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Prandtl number scaling of the unsteady natural convection boundary layer adjacent to a vertical flat plate for Pr > 1 subject to ramp surface heat flux

Saha, Suvash C., Brown, Richard J., & Gu, YuanTong (2012) Prandtl number scaling of the unsteady natural convection boundary layer adjacent to a vertical flat plate for Pr > 1 subject to ramp surface heat flux. International Journal of Heat and Mass Transfer, 55(23-24), pp. 7046-7055.

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Abstract

It is found in the literature that the existing scaling results for the boundary layer thickness, velocity and steady state time for the natural convection flow over an evenly heated plate provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings provide a good prediction of two other governing parameters’ dependency, the Rayleigh number and the aspect ratio. Therefore, an improved scaling analysis using a triple-layer integral approach and direct numerical simulations have been performed for the natural convection boundary layer along a semi-infinite flat plate with uniform surface heat flux. This heat flux is a ramp function of time, where the temperature gradient on the surface increases with time up to some specific time and then remains constant. The growth of the boundary layer strongly depends on the ramp time. If the ramp time is sufficiently long, the boundary layer reaches a quasi steady mode before the growth of the temperature gradient is completed. In this mode, the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the ramp time is sufficiently short, the boundary layer develops differently, but after the wall temperature gradient growth is completed, the boundary layer develops as though the startup had been instantaneous.

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ID Code: 51494
Item Type: Journal Article
Additional URLs:
Keywords: Boundary layer, vertical plate, ramp heat flux, Prandtl number
DOI: 10.1016/j.ijheatmasstransfer.2012.07.017
ISSN: 1879-2189
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in International Journal of Heat and Mass Transfer. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Heat and Mass Transfer, [VOL 55, ISSUE 23-24, (2012)] DOI: 10.1016/j.ijheatmasstransfer.2012.07.017
Deposited On: 09 Jul 2012 09:06
Last Modified: 04 Dec 2013 13:36

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