, no. 6, pp. 1523–1533, 2004. View at Publisher · View at Google Scholar
  17. M. S. Bruzón and M. L. Gandarias, “Applying a new algorithm to derive nonclassical symmetries,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 3, pp. 517–523, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. T. M. R. Filho and A. Figueiredo, “[SADE] a Maple package for the symmetry analysis of differential equations,” Computer Physics Communications, vol. 182, pp. 467–476, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH