Advertisement

Transport in Porous Media

, Volume 101, Issue 3, pp 365–371 | Cite as

A Comment on the Flow and Heat Transfer Past a Permeable Stretching/Shrinking Surface in a Porous Medium: Brinkman Model

Article

Abstract

An analytical solution is presented for the boundary-layer flow and heat transfer over a permeable stretching/shrinking surface embedded in a porous medium using the Brinkman model. The problem is seen to be characterized by the Prandtl number \(Pr\), a mass flux parameter \(s\), with \(s>0\) for suction, \(s=0\) for an impermeable surface, and \(s<0\) for blowing, a viscosity ratio parameter \(M\), the porous medium parameter \(\Lambda \) and a wall velocity parameter \(\lambda \). The analytical solution identifies critical values which agree with those previously determined numerically (Bachok et al. Proceedings of the fifth International Conference on Applications of Porous Media, 2013) and shows that these critical values, and the consequent dual solutions, can arise only when there is suction through the wall, \(s>0\).

Keywords

Boundary layer Heat transfer Suction/blowing  Stretching/shrinking sheet Porous Medium Dual solutions 

Notes

Acknowledgments

This work was supported by a Research University Grant (RUGS) from the Universiti Putra Malaysia.

References

  1. Bachok, N., Ishak, A., Pop, I.: Flow and heat transfer past a permeable stretching, shrinking surface in a porous medium: Brinkman model. In: Proc. 5th Int. Conf. Appl. Porous Media, pp. 109–117, Presa Universitară Clujeană, Cluj-Napoca, 25–28 Aug 2013Google Scholar
  2. Cortell, R.: Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing. Fluid Dyn. Res. 37, 231–245 (2005)CrossRefGoogle Scholar
  3. 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
  4. Ishak, A., Nazar, R., Pop, I.: Steady and unsteady boundary layers due to stretching vertical surface in a porous medium using Darcy–Brinkman equation model. Int. J. Appl. Mech. Eng. 11, 623–6375 (2006)Google Scholar
  5. Nazar, R., Amin, N., Filip, D., Pop, I.: The Brinkman model for the boundary layer mixed convection flow past a horizontal circular cylinder in a porous medium. Int. J. Heat Mass Transf. 46, 3167–3178 (2003)CrossRefGoogle Scholar
  6. Nield, D.A., Bejan, A.: Convection in porous media, 4th edn. Springer, New York (2013)CrossRefGoogle Scholar
  7. Rosca, A.V., Rosca, N.C., Grosan, T., Pop, I.: Non-Darcy mixed convection from a horizontal plate embedded in a nanofluid saturated porous media. Int. Comm. Heat Mass Transf. 39, 1080–1085 (2012)CrossRefGoogle Scholar
  8. Vafai, K., Tien, C.-L.: Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transf. 24, 195–203 (1981)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of LeedsLeeds UK
  2. 2.Department of Mathematics and Institute for Mathematical ResearchUniversiti Putra MalaysiaUPM SerdangMalaysia
  3. 3.School of Mathematical Science, Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaBangiMalaysia
  4. 4.Department of Applied MathematicsBabeş-Bolyai UniversityCluj-NapocaRomania

Personalised recommendations