Skip to main content
SpringerLink
Log in

Adomian Series Solution to a Rayleigh Power-Law Problem

  • Research Article - Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

A Rayleigh power-law problem of a semi-infinite plate moving in an electrically conducting non-Newtonian fluid is investigated. In a special case, exact solutions are established via the use of Crocco variables. Approximate solutions are obtained for the general problem via the Adomian decomposition method where we obtain the first few terms of an infinite power series expansion of the solution. This approximate solution is utilized to estimate a shear stress parameter. (Specifically, we use terms of the infinite series up to the third polynomial, which proves to give high accuracy.) Additionally, a Maclaurin series approach is utilized to approximate solutions as well as estimate the shear stress parameter for different values of the power-law index n. The results of the two methods are compared with results obtained via MATLAB integrators where the efficiency of the Adomian method is established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blasius, H.: Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Math. Phys. 56, 1–37 (1908)

    MATH  Google Scholar 

  2. Sapunkov, Y.G.: Rayleigh problem of non-Newtonian electro-conductive fluids. J. Appl. Math. Technol. Phys. 2, 50–55 (1970)

    Google Scholar 

  3. Vujanovic, B.; Strauss, A.M.; Djuvic, D.: A variational solution of the Rayleigh problem for a power-law non-Newtonian conducting fluid. Ing. Archiv. 41, 381–386 (1972)

    Article  MATH  Google Scholar 

  4. Vujanvic, M.H.: Magnetohydrodynamics flow for a non-Newtonian fluid power-law fluid having a pressure gradient and fluid injection. J. Eng. Math. 14, 47–55 (1980)

    Article  Google Scholar 

  5. Gao, W.; Wang, J.: Similarity solutions to the power-law generalized Newtonian fluid. J. Comput. Appl. Math. 222(2), 381–391 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bedjaoui, N.; Guedda, M.; Hammouch, Z.: Similarity solutions of the Rayleigh problem for Ostwald-de Wael electrically conducting fluids. Anal. Appl. 9(2), 135–159 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Soh, W.C.: Invariant solutions of the unidirectional flow of an electrically charged power-law non-Newtonian fluid over a flat plate in presence of a transverse magnetic field. Commun. Nonlinear Sci. Numer. Simul. 10, 537–548 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Elghabaty, S.S.; Abdel-Rahman, G.M.: Magnetohydrodynamic boundary-layer flow for a non-Newtonian fluid past a wedge. Astrophys. Space Sci. 141(1), 9–19 (1988)

    Article  Google Scholar 

  9. Pantokratoras, A.; Fang, T.: A note on the Blasius and Sakiadis flow of a non-Newtonian power-law fluid in a constant transverse magnetic field. Acta Mech. 218(1), 187–194 (2011)

    Article  MATH  Google Scholar 

  10. Chiam, T.C.: Solutions for the flow of a conducting power-law fluid in a transverse magnetic field and with a pressure gradient using Crocco variables. Acta Mech. 137(9), 225–235 (1999)

    Article  MATH  Google Scholar 

  11. Su, X.; Zheng, L.; Feng, J.: Approximate analytical solutions and approximate value of skin friction coefficient for boundary layer of power law fluids. Appl. Math. Mech. (English Edition) 29(9), 1215–1220 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hryniewicz, Z.: Dynamics of Rayleigh beam on nonlinear foundation due to moving load using Adomian decomposition and coiflet expansion. Soil Dyn. Earthq. Eng. 31(8), 1123–1131 (2011)

    Article  Google Scholar 

  13. Adomian, G.: Solving Frontier Problems in Physics: The Decomposition Method. Springer, Amsterdam (1994)

    Book  MATH  Google Scholar 

  14. Wei, D.; Al-Ashhab, S.: Similarity Solutions for a non-Newtonian power-law fluid flow. Appl. Math. Mech. (English Edition) 35(9), 1155–1166 (2014). https://doi.org/10.1007/s10483-014-1854-6

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author would like to thank the Deanship of Academic Research at Al Imam Mohammad Ibn Saud Islamic University in the Kingdom of Saudi Arabia for funding this project for the year 1435-1436H, and that is according to item (42) from the rules and regulations for the funding of research projects issued in its second edition for the year 1438H.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Al Imam Mohammad Ibn Saud Islamic University, P.O. Box 90950, Riyadh, 11623, Saudi Arabia

    Samer Al-Ashhab

Authors
  1. Samer Al-Ashhab
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Samer Al-Ashhab.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Al-Ashhab, S. Adomian Series Solution to a Rayleigh Power-Law Problem. Arab J Sci Eng 43, 4911–4916 (2018). https://doi.org/10.1007/s13369-018-3223-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-018-3223-1

Keywords

Search

Navigation