### Abstract

Numerical solutions of full Navier-Stokes and energy equations for two dimensional laminar free convection between two concentric spheres are obtained for Pr equals 0. 7 to approximately 120, Ra equals 1 to approximately 10**3 and radius ratios of the outer to inner sphere r//2/r//1 equals 5 to approximately 60. With decrease of r//2/r//1 the heat transfer coefficient for the inner sphere decreases first due to suppression of convective flow and transfer. The heat transfer coefficient at r//2/r//1 greater than equivalent to 60 can be regarded as that for a single sphere immersed in an infinite medium for Pr equals 0. 7 and Ra equals 1. The higher the Rayleigh number, the smaller is the radius ratio at which Nusselt number can be regarded as that for a single sphere. An accurate correlation equation for the Nusselt number is proposed. A correlation equation for the relation among drag forces induced by free convection flow, Rayleigh number and Prandtl number is also presented.

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

Title of host publication | Unknown Host Publication Title |

Publisher | ASME |

Pages | 55-60 |

Number of pages | 6 |

Volume | 4 |

Publication status | Published - 1987 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Unknown Host Publication Title*(Vol. 4, pp. 55-60). ASME.

**NUMERICAL ANALYSIS OF FREE CONVECTION AROUND AN ISOTHERMAL SPHERE (EFFECTS OF SPACE AND PRANDTL NUMBER).** / Fujii, M.; Takamatsu, Hiroshi; Fujii, T.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Unknown Host Publication Title.*vol. 4, ASME, pp. 55-60.

}

TY - GEN

T1 - NUMERICAL ANALYSIS OF FREE CONVECTION AROUND AN ISOTHERMAL SPHERE (EFFECTS OF SPACE AND PRANDTL NUMBER).

AU - Fujii, M.

AU - Takamatsu, Hiroshi

AU - Fujii, T.

PY - 1987

Y1 - 1987

N2 - Numerical solutions of full Navier-Stokes and energy equations for two dimensional laminar free convection between two concentric spheres are obtained for Pr equals 0. 7 to approximately 120, Ra equals 1 to approximately 10**3 and radius ratios of the outer to inner sphere r//2/r//1 equals 5 to approximately 60. With decrease of r//2/r//1 the heat transfer coefficient for the inner sphere decreases first due to suppression of convective flow and transfer. The heat transfer coefficient at r//2/r//1 greater than equivalent to 60 can be regarded as that for a single sphere immersed in an infinite medium for Pr equals 0. 7 and Ra equals 1. The higher the Rayleigh number, the smaller is the radius ratio at which Nusselt number can be regarded as that for a single sphere. An accurate correlation equation for the Nusselt number is proposed. A correlation equation for the relation among drag forces induced by free convection flow, Rayleigh number and Prandtl number is also presented.

AB - Numerical solutions of full Navier-Stokes and energy equations for two dimensional laminar free convection between two concentric spheres are obtained for Pr equals 0. 7 to approximately 120, Ra equals 1 to approximately 10**3 and radius ratios of the outer to inner sphere r//2/r//1 equals 5 to approximately 60. With decrease of r//2/r//1 the heat transfer coefficient for the inner sphere decreases first due to suppression of convective flow and transfer. The heat transfer coefficient at r//2/r//1 greater than equivalent to 60 can be regarded as that for a single sphere immersed in an infinite medium for Pr equals 0. 7 and Ra equals 1. The higher the Rayleigh number, the smaller is the radius ratio at which Nusselt number can be regarded as that for a single sphere. An accurate correlation equation for the Nusselt number is proposed. A correlation equation for the relation among drag forces induced by free convection flow, Rayleigh number and Prandtl number is also presented.

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M3 - Conference contribution

AN - SCOPUS:0023206433

VL - 4

SP - 55

EP - 60

BT - Unknown Host Publication Title

PB - ASME

ER -