Research Papers: Evaporation, Boiling, and Condensation

Scaling of Natural Convection of an Inclined Flat Plate: Sudden Cooling Condition

[+] Author and Article Information
Suvash C. Saha1

School of Engineering and Physical Sciences, James Cook University, Townsville, Queensland 4811, Australias_c_saha@yahoo.com

John C. Patterson, Chengwang Lei

School of Civil Engineering, University of Sydney, New South Wales 2006, Australia


Corresponding author.

J. Heat Transfer 133(4), 041503 (Jan 11, 2011) (9 pages) doi:10.1115/1.4002982 History: Received January 16, 2010; Revised November 05, 2010; Published January 11, 2011; Online January 11, 2011

The natural convection boundary layer adjacent to an inclined plate subject to sudden cooling boundary condition has been studied. It is found that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh–Bénard instability if the Rayleigh number exceeds a certain critical value. A scaling relation for the onset of instability of the boundary layer is achieved. The scaling relations have been developed by equating important terms of the governing equations based on the development of the boundary layer with time. The flow adjacent to the plate can be classified broadly into a conductive, a stable convective, or an unstable convective regime determined by the Rayleigh number. Proper scales have been established to quantify the flow properties in each of these flow regimes. An appropriate identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is also presented in this study. Different flow regimes based on the stability of the boundary layer have been discussed with numerical results.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Schematic of the geometry and the coordinate system

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Figure 2

Schematics of grid distribution

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Figure 3

Time series of temperature ((a), (c), and (e)) at a point (0.6 m, 0.00121 m) and the growth of the standard deviation of the temperature ((b), (d), and (f)) for four different grids

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Figure 4

Growth of the standard deviation of the temperature for different amplitude of perturbation source for Ra=8.50×106

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Figure 5

Temperature contours of the inclined plate with three different plate lengths

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Figure 6

Time series of the temperature at different position of the plates of two different lengths, which are W/4 distance far from the plate

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Figure 7

(a) Temperature contours and (b) streamlines for Ra=50, Pr=0.72, and A=0.1 at t/ts=0.7

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Figure 8

(a) Temperature contours and (b) streamlines for Ra=8.5×102, Pr=0.72, and A=0.1 at t/ts=1.02

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Figure 9

(a) Temperature contours and (b) streamlines for Ra=1.7×107, Pr=0.72, and A=0.1 at t/ts=1.22

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Figure 10

Normalized unsteady velocity against normalized time

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Figure 11

Numerically obtained onset time of instability against corresponding scaling values for 11 runs; solid line, linear fit



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