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RESEARCH PAPERS: Forced Convection

Analysis of Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk by the Integral Method

[+] Author and Article Information
S. Basu

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

B. M. Cetegen1

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

1

Corresponding author; phone: (860)486-2966; e-mail: cetegen@engr.uconn.edu

J. Heat Transfer 128(3), 217-225 (Sep 12, 2005) (9 pages) doi:10.1115/1.2150836 History: Received April 18, 2005; Revised September 12, 2005

An integral analysis of hydrodynamics and heat transfer in a thin liquid film flowing over a rotating disk surface is presented for both constant temperature and constant heat flux boundary conditions. The model is found to capture the correct trends of the liquid film thickness variation over the disk surface and compare reasonably well with experimental results over the range of Reynolds and Rossby numbers covering both inertia and rotation dominated regimes. Nusselt number variation over the disk surface shows two types of behavior. At low rotation rates, the Nusselt number exhibits a radial decay with Nusselt number magnitudes increasing with higher inlet Reynolds number for both constant wall temperature and heat flux cases. At high rotation rates, the Nusselt number profiles exhibit a peak whose location advances radially outward with increasing film Reynolds number or inertia. The results also compare favorably with the full numerical simulation results from an earlier study as well as with the reported experimental results.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematics of the thin film over a rotating disk

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Figure 2

Variation of normalized film thickness as a function of Reynolds number for (a) Ro=1000 and (b) Ro=0.5

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Figure 3

Normalized film thickness variation over the disk surface for different Rossby numbers for medium flow rate Re=105

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Figure 4

Comparison of film thickness for experimental and theoretical data for several Reynolds number and Rossby numbers. Case 1: Re=2.4×105, Ro=361; Case 2: Re=4.8×104, Ro=361; Case 3: Re=4.8×104, Ro=0.4

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Figure 5

Constant wall temperature Nusselt number variation over the disk surface for different Reynolds numbers for (a) low rotation Ro=1000 and (b) high rotation Ro=0.5 cases

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Figure 6

Nusselt number variation for different Rossby numbers for Re=105

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Figure 7

Constant wall heat flux Nusselt number variation over the disk surface for different Reynolds numbers for (a) low rotation Ro=1000 and (b) high rotation Ro=0.5 cases

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Figure 8

Nusselt number variation for different Rossby numbers for Re=105

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Figure 9

Comparison of calculated Nusselt Number with numerical data of Rice (24) for (a) Re=2.84×104; (b) Re=1.42×105 and rotation speeds of 50, 100rpm

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Figure 10

Comparison of Nusselt Number from the integral analysis and the experimental data of Ozar (23) for (a) Re=2.85×104 and (b) Re=1.42×105

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Figure 11

Variation of average Nusselt number (based on area) with Reynolds number for different rotation rates corresponding to the constant wall temperature

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Figure 12

Variation of average Nusselt number (based on area) with Reynolds number for different rotation rates corresponding to the constant wall heat flux case

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Figure 13

The comparison of the Nusselt number for constant heat flux obtained from full solution and the approximation of negligible inertia

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