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Prandtl number scaling of natural convection of the flow on an inclined at plate due to uniform surface heat flux

Saha, Suvash C. & Gu, YuanTong (2012) Prandtl number scaling of natural convection of the flow on an inclined at plate due to uniform surface heat flux. The ANZIAM Journal, 53, C387-C403.

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Abstract

A new scaling analysis has been performed for the unsteady natural convection boundary layer under a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages including an early stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as numerical results. Earlier scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scales for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency. However, those scalings performed very well with Rayleigh number and aspect ratio dependency. In this study, a modifed Prandtl number scaling has been developed using a triple-layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the new scaling performs considerably better than the previous scaling.

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ID Code: 52015
Item Type: Journal Article
Keywords: Natural convection, scaling analysis, uniform heat flux, inclined plate, Prandtl number
ISSN: 1446-8735
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
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 Australian Mathematical Society
Deposited On: 18 Jul 2012 08:51
Last Modified: 24 Jul 2012 21:02

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