### 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 x^{m} 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 λ_{c} (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 λ_{c} 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 language | English |
---|---|

Pages (from-to) | 307-321 |

Number of pages | 15 |

Journal | Transport in Porous Media |

Volume | 70 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 2007 |

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### Keywords

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

### ASJC Scopus subject areas

- Chemical Engineering(all)
- Catalysis

### Cite this

*Transport in Porous Media*,

*70*(3), 307-321. https://doi.org/10.1007/s11242-007-9101-z

**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.

Research output: Contribution to journal › Article

*Transport in Porous Media*, vol. 70, no. 3, pp. 307-321. https://doi.org/10.1007/s11242-007-9101-z

}

TY - JOUR

T1 - Steady mixed convection boundary-layer flow over a vertical flat surface in a porous medium filled with water at 4°C

T2 - Variable surface heat flux

AU - Ling, S. C.

AU - Mohd. Nazar, Roslinda

AU - Pop, I.

AU - Merkin, J. H.

PY - 2007/12

Y1 - 2007/12

N2 - 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.

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.

KW - Boundary Layer

KW - Maximum Density

KW - Mixed convection

KW - Porous medium

KW - Variable Heat flux

UR - http://www.scopus.com/inward/record.url?scp=38349149079&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349149079&partnerID=8YFLogxK

U2 - 10.1007/s11242-007-9101-z

DO - 10.1007/s11242-007-9101-z

M3 - Article

VL - 70

SP - 307

EP - 321

JO - Transport in Porous Media

JF - Transport in Porous Media

SN - 0169-3913

IS - 3

ER -