Mixed convection above a rotating disk

J. Arrieta-Sanagustín, M.G. Blyth

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Abstract

Mixed convection above a horizontal disk rotating in a semi-infinite fluid is examined when the disk is heated so that its temperature varies quadratically with distance away from its centre. Steady similarity solutions are presented for a range of values of the two dimensionless parameters, a Prandtl number and a Grashof number. The results are corroborated by asymptotic analyses undertaken in the limits of small and large Prandtl number. For finite Prandtl number, the existence of multiple solutions at fixed Grashof number is revealed. The similarity structure for steady solutions fails beyond a critical Grashof number and this is interpreted in terms of a finite-time singularity of the unsteady form of the governing equations.
Original languageEnglish
Pages (from-to)317-331
Number of pages15
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume66
Issue number3
DOIs
Publication statusPublished - 1 Aug 2013

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