Advertisement

Numerical solutions for the problem of the boundary layer flow of a Powell–Eyring fluid over an exponential sheet using the spectral relaxation method

  • M M KhaderEmail author
Original Paper

Abstract

The spectral relaxation method is a very powerful tool which was applied in this paper to get the numerical solution for the system of nonlinear ordinary differential equations which describe the problem of fluid flow of a Powell–Eyring model past an exponentially shrinking sheet with the presence of magnetic field and thermal radiation. The introduced method is based on the spectral relaxation method, which is successfully used to solve this type of equations. Also, this method is developed from the Gauss–Seidel idea of reducing the governing nonlinear system of ordinary differential equations into smaller systems of linear equations. Likewise, the influences of the governing parameters on the velocity and temperature profiles are studied graphically. Results of this study shed light on the accuracy and efficiency of the proposed method in solving this type of the nonlinear boundary layer equations.

Keywords

Boundary layer flow MHD Steady shrinking sheet Spectral relaxation method 

PACS Nos.

47.27.er 45.10.-b 04.25.-g 

Notes

References

  1. [1]
    S S Motsa and Z G Makukula Cent. Eur. J. Phys. 11 363 (2013)Google Scholar
  2. [2]
    S Shateyi Bound. Value Probl. 196 1 (2013)Google Scholar
  3. [3]
    D Vieru and C Fetecau Appl. Math. Comput. 200 459 (2008)MathSciNetGoogle Scholar
  4. [4]
    T Hayat, Z Iqbal, M Qasim and S Obaidat Int. J. Heat Mass Transf. 55 1817 (2012)CrossRefGoogle Scholar
  5. [5]
    N S Akbar and S Nadeem Heat Mass Transf. 46 531 (2010)ADSCrossRefGoogle Scholar
  6. [6]
    M M Khader Indian J. Phys. 11 1 (2019)Google Scholar
  7. [7]
    J C Pu and H C Hu Indian J. Phys. 93 229 (2019)ADSCrossRefGoogle Scholar
  8. [8]
    M Y Malik, A Hussain and S Nadeem Sci. Iran. Trans. Mech. Eng. (B) 20 313 (2013)Google Scholar
  9. [9]
    F Awad, S S Motsa and M Khumalo PLoS ONE 9 16 (2014)Google Scholar
  10. [10]
    N A Haroun, P Sibanda, S Mondal and S S Motsa Bound. Value Probl. 23 210 (2015)Google Scholar
  11. [11]
    S S Motsa Chem. Eng. Commun. 12 107 (2013)Google Scholar
  12. [12]
    C Canuto, M V Hussaini, A Quarteroni and T A Zang Spectral Methods in Fluid Dynamics (Berlin: Springer) (1988)CrossRefzbMATHGoogle Scholar
  13. [13]
    L N Trefethen Spectral Methods in MATLAB (Philadelphia: SIAM) (2000)CrossRefzbMATHGoogle Scholar
  14. [14]
    P K Kameswaran, P Sibanda and S S Motsa Bound. Value Probl. 242 1 (2013)Google Scholar
  15. [15]
    S S Motsa, P Dlamini and M Khumalo Nonlinear Dyn. 72 265 (2013)CrossRefGoogle Scholar
  16. [16]
    S S Motsa, P G Dlamini and M Khumalo Adv. Math. Phys. 2014 Article ID 341964 (2014)Google Scholar
  17. [17]
    A Ara, N A Khan, H Khan and F Sultan Ain Shams Eng. J. 5 1337 (2014)CrossRefGoogle Scholar

Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, College of ScienceImam Mohammad Ibn Saud Islamic University (IMSIU)RiyadhSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceBenha UniversityBenhaEgypt

Personalised recommendations