Lin, Wenxian, and Armfield, S.W. (2012) Unified Prandtl number scaling for start-up and fully developed natural-convection boundary layers for both Pr ≳1 and Pr ≳1 fluids with isothermal heating. Physical Review E, 86 (6). 066312. pp. 1-10.

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Abstract

Recent studies have used scaling analysis to obtain simple power-law relations that accurately predict the Prandtl (Pr) number dependency of natural-convection boundary layers subjected to both isothermal and ramped heating conditions, when Pr>1. The analysis used in those studies cannot be extended to Pr<1 fluids, and it is not clear at present whether such simple scaling relations can be developed for Pr<1 fluids. In the present study, the Pr>1 scalings are shown to perform well for the start-up stage of the Pr<1 flow, but not for the fully developed flow. The Pr>1 scalings are modified to provide unified Prandtl number scalings for fully developed natural-convection boundary layers for both Pr≳1 and Pr≲1, with the unknown powers obtained empirically via direct numerical simulation. The modified scalings are shown to perform well for the fully developed flow, with the exception being the prediction of the inner viscous boundary-layer thickness

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