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Solution of a viscoelastic boundary layer equation by orthogonal collocation

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Summary

The applicability of the method of orthogonal collocation to the solution of Newtonian and viscoelastic boundary layer problems is investigated. To this end, the method is applied to the boundary layer equation describing the flow of a second-order fluid near a two-dimensional stagnation point. The efficiency of a number of different approximating bases is investigated. It is shown that the method is applicable to both Newtonian and weakly viscoelastic fluids, and that it compares very favorably with other weighted residual methods.

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References

  1. B. A. Finlayson,The Method of Weighted Residuals and Variational Principles, Academic Press, 1972.

  2. H. E. Bethel, On a Convergent Multi-Moment Method for the Laminar Boundary Layer Equations.Aeronaut. Q., 18 (1967), 332.

    Google Scholar 

  3. H. H. Bossel, Boundary Layer Computation by an N Parameter Integral Method Using Exponentials,AIAA Journal, 8 (1970) 1841.

    MATH  Google Scholar 

  4. M. K. Jain, An Extremal Point Collocation Method for Fluid Flow Problems,Appl. Sci. Res. (A), 11 (1962) 177.

    MATH  Google Scholar 

  5. J. V. Villadsen and W. E. Stewart, Solution of Boundary-Value Problems by Orthogonal CollocationChem. Eng. Sci., 22 (1967) 1483.

    Google Scholar 

  6. D. W. Beard and K. Walters, Elastico-viscous Boundary Layer Flows I. Two-Dimensional Flow-Hear a Stagnation Point,Proc Comb. Phil. Soc., 60 (1964) 667.

    MathSciNet  Google Scholar 

  7. R. T. Davis, Boundary Layer Theory for Viscoelastic Liquids,Proc 10th Midwestern Mechanics Conference, (1967) 1145.

  8. K. R. Frater, On the Solution of Some Boundary-value Problems Arising in Elastico-viscous Fluid Mechanics,Z. angew. Math. Phys., 21 (1970) 134.

    MATH  Google Scholar 

  9. G. K. Rajeswari and S. L. Rathna, Flow of a Particular Class of non-Newtonian Viscoelastic and Pisco-inelastic Fluids near a Stagnation Point,Z. angew. Math. Phys., 13 (1962) 43.

    MathSciNet  Google Scholar 

  10. M. H. Davies, A Note on Elastico-Viscous Boundary Layer Flows,Z. angew. Math. Phys., 17 (1966) 189.

    Google Scholar 

  11. M. M. Denn, Boundary Layer Flows for a Class of Elastic Liquids,Chem. Eng. Sci. 22 (1967) 395.

    Google Scholar 

  12. J. Peddieson, Wedge and Cone Flows of Viscoelastic Liquids,A.I.Ch.E. Journal, 19 (1973) 377.

    Google Scholar 

  13. N. I. Akhiezer and I. M. Glazman,Theory of Linear Operators in Hilbert Space, Chp. 1, Ungar, 1961.

  14. M. Abramowitz and I. A. Stegun (Eds.),Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series No. 55, Chps. 22 and 25, 1966.

  15. D. W. Marquardt, An Algorithm for Least-Squares Estimation on Nonlinear Parameters,J. Soc. Indust. Appl. Math. 11 (1963) 431.

    Article  MATH  MathSciNet  Google Scholar 

  16. H. Goertler, Zahlentafeln Universeller Funktionen zur neuen Reihe für die Berechnung laminarer Grenzschichten,Deutsche Versuchsanstalt für Luftfahrt E.V., Bericht No. 34 (1957).

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  1. Chemical Engineering Department, University of Puerto Rico, Mayaguez, 00708, Puerto Rico

    R. W. Serth

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  1. R. W. Serth
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Serth, R.W. Solution of a viscoelastic boundary layer equation by orthogonal collocation. J Eng Math 8, 89–92 (1974). https://doi.org/10.1007/BF02353609

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