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



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, \(s>0\).


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



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


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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

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