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Transport in Porous Media

, Volume 96, Issue 2, pp 237–253 | Cite as

Mixed Convection Boundary-Layer Flow Along a Vertical Cylinder Embedded in a Porous Medium Filled by a Nanofluid

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

Abstract

The steady mixed convection boundary-layer flow on a vertical circular cylinder embedded in a porous medium filled by a nanofluid is studied for both cases of a heated and a cooled cylinder. The governing system of partial differential equations is reduced to ordinary differential equations by assuming that the surface temperature of the cylinder and the velocity of the external (inviscid) flow vary linearly with the axial distance x measured from the leading edge. Solutions of the resulting ordinary differential equations for the flow and heat transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle volume fraction \({\phi}\), the mixed convection or buoyancy parameter λ and the curvature parameter γ. Results are presented for the specific case of copper nanoparticles. A critical value λ c of λ with λ c < 0 is found, with the values of | λ c| increasing as the curvature parameter γ or nanoparticle volume fraction \({\phi}\) is increased. Dual solutions are seen for all values of λλ c for both aiding, λ > 0 and opposing, λ < 0, flows. Asymptotic solutions are also determined for both the free convection limit \({(\lambda \gg 1)}\) and for large curvature parameter \({(\gamma \gg 1)}\).

Keywords

Dual solutions Mixed convection Nanofluid Porous medium Vertical cylinder 

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Azizah Mohd Rohni
    • 1
  • Syakila Ahmad
    • 2
  • John H. Merkin
    • 3
  • Ioan Pop
    • 4
    Email author
  1. 1.School of Quantitative SciencesUniversiti Utara MalaysiaSintokMalaysia
  2. 2.School of Mathematical SciencesUniversiti Sains MalaysiaUSMMalaysia
  3. 3.Department of Applied MathematicsUniversity of LeedsLeedsUK
  4. 4.Department of MathematicsBabeş-Bolyai UniversityCluj-NapocaRomania

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