Skip to main content
SpringerLink
Log in

MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

This paper investigates the magnetohydrodynamic (MHD) boundary layer flow of an incompressible upper-convected Maxwell (UCM) fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear problem is solved by using the successive Taylor series linearization method (STSLM). The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.

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.

Similar content being viewed by others

Abbreviations

x :

horizontal direction

y :

vertical direction

u :

velocity component in x-direction

v :

velocity component in y-direction

λ :

relaxation time

B 0 :

strength of the magnetic field

ν :

kinematic viscosity

ρ :

fluid density

σ :

electrical conductivity

V s :

suction/injection velocity

ψ :

stream function

η :

similarity variable

f(η):

dimensionless function of η

K :

elasticity parameter

M :

dimensionless magnetic parameter

R :

dimensionless suction/injection velocity

N :

collocation point

L :

interval length

References

  1. Lazurkin, J. S. Cold-drawing of glass-like and crystalline polymers. Journal of Polymer Science, 30, 595–604 (1958)

    Article  Google Scholar 

  2. Ginzburg, B. M. On the cold drawing of semicrystalline polymers. Journal of Macromolecular Science, Part B, 44, 217–223 (2005)

    Article  Google Scholar 

  3. Casas, F., Alba-Simionesco, C., Lequeux, F., and Montes, H. Cold drawing of ploymers: plasticity and aging. Journal of Non-Crystalline Solids, 352, 5076–5080 (2006)

    Article  Google Scholar 

  4. Crane, L. J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 21, 645–647 (1970)

    Article  Google Scholar 

  5. Wang, C. Y. Fluid flow due to stretching cylinder. Physics of Fluids, 31, 466–468 (1988)

    Article  Google Scholar 

  6. Wang, C. Y. Stretching a surface in a rotating fluid. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 39, 177–185 (1988)

    Article  MATH  Google Scholar 

  7. Gupta, P. S. and Gupta, A. S. Heat and mass transfer on a stretching sheet with suction or blowing. Canadian Journal of Chemical Engineering, 55, 744–746 (1977)

    Article  Google Scholar 

  8. Dandapat, B. S., Kitamura, A., and Santra, B. Transient film profile of thin liquid film flow on a stretching surface. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 57, 623–635 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Santra, B. and Dandapat, B. S. Thin film flow over nonlinear stretching sheet. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 60, 688–700 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chiam, T. C. Heat transfer in a fluid with variable thermal conductivity over a linear stretching sheet. Acta Mechanica, 129, 63–72 (1998)

    Article  MATH  Google Scholar 

  11. Liao, S. J. A new branch of solutions of boundary layer flows over an impermeable stretched plate. International Journal of Heat and Mass Transfer, 48, 2529–2539 (2006)

    Article  Google Scholar 

  12. Mukhopadhyay, S. Effects of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium. International Journal of Heat and Mass Transfer, 52, 3261–3265 (2009)

    Article  MATH  Google Scholar 

  13. Parsad, K. V., Pal, D., and Datti, P. S. MHD power-law fluid flow and heat transfer over a nonisothermal stretching sheet. Communications in Nonlinear Science and Numerical Simulation, 14, 2178–2189 (2009)

    Article  Google Scholar 

  14. Fang, T. and Zhong, Y. Viscous flow over a stretching sheet with an arbitrary surface velocity. Communications in Nonlinear Science and Numerical Simulation, 15, 3768–3776 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ishak, A., Nazar, R., and Pop, I. Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet. Meccanica, 43, 411–418 (2008)

    Article  MATH  Google Scholar 

  16. Ishak, A. Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect. Meccanica, 45, 367–373 (2010)

    Article  MATH  Google Scholar 

  17. Abel, M. S., Siddheshwar, P. G., and Mahesha, N. Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a nonuniform property micropolar liquid. Applied Mathematics and Computation, 217, 5895–5909 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Pahlavan, A. A., Aliakbar, V., Farahani, F. V., and Sadeghy, K. MHD flow of UCM fluids above stretching sheet using two-auxiliary-parameter homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation, 14, 473–488 (2009)

    Article  Google Scholar 

  19. Pahlavan, A. A., Aliakbar, V., and Sadeghy, K. The influence of thermal radiation on MHD flow of Maxwellian fluid above stretching sheet. Communications in Nonlinear Science and Numerical Simulation, 14, 779–794 (2009)

    Article  Google Scholar 

  20. Hayat, T., Abbas, Z., and Sajid, M. MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface. Chaos, Solitons and Fractals, 39, 840–848 (2009)

    Article  MATH  Google Scholar 

  21. Makukula, Z. G., Sibanda, P., and Motsa, S. S. A novel numerical technique for two-dimensional laminar flow between two moving porous walls. Mathematical Problems in Engineering, 2010, 528956 (2010) DOI 10.1155/2010/528956

    Article  MathSciNet  Google Scholar 

  22. Makukula, Z. G., Sibanda, P., and Motsa, S. S. A note on the solution of the von Karman equations using series and Chebyshev spectral methods. Boundary Value Problems, Article ID 471793, 17 pages (2010) DOI 10.1155/2010/471793

  23. Makukula, Z. G., Sibanda, P., and Motsa, S. S. On new solutions for heat transfer in a viscoelastic fluid between parallel plates. International Journal of Mathematical Models and Methods in Applied Sciences, 4, 221–230 (2010)

    Google Scholar 

  24. Motsa, S. S. and Shateyi, S. A new approach for the solution of three-dimensional magnetohydrodynamic rotating flow over a shrinking sheet. Mathematical Problems in Engineering, 2010, 586340 (2010) DOI 10.1155/2010/586340

    Google Scholar 

  25. Shateyi, S. and Motsa, S. S. Variable viscosity on magnetohydrodynamic fluid flow and heat transfer over an unsteady stretching surface with Hall effect. Boundary Value Problems, 2010, 257568 (2010) DOI 10.1155/2010/257568

    Article  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

  27. Trefethen, L. N. Spectral Methods in MATLAB, SIAM, Philadelphia, 51–75 (2000)

    Book  MATH  Google Scholar 

  28. Alizadeh-Pahlavan, A., Aliakbar, V., Vakili-Farahani, F., and Sadeghy, K. MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method. Communications in Nonlinear Science and Numerical Simulations, 14, 473–488 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematial Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, 3209, Pietermaritzburg, South Africa

    S. S. Motsa

  2. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    T. Hayat

  3. Department of Physics, King Saud University, Riyadh, 11451, Saudi Arabia

    O. M. Aldossary

Authors
  1. S. S. Motsa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. M. Aldossary
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. S. Motsa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Motsa, S.S., Hayat, T. & Aldossary, O.M. MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method. Appl. Math. Mech.-Engl. Ed. 33, 975–990 (2012). https://doi.org/10.1007/s10483-012-1599-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-012-1599-x

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation