Skip to main content
SpringerLink
Log in

Axisymmetric magnetohydrodynamic flow of micropolar fluid between unsteady stretching surfaces

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

Abstract

This investigation examines the time dependent magnetohydrodynamic (MHD) flow problem of a micropolar fluid between two radially stretching sheets. Both strong and weak concentrations of microelements are taken into account. Suitable transformations are employed for the conversion of partial differential equations into ordinary differential equations. Solutions to the resulting problems are developed with a homotopy analysis method (HAM). The angular velocity, skin friction coefficient, and wall couple stress coefficient are illustrated for various parameters.

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. Eringen, A. C. Theory of micropolar fluids. Journal of Mathematics and Mechanics, 16(1), 1–18 (1966)

    MathSciNet  Google Scholar 

  2. Gorla, R. S. R., Mansour, M. A., and Mohammedien, A. A. Combined convection in an axisymmetric stagnation flow of micropolar fluid. International Journal of Numerical Methods for Heat and Fluid Flow, 6(4), 47–55 (1996)

    Article  MATH  Google Scholar 

  3. Gorla, R. S. R. and Takhar, H. S. Boundary layer flow of micropolar fluid on rotating axisymmetric surfaces with a concentrated heat source. Acta Mechanica, 105, 1–10 (1994)

    Article  MATH  Google Scholar 

  4. Guram, G. S. and Smith, A. C. Stagnation flows of micropolar fluids with strong and weak interactions. Computer and Mathematics with Applications, 6(2), 213–233 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kumari, M. and Nath, G. Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point. International Journal of Engineering and Science, 22(6), 755–768 (1984)

    Article  Google Scholar 

  6. Abdullah, I. and Amin, N. A micropolar fluid model of blood flow through a tapered artery with a stenosis. Mathematical Methods in the Applied Science, 33(16), 1910–1923 (2010)

    MathSciNet  MATH  Google Scholar 

  7. Seddeek, M. A. Flow of a magneto-micropolar fluid past a continuously moving plate. Physics Letters A, 306(4), 255–257 (2003)

    Article  Google Scholar 

  8. Nazar, R., Amin, N., Filip, D., and Pop, I. Stagnation point flow of a micropolar fluid towards a stretching sheet. International Journal of Non-Linear Mechanics, 39(7), 1227–1235 (2004)

    Article  MATH  Google Scholar 

  9. Takhar, H. S., Bhargava, R., Agrawal, R. S., and Balaji, A. V. S. Finite element solution of a micropolar fluid flow and heat transfer between two porous disks. International Journal of Engineering and Science, 38(7), 1907–1922 (2000)

    Article  Google Scholar 

  10. Abo-Eldahab, E. M. and Ghonaim, A. F. Radiation effects on heat transfer of a micropolar fluid through a porous medium. Applied Mathematics and Computation, 169(1), 500–510 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nazar, R., Amin, N., and Pop, I. Free convection boundary layer flow on an isothermal sphere in a micropolar fluid. International Communications Heat and Mass Transfer, 29(3), 377–386 (2002)

    Article  Google Scholar 

  12. Sahoo, B. Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet. Central European Journal of Physics, 8(3), 498–508 (2010)

    Article  Google Scholar 

  13. Sahoo, B. Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet. Applied Mathematics and Mechanics (English Edition), 31(2), 159–173 (2010) DOI 10.1007/s10483-010-0204-7

    Article  MathSciNet  MATH  Google Scholar 

  14. Hayat, T. and Nawaz, M. Effect of heat transfer on magnetohydrodynamic axisymmetric flow between two stretching sheets. Zeitsch Rift für Naturforschung A, 65a(11), 1–8 (2010)

    Google Scholar 

  15. Liao, S. J. Beyond Perturbation: Introduction to Homotopy Analysis Method, CRC Press LLC, Florida (2003)

    Book  Google Scholar 

  16. Liao, S. J. Notes on the homotopy analysis method: some definitions and theorems. Communications in Nonlinear Science and Numerical Simulation, 14(4), 983–997 (2009)

