On Obtaining Non-Similar Solutions from Similar Solutions
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.
KeywordsNatural Convection Fundamental Solution Similarity Solution Excess Pore Pressure Associate Boundary Condition
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- 1.Hansen, A.G., Similarity Analysis of Boundary Value Problems in Engineering, Prentice-Hall (1964).Google Scholar
- 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.Morgenstern,N.R. and Nixon, J. F., “One-Dimensional Consolidation of Thawing Soils”, Can. Geotech. J., 8 (1971).Google Scholar
- 4.Stakgold, I., Boundary Value Problems of Math. Phys., Vol.11, MacMilan, 1968.Google Scholar
- 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.Seshadri, R. and Na, T.Y., “Ground Water Movement Due to Arbitrary Changes in Water Level”, Appl. Sci. Res., 39 (1982).Google Scholar
- 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.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.Bird, R.B.,“Unsteady Pseudo-plastic Flow Near a Wall”, A.I.Ch.E. Journal, Vol. 5, No. 4 (1959).Google Scholar
- 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