Prandtl number scaling of unsteady natural convection boundary layers for Pr>1 fluids under isothermal heating

Lin, Wenxian, Armfield, S.W., Patterson, J.C., and Lei, Chengwang (2009) Prandtl number scaling of unsteady natural convection boundary layers for Pr>1 fluids under isothermal heating. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 79 (6). 066313.

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Abstract

In this paper, the scalings incorporating the Prandtl number (Pr) dependence have been obtained by a scaling analysis for the unsteady natural convection boundary layer of an initially quiescent isothermal Newtonian fluid of Pr>1 produced by the sudden imposition of a higher temperature on a vertical plate. It is shown that the transient flow behavior of the resulting boundary layer can be described by a three-region structure and at the start-up stage the boundary layer development is one dimensional and independent of height due to the dominance of pure conduction; however, at steady state it becomes two dimensional and height dependent as the flow becomes dominated by convection. Numerical results demonstrate that the scalings representing the thermal boundary layer development accurately represent their Pr dependence over the whole stage of flow development. The scalings representing the viscous boundary layer development are generally in good agreement with the numerical results with the Pr variation over the whole stage of flow development, although there are small deviations from the numerical results with the Pr variation that are within acceptable limits for scaling.

Item ID: 4792
Item Type: Article (Research - C1)
ISSN: 1550-2376
Keywords: boundary layers, convection, heating
Funders: Australian Research Council
Date Deposited: 21 Jul 2009 05:29
FoR Codes: 09 ENGINEERING > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics @ 100%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 40%
97 EXPANDING KNOWLEDGE > 970109 Expanding Knowledge in Engineering @ 60%
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