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

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

Item ID: 24257
Item Type: Article (Research - C1)
ISSN: 1550-2376
Keywords: Prandtl number; natural convection; boundary layer; unsteady flow; direct numerical simulation
Funders: National Natural Science Foundation of China, Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China, Australian Research Council
Projects and Grants: NSFC (Grant No. 11072211)
Date Deposited: 19 Dec 2012 05:02
FoR Codes: 09 ENGINEERING > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics @ 50%
09 ENGINEERING > 0915 Interdisciplinary Engineering > 091505 Heat and Mass Transfer Operations @ 50%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970109 Expanding Knowledge in Engineering @ 100%
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