Advertisement

Transport in Porous Media

, Volume 92, Issue 1, pp 1–14 | Cite as

Unsteady mixed convection boundary-layer flow with suction and temperature slip effects near the stagnation point on a vertical permeable surface embedded in a porous medium

  • Azizah Mohd Rohni
  • Syakila Ahmad
  • Ioan PopEmail author
  • John H. Merkin
Article

Abstract

The unsteady mixed convection boundary-layer flow near the two-dimensional stagnation point on a vertical permeable surface embedded in a fluid-saturated porous medium with suction and a temperature slip effect is studied numerically. Similarity equations are obtained through the application of a similarity transformation technique. The shooting method is used to solve these similarity equations for different values of the mixed convection, wall mass suction, the unsteadiness and the slip parameters. Results show that multiple solutions exist for certain ranges of these parameters. Some limiting forms are then discussed, namely strong suction, the free convection limit, the situation when there is a large temperature slip and when the time dependence dominates.

Keywords

Porous medium Unsteady Mixed convection Suction Numerical results 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ali M.E., Magyari E.: Unsteady fluid and heat flow induced by a submerged stretching surface while its steady motion is slowed down gradually. Int. J. Heat Mass Transf. 50, 188–195 (2007)CrossRefGoogle Scholar
  2. Aly E.H., Elliott L., Ingham D.B.: Mixed convection boundary-layer flow over a vertical surface embedded in a porous medium. Eur. J. Mech. B 22, 529–543 (2003)CrossRefGoogle Scholar
  3. Andersson H.I., Aarseth J.B., Dandapat B.S.: Heat transfer in a liquid film on an unsteady stretching surface. Int. J. Heat Mass Transf. 43, 69–74 (2000)CrossRefGoogle Scholar
  4. Birkhoff G.: Hydrodynamics, a Study in Fact and Similitude, Revised edn. Princeton University Press, Princeton (1960)Google Scholar
  5. Cheng P.: Similarity solutions for mixed convection from horizontal impermeable surfaces in saturated porous media. Int. J. Heat Mass Transf. 20, 893–898 (1977)CrossRefGoogle Scholar
  6. Fang T.-G., Zhang J., Yao S.-S.: Viscous flow over an unsteady shrinking sheet with mass transfer. Chin. Phys. Lett. 26, 014703-1–014703-4 (2009)Google Scholar
  7. Harris S.D., Ingham D.B., Pop I.: Transient free convection on a vertical plate subjected to a change in surface heat flux in porous media. Fluid Dynamics Res. 18, 313–324 (1996)CrossRefGoogle Scholar
  8. Harris S.D., Ingham D.B., Pop I.: Thermal capacity effect on transient free convection adjacent to a vertical surface in a porous medium. Transp. Porous Media 46, 1–18 (2002)CrossRefGoogle Scholar
  9. Harris S.D., Ingham D.B., Pop I.: Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transp. Porous Media 77, 267–285 (2009)CrossRefGoogle Scholar
  10. Ingham, D.B., Pop, I. (eds): Transport Phenomena in Porous Media III. Elsevier, Oxford (2005)Google Scholar
  11. Merkin J.H.: Mixed convection boundary layer flow on a vertical surface in a saturated porous medium. J. Eng. Math. 14, 301–313 (1980)CrossRefGoogle Scholar
  12. Merkin J.H.: On dual solutions occurring in mixed convection in a porous medium. J. Eng. Math. 20, 171–179 (1985)CrossRefGoogle Scholar
  13. Merrill K., Beauchesne M., Previte J., Paullet J., Weidman P.: Final steady flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transf. 49, 4681–4686 (2006)CrossRefGoogle Scholar
  14. Mukhopadhyay S., Andersson H.: Effects of slip and heat transfer analysis of flow over an unsteady stretching surface. Heat Mass Transf. 45, 1447–1452 (2009)CrossRefGoogle Scholar
  15. Nazar R., Amin N., Pop I.: Unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Transfer 47, 2681–2688 (2004)CrossRefGoogle Scholar
  16. Nield D.A., Bejan A.: Convection in Porous Media, 3rd edn. Springer, New York (2006)Google Scholar
  17. Pop I., Ingham D.B.: Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media. Pergamon Press, Oxford (2001)Google Scholar
  18. Slater L.J.: Confluent hypergeometric functions. Cambridge University Press, Cambridge (1960)Google Scholar
  19. Tie-Gang F., Ji Z., Shan-Shan Y.: Viscous flow over an unsteady shrinking sheet with mass transfer. Chin. Phys. Let. 26, 014703-1–014703-4 (2009)Google Scholar
  20. Vadasz, P. (eds): Emerging Topics in Heat and Mass Transfer in Porous Media. Springer, Berlin (2008)Google Scholar
  21. Vafai, K. (eds): Handbook of Porous Media, 2nd edn. Taylor & Francis, New York (2005)Google Scholar
  22. Vafai K.: Porous Media: Applications in Biological Systems and Biotechnology. CRC Press, Tokyo (2010)CrossRefGoogle Scholar
  23. Wang C.Y.: Liquid film on an unsteady stretching surface. Q. Appl. Math. 48, 601–610 (1990)Google Scholar
  24. Yang K.T.: Unsteady laminar boundary layers in an incompressible stagnation flow, Trans. ASME J. Appl. Mech. 25, 421–427 (1958)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Azizah Mohd Rohni
    • 1
  • Syakila Ahmad
    • 2
  • Ioan Pop
    • 3
    Email author
  • John H. Merkin
    • 4
  1. 1.UUM College of Arts & Sciences, Physical Science Division, Building of Quantitative SciencesUniversiti Utara MalaysiaSintokMalaysia
  2. 2.School of Mathematical SciencesUniversiti Sains MalaysiaPenangMalaysia
  3. 3.Faculty of MathematicsUniversity of ClujClujRomania
  4. 4.Department of Applied MathematicsUniversity of LeedsLeedsUK

Personalised recommendations