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A spectral method for the electrohydrodynamic flow in a circular cylindrical conduit

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Abstract

This paper presents a combination of the hybrid spectral collocation technique and the spectral homotopy analysis method (SHAM for short) for solving the nonlinear boundary value problem (BVP for short) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. The accuracy of the present solution is found to be in excellent agreement with the previously published solution. The authors use an averaged residual error to find the optimal convergence-control parameters. Comparisons are made between SHAM generated results, results from literature and Matlab ode45 generated results, and good agreement is observed.

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References

  1. Mckee, S., Calculation of electrohydrodynamic flow in a circular cylindrical conduit, Z. Angew Math. Mech., 77, 1997, 457–465.

    Article  MATH  MathSciNet  Google Scholar 

  2. Paullet, J. E., On the solutions of electrohydrodynamic flow in a circular cylindrical conduit, Z. Angew Math. Mech., 79, 1999, 357–360.

    Article  MATH  MathSciNet  Google Scholar 

  3. Hosseini, F. H., Saberi Nik, H. and Buzhabadi, R., Homotopy analysis method for solving foam drainage equation with space- and time-Fractional derivatives, International Journal of Differential Equations, 2011, DOI: 10.1155/2011/237045.

    Google Scholar 

  4. Effati, S., Saberi Nik, H. and Buzhabadi, R., Solving famous nonlinear coupled equations with parameters derivative by homotopy analysis method, International Journal of Differential Equations, 2011, DOI: 10.1155/2011/545607.

    Google Scholar 

  5. Zhang, Z. Y., Li, Y. X., Liu, Z. H. and Miao, X. J., New exact solutions to the perturbed nonlinear Schrödingers equation with Kerr law nonlinearity via modified trigonometric function series method, Commun. Nonlinear Sci. Numer. Simulat., 16(8), 2011, 3097–3106.

    Article  MATH  MathSciNet  Google Scholar 

  6. Zhang, Z. Y., Gan, X. Y., Yu, D. M., et al., A note on exact traveling wave solutions of the perturbed nonlinear schrodinger’s equation with Kerr law nonlinearity, Commun. Theor. Phys., 57, 2012, 764–770.

    Article  MATH  MathSciNet  Google Scholar 

  7. Liao, S. J., The proposed homotopy analysis technique for the solution of nonlinear problems, Shanghai Jiao Tong University, 1992.

    Google Scholar 

  8. Liao, S. J., On the homotopy anaylsis method for nonlinear problems, Appl. Math. Comput., 147, 2004, 499–513.

    Article  MATH  MathSciNet  Google Scholar 

  9. Liao, S. J., Comparison between the homotopy analysis method and homotopy perturbation method, Appl. Math. Comput., 169, 2005, 1186–1194.

    Article  MATH  MathSciNet  Google Scholar 

  10. Liao, S. J., Homotopy analysis method: a new analytical technique for nonlinear problems, Commun. Nonlinear Sci. Numer. Simulat., 2(2), 1997, 95–100.

    Article  Google Scholar 

  11. Hayat, T., Javed, T. and Sajid, M., Analytic solution for rotating flow and heat transfer analysis of a third-grade fluid, Acta Mech., 191, 2007, 219–229.

    Article  MATH  Google Scholar 

  12. Abbasbandy, S., Soliton solutions for the 5th-order KdV equation with the homotopy analysis method, Nonlinear Dyn., 51, 2008, 83–87.

    Article  MATH  MathSciNet  Google Scholar 

  13. Zhu, S. P., An exact and explicit solution for the valuation of American put options, Quantitative Finance, 6, 2006, 229–242.

    Article  MATH  MathSciNet  Google Scholar 

  14. Motsa, S. S., Sibanda, P. and Shateyi, S., A new spectral-homotopy analysis method for solving a nonlinear second order BVP, Commun. Nonlinear Sci. Numer. Simulat., 15, 2010, 2293–2302.

    Article  MATH  MathSciNet  Google Scholar 

  15. Motsa, S. S., Sibanda, P., Awad, F. G. and Shateyi, S., A new spectral-homotopy analysis method for the MHD Jeffery-Hamel problem, Computer and Fluids, 39, 2010, 1219–1225.

    Article  MATH  MathSciNet  Google Scholar 

  16. Saberi Nik, H., Effati, S., Motsa, S. S. and Shirazian, M., Spectral homotopy analysis method and its convergence for solving a class of nonlinear optimal control problems, Numer. Algor., 65, 2014, 171–194.

    Article  MATH  MathSciNet  Google Scholar 

  17. Saberi Nik, H., Effati, S., Motsa, S. S. and Shateyi, S., A new piecewise-spectral homotopy analysis method for solving chaotic systems of initial value problems, Mathematical Problems in Engineering, 2013, DOI: org/10.1155/2013/583193.

    Google Scholar 

  18. Mastroberardino, A., Homotopy analysis method applied to electrohydrodynamic flow, Commun. Nonlinear Sci. Numer. Simulat., 16, 2011, 2730–2736.

    Article  MATH  MathSciNet  Google Scholar 

  19. Liao, S. J., Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall/CRC Press, Boca, Raton, London, New Yrok, Washington, 2003.

    Book  Google Scholar 

  20. Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1988.

    Book  MATH  Google Scholar 

  21. Trefethen, L. N., Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.

    Book  MATH  Google Scholar 

  22. Liao, S. J., An optimal homotopy-analysis approach for strongly nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simulat., 15, 2010, 2003–2016.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Imam Khomeini International University, Ghazvin, 34149-16818, Iran

    Mohsen Moghtadaei & Saeid Abbasbandy

  2. Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran

    Hassan Saberi Nik

Authors
  1. Mohsen Moghtadaei
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  2. Hassan Saberi Nik
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  3. Saeid Abbasbandy
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Correspondence to Hassan Saberi Nik.

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Moghtadaei, M., Saberi Nik, H. & Abbasbandy, S. A spectral method for the electrohydrodynamic flow in a circular cylindrical conduit. Chin. Ann. Math. Ser. B 36, 307–322 (2015). https://doi.org/10.1007/s11401-015-0882-z

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  • DOI: https://doi.org/10.1007/s11401-015-0882-z

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