Steady mixed convection boundary-layer flow over a vertical flat surface in a porous medium filled with water at 4°C

Variable surface heat flux

S. C. Ling, Roslinda Mohd. Nazar, I. Pop, J. H. Merkin

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water at 4°C (maximum density) when the surface heat flux varies as xm and the velocity outside the boundary layer varies as x(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions when the mixed convection parameter λ is greater than some critical value λc (dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > -1 being required for solutions. The nature of the critical point λc is considered as well as various limiting forms; the forced convection limit (λ= 0), the free convection limit (λ → ∞) and the limits as m → ∞ and as m → -1.

Original languageEnglish
Pages (from-to)307-321
Number of pages15
JournalTransport in Porous Media
Volume70
Issue number3
DOIs
Publication statusPublished - Dec 2007

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Mixed convection
Boundary layer flow
Porous materials
Heat flux
Water
Forced convection
Natural convection
Boundary layers

Keywords

  • Boundary Layer
  • Maximum Density
  • Mixed convection
  • Porous medium
  • Variable Heat flux

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Catalysis

Cite this

Steady mixed convection boundary-layer flow over a vertical flat surface in a porous medium filled with water at 4°C : Variable surface heat flux. / Ling, S. C.; Mohd. Nazar, Roslinda; Pop, I.; Merkin, J. H.

In: Transport in Porous Media, Vol. 70, No. 3, 12.2007, p. 307-321.

Research output: Contribution to journalArticle

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AB - The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water at 4°C (maximum density) when the surface heat flux varies as xm and the velocity outside the boundary layer varies as x(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions when the mixed convection parameter λ is greater than some critical value λc (dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > -1 being required for solutions. The nature of the critical point λc is considered as well as various limiting forms; the forced convection limit (λ= 0), the free convection limit (λ → ∞) and the limits as m → ∞ and as m → -1.

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