Skip to main content
SpringerLink
Log in

MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface

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

Abstract

Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable surface in the presence of magnetic field. To achieve this, one parameter linear group transformation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method (HAM) to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non-Newtonian fluid (Powell-Eyring model) parameters ɛ and δ on the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ɛ whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.

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. Chen, T. S., Sparrow, E. M., and Mucoglu, A. Mixed convection in boundary layer flow on a horizontal plate. Journal of Heat Transfer, 99, 66–71 (1977)

    Article  Google Scholar 

  2. Ramachandran, N., Armaly, B. F., and Chen, T. S. Mixed convection over a horizontal plate. Journal of Heat Transfer, 105, 420–423 (1983)

    Article  Google Scholar 

  3. Afzal, N. and Hussain, T. Mixed convection over a horizontal plate. Journal of Heat Transfer, 106, 240–241 (1984)

    Article  Google Scholar 

  4. Karwe, M. V. and Jaluria, Y. Fluid flow and mixed convection transport from a moving plate in rolling and extrusion processes. Journal of Heat Transfer, 110, 655–661 (1988)

    Article  Google Scholar 

  5. Hady, F. M., Bakier, A. Y., and Gorla, R. S. R. Mixed convection boundary layer flow on a continuous flat plate with variable viscosity. Heat and Mass Transfer, 31, 169–172 (1996)

    Article  Google Scholar 

  6. Hossain, M. A. and Takhar, H. S. Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat and Mass Transfer, 31, 243–248 (1996)

    Article  Google Scholar 

  7. Al-Sanea, S. A. Mixed convection heat transfer along a continuously moving heated vertical plate with suction or injection. International Journal of Heat and Mass Transfer, 47, 1445–1465 (2004)

    Article  MATH  Google Scholar 

  8. Schneider, W. Lift, thrust and heat transfer due to mixed convection flow past a horizontal plate of finite length. Journal of Fluid Mechanics, 529, 51–69 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hayat, T., Abbas, Z., and Javed, T. Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet. Physics Letters A, 372, 637–647 (2008)

    Article  MATH  Google Scholar 

  10. Bluman, G. and Kumei, S. Symmetries and Differential Equations, Springer-Verlag, New York (1989)

    Book  MATH  Google Scholar 

  11. Morgan, A. J. A. The reduction by one of the number of independent variables in some systems of partial differential equations. Quarterly Journal of Mathematics, 3, 250–259 (1952)

    Article  MATH  Google Scholar 

  12. Birkhoff, G. Hydrodynamics, Princeton University Press, Princeton (1960)

    MATH  Google Scholar 

  13. Hansen, A. G. Similarity Analyses of Boundary Value Problems in Engineering, Prentice Hall, New Jersey (1965)

    Google Scholar 

  14. Na, T. Y. and Hansen, A. G. Similarity solutions of a class of laminar, three dimensional, boundary layer equations of power law fluids. International Journal of Non-Linear Mechanics, 2, 373–385 (1967)

    Article  MATH  Google Scholar 

  15. Pakdemirli, M. Similarity analysis of boundary layer equations of a class of non-Newtonian fluids. International Journal of Non-Linear Mechanics, 29, 187–196 (1994)

    Article  MATH  Google Scholar 

  16. Layek, G. C., Mukhopadhyay, S., and Samad, S. A. Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing. International Communications in Heat and Mass Transfer, 34, 347–356 (2007)

    Article  Google Scholar 

  17. Kandasamy, R., Hayat, T., and Obaidat, S. Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink. Nuclear Engineering and Design, 241, 2155–2161 (2011)

    Article  Google Scholar 

  18. Fan, J., Shi, J., and Xu, X. Similarity solution of free convective boundary-layer behavior at a stretching surface. Heat and Mass Transfer, 35, 191–196 (1999)

    Article  Google Scholar 

  19. Powell, R. E. and Eyring, H. Mechanism for relaxation theory of viscosity. nature, 154, 427–428 (1944)

    Article  Google Scholar 

  20. Eldab, N. T., El-Naby, M. A. A., Ashraf, F., and Amaney, S. Numerical study of the flow of magnetohydrodynamic non-Newtonian fluid obeying the Eyring-Powell model through a non-Darcy porous medium with coupled heat and mass transfer. Journal of Porous Media, 11, 691–700 (2008)

    Article  Google Scholar 

  21. Patel, M. and Timol, M. G. Numerical treatment of Powell-Eyring fluid flow using method of asymptotic boundary conditions. Applied Numerical Mathematics, 59, 2584–2592 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  22. Islam, S., Shah, A., Zhou, C. Y., and Ali, I. Homotopy pertubation analysis of slider bearing with Powell-Eyring fluid. Zeitschrift für Angewandte Mathematik und Physik, 60, 1178–1193 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  23. Hayat, T., Iqbal, Z., Qasim, M., and Obaidat, S. Steady flow of an Powell-Eyring fluid over a moving surface with convective boundary conditions. International Journal of Heat and Mass Transfer, 55, 1817–1822 (2012)

    Article  Google Scholar 

  24. Jalil, M., Asghar, S., and Imran, S. M. Self similar solutions for the flow and heat transfer of Powell-Eyring fluid over a moving surface in a parallel free stream. International Journal of Heat and Mass Transfer, 65, 73–79 (2013)

    Article  Google Scholar 

  25. Jalil, M. and Asghar, S. Flow and heat transfer of Powell-Eyring fluid over a stretching surface: a Lie group analysis. Journal of Fluids Engineering, 135, 121201 (2013)

    Article  Google Scholar 

  26. Liao, S. J. The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems, Ph.D. dissertation, Shanghai Jiao Tong University, Shanghai (1992)

    Google Scholar 

  27. Liao, S. J. Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton (2003)

    Book  Google Scholar 

  28. Liao, S. J. Homotopy Analysis Method in Nonlinear Differential Equations, Springer and Higher Education Press, Heidelberg (2012)

    Book  MATH  Google Scholar 

  29. Liao, S. J. Advances in the Homotopy Analysis Method, World Scientific Press, New York (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Science & Technology, Berhampur, 761008, India

    S. Panigrahi, M. Reza & A. K. Mishra

  2. Department of Mathematics, Berhampur University, Berhampur, 760007, India

    S. Panigrahi & A. K. Mishra

Authors
  1. S. Panigrahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Reza
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. K. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Panigrahi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Panigrahi, S., Reza, M. & Mishra, A.K. MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface. Appl. Math. Mech.-Engl. Ed. 35, 1525–1540 (2014). https://doi.org/10.1007/s10483-014-1888-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-014-1888-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation