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RESEARCH PAPERS: Forced Convection

Effect of Hydraulic Jump on Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk Analyzed by Integral Method

[+] Author and Article Information
S. Basu

Mechanical Engineering Department, University of Connecticut, Storrs, CT 06269-3139

B. M. Cetegen

Mechanical Engineering Department, University of Connecticut, Storrs, CT 06269-3139cetegen@engr.uconn.edu

J. Heat Transfer 129(5), 657-663 (Jun 26, 2006) (7 pages) doi:10.1115/1.2712854 History: Received April 11, 2006; Revised June 26, 2006

Flow and heat transfer in a liquid film flowing over the surface of a rotating disk was analyzed by integral technique. The integral analysis includes the prediction of the hydraulic jump and its effects on heat transfer. The results of this analysis are compared to the earlier results that did not include this effect. At low inlet Reynolds numbers and high Rossby numbers, corresponding to low film inertia and low rotation rates, respectively, a hydraulic jump appears on the disk surface. The location of the jump and the liquid film height at this location are predicted. A scaling analysis of the equations governing the film thickness provided a semi-empirical expression for these quantities that was found to be in very good agreement with numerical results. Heat transfer analysis shows that the Nusselt numbers for both constant disk surface temperature and constant disk surface heat flux boundary conditions are lowered in the vicinity of the hydraulic jump due to the thickened liquid film. This effect can be more pronounced for the constant heat flux case depending on the location of the hydraulic jump. The Nusselt number exhibits a turning point at the jump location and can have higher values downstream of the hydraulic jump compared to those obtained from the analysis that does not include the gravitational effects.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematics of liquid film flow over a rotating disk

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Figure 2

Normalized film thickness for various values of Reynolds number at a Rossby number of 5000

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Figure 3

Normalized film thickness for various values of Rossby numbers at a Reynolds number of 5000 for the cases with and without Froude number effect

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Figure 4

Normalized film thickness for various values of Rossby numbers for a Reynolds number of 20,000

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Figure 5

Nusselt number variation for constant wall temperature case for different Rossby numbers at a Reynolds number of 5000. (a) Ro=0.1,10, 5×103, (b) Ro=0.1,10. Location of the hydraulic jump is delineated by a vertical dashed line.

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Figure 6

Variation of Nusselt number for different Reynolds numbers for a Rossby number of 5000. Locations of the hydraulic jump are delineated by vertical dashed lines.

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Figure 7

Variation of Nusselt number for constant wall heat flux case for different Rossby numbers for a Reynolds number of 5000. (a) Ro=0.1,10, 5×103, (b) Ro=0.1,10.

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Figure 8

Variation of Nusselt number for constant wall heat flux for Reynolds numbers of 5×103 and 2×104 at a Rossby number of 10

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Figure 9

Variation of Nusselt number for constant wall heat flux for different Reynolds numbers for a Rossby number of 5000

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Figure 10

Variation of area averaged Nusselt number for constant heat flux and constant wall temperature cases for Ro=5000

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