### Abstract

A mathematical model for the unsteady forced convection boundary-layer flow near a forward stagnation point is considered when there is Newtonian heating on the surface whereby the heat transfer is proportional to the local surface temperature. In a previous paper (Salleh et al. J Eng Math 69:101-110, 2011), a critical value γ _{c}, dependent on the Prandtl number σ, of the heat transfer coefficient γ was identified, with solutions for the corresponding steady problem possible only for γ < γ _{c}. The unsteady problem considered here shows that these steady states are attained at large times when γ < γ _{c}. For γ > γ _{c}, the solution still continues to large time, now growing exponentially with time. This rate of growth is determined by an eigenvalue problem which we solve numerically for general values of γ and σ and asymptotically for large γ and both large and small σ.

Original language | English |
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Pages (from-to) | 53-60 |

Number of pages | 8 |

Journal | Journal of Engineering Mathematics |

Volume | 74 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 2012 |

### Fingerprint

### Keywords

- Forced convection
- Newtonian heating
- Stagnation point flow
- Unsteady boundary-layer flow

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### Cite this

*Journal of Engineering Mathematics*,

*74*(1), 53-60. https://doi.org/10.1007/s10665-011-9487-z

**The development of forced convection heat transfer near a forward stagnation point with Newtonian heating.** / Merkin, J. H.; Mohd. Nazar, Roslinda; Pop, I.

Research output: Contribution to journal › Article

*Journal of Engineering Mathematics*, vol. 74, no. 1, pp. 53-60. https://doi.org/10.1007/s10665-011-9487-z

}

TY - JOUR

T1 - The development of forced convection heat transfer near a forward stagnation point with Newtonian heating

AU - Merkin, J. H.

AU - Mohd. Nazar, Roslinda

AU - Pop, I.

PY - 2012/6

Y1 - 2012/6

N2 - A mathematical model for the unsteady forced convection boundary-layer flow near a forward stagnation point is considered when there is Newtonian heating on the surface whereby the heat transfer is proportional to the local surface temperature. In a previous paper (Salleh et al. J Eng Math 69:101-110, 2011), a critical value γ c, dependent on the Prandtl number σ, of the heat transfer coefficient γ was identified, with solutions for the corresponding steady problem possible only for γ < γ c. The unsteady problem considered here shows that these steady states are attained at large times when γ < γ c. For γ > γ c, the solution still continues to large time, now growing exponentially with time. This rate of growth is determined by an eigenvalue problem which we solve numerically for general values of γ and σ and asymptotically for large γ and both large and small σ.

AB - A mathematical model for the unsteady forced convection boundary-layer flow near a forward stagnation point is considered when there is Newtonian heating on the surface whereby the heat transfer is proportional to the local surface temperature. In a previous paper (Salleh et al. J Eng Math 69:101-110, 2011), a critical value γ c, dependent on the Prandtl number σ, of the heat transfer coefficient γ was identified, with solutions for the corresponding steady problem possible only for γ < γ c. The unsteady problem considered here shows that these steady states are attained at large times when γ < γ c. For γ > γ c, the solution still continues to large time, now growing exponentially with time. This rate of growth is determined by an eigenvalue problem which we solve numerically for general values of γ and σ and asymptotically for large γ and both large and small σ.

KW - Forced convection

KW - Newtonian heating

KW - Stagnation point flow

KW - Unsteady boundary-layer flow

UR - http://www.scopus.com/inward/record.url?scp=84860871240&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860871240&partnerID=8YFLogxK

U2 - 10.1007/s10665-011-9487-z

DO - 10.1007/s10665-011-9487-z

M3 - Article

AN - SCOPUS:84860871240

VL - 74

SP - 53

EP - 60

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 1

ER -