On Obtaining Non-Similar Solutions from Similar Solutions

  • R. Seshadri
  • T. Y. Na


We have seen in the earlier chapters, that a similarity representation is obtainable for a boundary value problem provided the governing differential equations and the associated boundary conditions are invariant under a group of transformations. However, if any of the equations and boundary conditions is not invariant under a group, then the problem becomes nonsimilar.


Natural Convection Fundamental Solution Similarity Solution Excess Pore Pressure Associate Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hansen, A.G., Similarity Analysis of Boundary Value Problems in Engineering, Prentice-Hall (1964).Google Scholar
  2. 2.
    Na, T.Y. and Hansen, A.G., “Similarity Analysis of Flow Near an Oscillating Plate”,ASME paper 65-FE-21, presented in the ASME Fluid Engineering Conference, July 12, 1965.Google Scholar
  3. 3.
    Morgenstern,N.R. and Nixon, J. F., “One-Dimensional Consolidation of Thawing Soils”, Can. Geotech. J., 8 (1971).Google Scholar
  4. 4.
    Stakgold, I., Boundary Value Problems of Math. Phys., Vol.11, MacMilan, 1968.Google Scholar
  5. 5.
    Cristescu, N., Dynamic Plasticity, North Holland Pub. Co., Amsterdam (1967).MATHGoogle Scholar
  6. 6.
    Garabedian, P.R.,Partial Differential Equations, Wiley, (1964).MATHGoogle Scholar
  7. 7.
    Bluman, G.W., Construction of Solutions to Partial Differntial Equations by the use of Thisformation Groups, Ph.D. Thesis, California Institute of Technology (1967).Google Scholar
  8. 8.
    Seshadri, R. and Na, T.Y., “Ground Water Movement Due to Arbitrary Changes in Water Level”, Appl. Sci. Res., 39 (1982).Google Scholar
  9. 9.
    Bear, J., Dynamics of Fluids in Porous Media, American Elsevier Pub. Co. (1972).MATHGoogle Scholar
  10. 10.
    Na, T.Y., Computational Methods in Engineering Boundary Value Problems, Academic Press Inc. (1979).MATHGoogle Scholar
  11. 11.
    Na, T.Y., “Numerical Solution of Natural Convection Flow Past a Non-Isothermal Vertical Flat Plate”, AppL Sci. Res., 33 (1978).Google Scholar
  12. 12.
    Na, T.Y., Seshadri, R. and Singh, M.C., “On Obtaining Non-similar Solutions from Similarity Solutions”, 4th Int’l Sym. On Large Eng. Systems, University of Calgary, Calgary, Canada (1982).Google Scholar
  13. 13.
    Bird, R.B.,“Unsteady Pseudo-plastic Flow Near a Wall”, A.I.Ch.E. Journal, Vol. 5, No. 4 (1959).Google Scholar
  14. 14.
    Zeldovich, Ya. B. and Raizer, Yu. P., Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, (Translation) Vol.2, Academic Press (1967).Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • R. Seshadri
    • 1
  • T. Y. Na
    • 2
  1. 1.Syncrude Canada LimitedFort McMurrayCanada
  2. 2.Department of Mechanical EngineeringUniversity of Michigan—DearbornDearbornUSA

Personalised recommendations