    Article  MathSciNet  Google Scholar 

  17. Liao, S. J. A new branch of solutions of unsteady boundary layer flows over an impermeable stretched plate. International Journal of Heat and Mass Transfer, 48(12), 2529–2539 (2005)

    Article  MATH  Google Scholar 

  18. Cheng, J. and Liao, S. J. Series solutions of nano-boundary layer flows by means of the homotopy analysis method. Journal of Mathematical Analysis and Applications, 343(1), 233–245 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Abbasbandy, S. Homotopy analysis method for the Kawahara equation. Nonlinear Analysis: Real World Applications, 11(1), 307–312 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. Abbasbandy, S. and Hayat, T. Solution of the MHD Falkner-Skan flow by homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation, 14(9–10), 3591–3598 (2009)

    Article  MathSciNet  Google Scholar 

  21. Abbasbandy, S. and Shirzadi, A. A new application of the homotopy analysis method: solving the Sturm-Liouville problems. Communications in Nonlinear Science and Numerical Simulation, 16(1), 112–126 (2011)

    Article  MathSciNet  Google Scholar 

  22. Hashim, I., Abdulaziz, O., and Momani, S. Homotopy analysis method for fractional IVPs. Communications in Nonlinear Science and Numerical Simulation, 14(3), 674–684 (2009)

    Article  MathSciNet  Google Scholar 

  23. Bataineh, A. S., Noorani, M. S. M., and Hashim, I. On a new reliable modification of homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation, 14(2), 409–423 (2009)

    Article  MathSciNet  Google Scholar 

  24. Bataineh, A. S., Noorani, M. S. M., and Hashim, I. Modified homotopy analysis method for solving systems of second-order BVPs. Communications in Nonlinear Science and Numerical Simulation, 14(2), 430–442 (2009)

    Article  MathSciNet  Google Scholar 

  25. Allan, F. M. Derivation of the Adomian decomposition method using the homotopy analysis method. Applied Mathematics and Computation, 190(1), 6–14 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. Hayat, T. and Nawaz, M. Soret and Dufour effects on the mixed convection flow of a second grade fluid subject to Hall and ion-slip currents. International Journal for Numerical Methods in Fluids (2010) DOI 10.1002/fld.2405

  27. Hayat, T., Qasim, M., and Abbas, Z. Radiation and mass transfer effects on the magnetohydrodynamic unsteady flow induced by a stretching sheet. Zeitsch Rift für Naturforschung A, 65a(3), 231–239 (2010)

    Google Scholar 

  28. Hayat, T., Mustafa, M., and Pop, I. Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid. Communications in Nonlinear Science and Numerical Simulation, 15(5), 1183–1196 (2010)

    Article  MathSciNet  Google Scholar 

  29. Hayat, T. and Nawaz, M. Magnetohydrodynamic three-dimensional flow of a second-grade fluid with heat transfer. Zeitsch Rift für Naturforschung A, 65a(8), 683–691 (2010)

    Google Scholar 

  30. Hayat, T. and Nawaz, M. Hall and ion-slip effects on three-dimensional flow of a second grade fluid. International Journal for Numerical Methods in Fluids (2010) DOI 10.1002/fld.2251

  31. Hayat, T. and Awais, M. Three-dimensional flow of an upper-convected Maxwell (UCM) fluid. International Journal for Numerical Methods in Fluids (2010) DOI 10.1002/fld.2289

  32. Hayat, T., Mustafa, M., and Mesloub, S. Mixed convection boundary layer flow over a stretching surface filled with a Maxwell fluid in the presence of Soret and Dufour’s effects. Zeitsch Rift für Naturforschung A, 65a(5), 401–410 (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    T. Hayat & M. Nawaz

  2. Department of Mathematics, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia

    S. Obaidat

Authors
  1. T. Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Nawaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Obaidat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Nawaz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hayat, T., Nawaz, M. & Obaidat, S. Axisymmetric magnetohydrodynamic flow of micropolar fluid between unsteady stretching surfaces. Appl. Math. Mech.-Engl. Ed. 32, 361–374 (2011). https://doi.org/10.1007/s10483-011-1421-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-011-1421-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation