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**A note on the similarity equations arising in free convection boundary layers with blowing and suction.**
*(English)*
Zbl 0803.76078

Summary: The similarity equations for the free convection boundary-layer flow on a vertical plate with prescribed wall temperature and transpiration velocity are considered. The range of existence of solution is discussed first. For blowing this is seen to be independent of the transpiration parameter \(\gamma\), depending only on the Prandtl number. For suction this range of existence of solutions is seen to depend on \(\gamma\) as well. Asymptotic solutions for strong suction and strong blowing are derived and compared with numerical solutions of the similarity equations.

### MSC:

76R10 | Free convection |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

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\textit{J. H. Merkin}, Z. Angew. Math. Phys. 45, No. 2, 258--274 (1994; Zbl 0803.76078)

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### References:

[1] | R. Eichhorn,The effect of mass transfer on free connection. J. Heat Transfer82, 260-263 (1960). |

[2] | J. F. Clarke,Transpiration and natural convection: the vertical flat plate problem. J. Fluid Mech.57, 45-61 (1973). · Zbl 0257.76085 |

[3] | P. G. Parikh, R. J. Moffat, W. M. Kays and D. Bershader,Free convection over a vertical porous plate with transpiration. Int. J. Heat Mass Transfer17, 1465-1474 (1974). · Zbl 0289.76052 |

[4] | E. M. Sparrow and R. D. Cess,Free convection with blowing and suction. J. Heat Transfer83, 387-389 (1961). |

[5] | J. H. Merkin,Free convection with blowing and suction. Int. J. Heat Mass Transfer15, 989-999 (1972). · Zbl 0236.76068 |

[6] | M. Vedhanayagam, R. A. Altenkirch and R. Eichhorn,A transformation of the boundary layer equations for free convection past a vertical flat plate with arbitrary blowing and wall temperature variations. Int. J. Heat Mass Transfer23, 1286-1288 (1980). |

[7] | H. J. H. Brouwers,The film model applied to free convection over a vertical plate with blowing or suction. Int. J. Heat Mass Transfer35, 1841-1844 (1992). |

[8] | H. J. H. Brouwers,A film model for free convection over a vertical plate with blowing or suction. To appear in Wärme- und Stoffübertragung. |

[9] | J. F. Clarke and N. Riley,Natural convection induced in a gas by the presence of a hot porous horizontal surface. Q. Jl. Mech. Appl. Math.28, 373-396 (1975). · Zbl 0322.76037 |

[10] | J. F. Clarke and N. Riley,Free convection and the burning of a horizontal fuel surface. J. Fluid Mech.74, 414-431 (1976). · Zbl 0333.76054 |

[11] | H. T. Lin and W. S. Yu,Free convection on a horizontal plate with blowing and suction. J. Heat Transfer110, 793-796 (1988). |

[12] | M. A. Chaudhary and J. H. Merkin,The effects of blowing and suction on free convection boundary layers on vertical surfaces with prescribed heat flux. J. Engineering Math.27, 265-292 (1993). · Zbl 0781.76077 |

[13] | J. H. Merkin,A note on the similarity solutions for free convection on a vertical plate. J. Engineering Math.19, 189-201 (1985). · Zbl 0577.76083 |

[14] | J. H. Merkin,The effects of blowing and suction on free convection boundary layers. Int. J. Heat Mass Transfer18, 237-244 (1975). · Zbl 0295.76019 |

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