A numerical analysis of free convection around an isothermal sphere. Effects of space and prandtl number

Hiroshi Takamatsu, Motoo Fujii, Tetsu Fujii

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Numerical solutions of full Navier-Stokes and energy equations for two dimensional laminar free convection between two concentric spheres are obtained for Pr=0.7~120, Ra=1~103 and radius ratios of outer to inner spheres r2/r1=560. With decrease of r2/r1, the heat transfer coefficient for the inner sp. here decreases first due to suppression of convective flow and then increases as the conduction heat transfer becomes predominant. For Pr=0.7 and Ra=1, the heat transfer coefficient at r2/r1≥60 can be regarded as that for a single sphere immersed in an infinite medium. The higher the Rayleigh number, the smaller the radius ratio at which the Nusselt number can be regarded as that for a single sp. here. An accurate expression of the Nusselt number is proposed. An expression for the relation among drag force induced by free convection flow, Rayleigh number and Prandtl number is also presented.

Original languageEnglish
Pages (from-to)1314-1319
Number of pages6
JournalTransactions of the Japan Society of Mechanical Engineers Series B
Issue number488
Publication statusPublished - Jan 1 1987


All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering

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