### Abstract

The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number. $${m = \frac{1}{5}}$$m=15 is found to be a transitional case with different behaviour depending on whether $${m > \frac{1}{5}}$$m>15 or $${m <\frac{1}{5}}$$m \frac{1}{5}}$$m>15, there is a critical value λ_{c} with solutions only for λ ≥ λ_{c}, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For $${0 <m <\frac{1}{5}}$$0 \frac{1}{5}}$$m>15 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m \frac{1}{5}}$$m>15.

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

Pages (from-to) | 2441-2460 |

Number of pages | 20 |

Journal | Acta Mechanica |

Volume | 226 |

Issue number | 8 |

DOIs | |

Publication status | Published - Mar 20 2015 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanical Engineering
- Computational Mechanics

### Cite this

*Acta Mechanica*,

*226*(8), 2441-2460. https://doi.org/10.1007/s00707-015-1334-2

**Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition.** / Rahman, M. M.; Merkin, J. H.; Pop, I.

Research output: Contribution to journal › Article

*Acta Mechanica*, vol. 226, no. 8, pp. 2441-2460. https://doi.org/10.1007/s00707-015-1334-2

}

TY - JOUR

T1 - Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition

AU - Rahman, M. M.

AU - Merkin, J. H.

AU - Pop, I.

PY - 2015/3/20

Y1 - 2015/3/20

N2 - The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number. $${m = \frac{1}{5}}$$m=15 is found to be a transitional case with different behaviour depending on whether $${m > \frac{1}{5}}$$m>15 or $${m <\frac{1}{5}}$$m \frac{1}{5}}$$m>15, there is a critical value λc with solutions only for λ ≥ λc, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For $${0 15 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m \frac{1}{5}}$$m>15.

AB - The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number. $${m = \frac{1}{5}}$$m=15 is found to be a transitional case with different behaviour depending on whether $${m > \frac{1}{5}}$$m>15 or $${m <\frac{1}{5}}$$m \frac{1}{5}}$$m>15, there is a critical value λc with solutions only for λ ≥ λc, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For $${0 15 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m \frac{1}{5}}$$m>15.

UR - http://www.scopus.com/inward/record.url?scp=84931562177&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84931562177&partnerID=8YFLogxK

U2 - 10.1007/s00707-015-1334-2

DO - 10.1007/s00707-015-1334-2

M3 - Article

VL - 226

SP - 2441

EP - 2460

JO - Acta Mechanica

JF - Acta Mechanica

SN - 0001-5970

IS - 8

ER -