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Research Papers: Jets, Wakes, and Impingment Cooling

Heat Transfer in the Flow of a Cold, Axisymmetric Vertical Liquid Jet Against a Hot, Horizontal Plate

[+] Author and Article Information
Jian-Jun Shu1

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Graham Wilks

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

1

Corresponding author.

J. Heat Transfer 130(1), 012202 (Jan 25, 2008) (11 pages) doi:10.1115/1.2780180 History: Received December 15, 2006; Revised May 03, 2007; Published January 25, 2008

The paper considers heat transfer characteristics of thin film flow over a hot horizontal flat plate resulting from a cold vertical jet of liquid falling onto the surface. A numerical solution of high accuracy is obtained for large Reynolds numbers using the modified Keller box method. For the flat plate, solutions for axisymmetric jets are obtained. In a parallel approximation theory, an advanced polynomial approximation for the velocity and temperature distribution is employed and results are in good agreement with those obtained using a simple Pohlhausen polynomial and the numerical solutions.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) The vertical jet and resultant film for the axisymmetric flat plate. (i) imbedded stagnation boundary layer, (ii) outer inviscid deflection region, (iii) quasi-Blasius viscous diffusion, (iv) transition around viscous penetration, and (v) similarity film flow. The dashed line represents the hydrodynamic boundary layer. (b) Basis of approximate solution.

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Figure 2

(a) Comparison of free surface velocity for the respective profiles; (b) free surface velocity for the numerical solution and the present profile

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Figure 3

Velocity profile development within the deflected film

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Figure 4

(a) Comparison of film thickness for the respective profiles; (b) film thickness for the numerical solution and the present profile

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Figure 5

Film, viscous, and thermal boundary-layer thicknesses for Pr=(a) 2, (b) 5, and (c) 10 using the present profile

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Figure 6

Temperature profile development within the deflected film

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Figure 7

(a) Skin friction for the present and the Chaudhury profiles; (b) skin friction for the numerical solution and the present profile

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Figure 8

(a) Heat transfer coefficient for various Prandtl numbers; (b) heat transfer coefficient for the numerical solution and the present profile at Pr=2

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Figure 9

(a) Free surface temperature for the numerical solution and the present profile at Pr=2 (b) free surface temperature for various Prandtl numbers

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