##
**Free convection flow about a cone under mixed thermal boundary conditions and a magnetic field.**
*(English)*
Zbl 1099.76060

Summary: We perform a similarity analysis to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a vertical down-pointing cone under mixed thermal boundary conditions. Boundary-layer velocity and temperature profiles are determined numerically for various values of magnetic parameter and Prandtl number. The results show that the magnetic field suppresses the velocity profiles and increases the skin friction. The temperature profiles are expanded with increasing values of the magnetic parameter resulting in higher surface temperatures. We also obtain a transformation relating the similarity solutions for boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter.

### MSC:

76R10 | Free convection |

76W05 | Magnetohydrodynamics and electrohydrodynamics |

76M55 | Dimensional analysis and similarity applied to problems in fluid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

PDF
BibTeX
XML
Cite

\textit{M. C. Ece}, Appl. Math. Modelling 29, No. 11, 1121--1134 (2005; Zbl 1099.76060)

Full Text:
DOI

### References:

[1] | Sparrow, E.M.; Cess, R.D., The effect of a magnetic field on free convection heat transfer, Int. J. heat mass transfer, 3, 267-274, (1961) · Zbl 0102.41201 |

[2] | Gupta, A.S., Laminar free convection flow of an electrically conducting fluid from a vertical plate with uniform surface heat flux and variable wall temperature in the presence of a magnetic field, J. appl. math. phys. (ZAMP), 13, 324-332, (1963) |

[3] | Singh, K.R.; Cowling, T.G., Thermal convection in magnetohydrodynamics, Q. J. mech. appl. math., 16, 1-15, (1963) · Zbl 0108.20705 |

[4] | Emery, A.F., The effect of magnetic field upon the free convection of a conducting fluid, J. heat transfer, 85, 2, 119-124, (1963), Series C |

[5] | Riley, N., Magnetohydrodynamic free convection, J. fluid mech., 18, 577-586, (1964) · Zbl 0124.43903 |

[6] | Kuiken, H.K., Magnetohydrodynamic free convection in a strong cross field, J. fluid mech., 40, 21-38, (1970) · Zbl 0184.53704 |

[7] | Wilks, G., Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross field, J. appl. math. phys. (ZAMP), 27, 621-631, (1976) · Zbl 0351.76129 |

[8] | Wilks, G.; Hunt, R., Magnetohydrodynamic free convection flow about a semi-infinite plate at whose surface the heat flux is uniform, J. appl. math. phys. (ZAMP), 35, 34-49, (1984) · Zbl 0546.76133 |

[9] | Takhar, H.S., Hydromagnetic free convection from a flat plate, Ind. J. phys., 45, 289-311, (1971) |

[10] | Chen, T.S.; Yih, C.F., Combined heat and mass transfer in natural convection along vertical cylinder, J. heat mass transfer, 23, 451-461, (1980) · Zbl 0422.76056 |

[11] | Takhar, H.S.; Nath, G., Self similar solution of the unsteady flow in the stagnation point region of a rotating sphere with a magnetic field, Heat mass transfer, 36, 89-96, (2000) |

[12] | Takhar, H.S.; Chamkha, A.J.; Nath, G., Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces, Heat mass transfer, 37, 397-402, (2001) |

[13] | Takhar, H.S.; Chamkha, A.J.; Nath, G., Unsteady mixed convection flow from a rotating vertical cone with magnetic field, Heat mass transfer, 39, 297-304, (2003) |

[14] | Hoffman, J.D., Numerical methods for engineers and scientists, (1992), McGraw-Hill · Zbl 0823.65006 |

[15] | Ramanaiah, G.; Malarvizhi, G., Free convection about a wedge and a cone subjected to mixed thermal boundary conditions, Acta mech., 93, 119-123, (1992) · Zbl 0800.76408 |

[16] | Wylie, C.R., Advanced engineering mathematics, (1975), McGraw-Hill · Zbl 0313.00001 |

[17] | Ece, M.C., Free convection to power-law fluids from a vertical cone of variable surface temperature, Int. J. energy res., 25, 4, 1221-1232, (2001) |

[18] | Ece, M.C., Free convection laminar boundary-layer flow of a power-law fluid about a vertical cone of variable surface heat flux, J. theor. appl. fluid mech., 2, 1, 1-11, (1999-2000) |

[19] | Na, T.Y.; Chiou, J.P., Laminar natural convection over a frustrum of a cone, Appl. sci. res., 35, 409-421, (1979) · Zbl 0435.76024 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.