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

Lin, Wenxian;Armfield, S.W.;Patterson, J.C.;Lei, Chengwang

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.

Journal

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

Publication Name

N/A

Volume

ISBN/ISSN

1550-2376

Edition

N/A

Issue

Pages Count

Location

N/A

Publisher

American Physical Society

Publisher Url

N/A

Publisher Location

N/A

Publish Date

N/A

Url

N/A

Date

N/A

EISSN

N/A

DOI

10.1103/PhysRevE.79.066313