### Abstract

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ_{0} is found for which there are dual solutions for a range λ_{c} < λ < 0 of λ (the value of λ_{c} dependent on δ) and single solutions for all λ ≥ 0. Another value of δ_{1} of δ, with δ_{1} > δ_{0}, is found for which there are dual solutions for a range 0 < λ < λ_{c} of positive values of λ, with solutions for all λ ≤ 0. There is also a range δ_{0} < δ < δ_{1} where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.

Original language | English |
---|---|

Pages (from-to) | 139-151 |

Number of pages | 13 |

Journal | Transport in Porous Media |

Volume | 76 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 |

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### Keywords

- Boundary-layer flow
- Dual solutions
- Mixed convection
- Porous medium

### ASJC Scopus subject areas

- Chemical Engineering(all)
- Catalysis

### Cite this

*Transport in Porous Media*,

*76*(1), 139-151. https://doi.org/10.1007/s11242-008-9240-x

**Mixed convection boundary-layer flow in a porous medium filled with water close to its maximum density.** / Ling, S. C.; Mohd. Nazar, Roslinda; Pop, I.; Merkin, J. H.

Research output: Contribution to journal › Article

*Transport in Porous Media*, vol. 76, no. 1, pp. 139-151. https://doi.org/10.1007/s11242-008-9240-x

}

TY - JOUR

T1 - Mixed convection boundary-layer flow in a porous medium filled with water close to its maximum density

AU - Ling, S. C.

AU - Mohd. Nazar, Roslinda

AU - Pop, I.

AU - Merkin, J. H.

PY - 2009

Y1 - 2009

N2 - The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.

AB - The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus putting a finite limit on the range of existence of solutions.

KW - Boundary-layer flow

KW - Dual solutions

KW - Mixed convection

KW - Porous medium

UR - http://www.scopus.com/inward/record.url?scp=59149091132&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=59149091132&partnerID=8YFLogxK

U2 - 10.1007/s11242-008-9240-x

DO - 10.1007/s11242-008-9240-x

M3 - Article

AN - SCOPUS:59149091132

VL - 76

SP - 139

EP - 151

JO - Transport in Porous Media

JF - Transport in Porous Media

SN - 0169-3913

IS - 1

ER -