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Research Papers: Jets, Wakes, and Impingement Cooling

# Numerical Simulation of Transient Thermal Transport on a Rotating Disk Under Partially Confined Laminar Liquid Jet Impingement

[+] Author and Article Information
Jorge C. Lallave, Muhammad M. Rahman

Department of Mechanical Engineering, University of South Florida, Tampa, FL 33620

J. Heat Transfer 132(5), 052201 (Mar 05, 2010) (8 pages) doi:10.1115/1.4000442 History: Received November 26, 2008; Revised July 24, 2009; Published March 05, 2010; Online March 05, 2010

## Abstract

This paper considers the transient conjugate heat transfer characterization of a partially confined liquid jet impinging on a rotating and uniformly heated solid disk of finite thickness and radius. A constant heat flux was imposed at the bottom surface of the solid disk at $t=0$, and heat transfer was monitored for the entire duration of the transient until the steady state condition was reached. Calculations were done for a number of disk materials using water as the coolant, covering a range of Reynolds numbers (225–900), Ekman numbers $(7.08×10−5−∞)$, nozzle-to-target spacing $(β=0.25–1.0)$, confinement ratios $(rp/rd=0.2–0.75)$, disk thicknesses to nozzle diameter ratios $(b/dn=0.25–1.67)$, and solid to fluid thermal conductivity ratios (36.91–697.56). It was found that a higher Reynolds number decreases the time to achieve the steady state condition and increases the local and average Nusselt number. The duration of the transient increases with the increment of the Ekman number and disk thickness, and the reduction in the thermal diffusivity of the disk material.

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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 1

Three-dimensional schematic of axisymmetric semiconfined liquid jet impingement on a uniformly heated spinning disk

Figure 2

Local Nusselt number distributions for different number of elements in r and z directions (Re=750, b/dn=0.5, Ek=4.25×10−4, β=0.5, and rp/rd=0.667)

Figure 3

Local Nusselt number and dimensionless interface temperature distributions for a silicon disk with water as the cooling fluid for different Fourier numbers (Re=275, Ek=4.25×10−4, β=0.5, b/dn=0.5, and rp/rd=0.667)

Figure 4

Average Nusselt number and dimensionless temperature variations with time for different Reynolds numbers (Ek=4.25×10−4, β=0.5, silicon disk, b/dn=0.5, and rp/rd=0.667)

Figure 5

Average Nusselt number and dimensionless temperature variations with time for different Ekman numbers (Re=550, β=0.25, silicon disk, b/dn=0.5, and rp/rd=0.667)

Figure 6

Average Nusselt number and dimensionless temperature variations with time for different nozzle to target spacing (Re=750, Ek=4.25×10−4, silicon disk, b/dn=0.5, and, rp/rd=0.667)

Figure 7

Average Nusselt number and dimensionless temperature variations with time for different plate to disk confinement ratios (Re=450, Ek=4.25×10−4, β=0.5, silicon disk, and b/dn=0.5)

Figure 8

Average Nusselt number and dimensionless temperature variations with time for different solid materials (Re=875, Ek=2.13×10−4, b/dn=0.5, β=0.5, and rp/rd=0.667)

Figure 9

Average Nusselt number and dimensionless temperature variations with time for different silicon disk thicknesses (Re=450, Ek=4.25×10−4, β=0.5, and rp/rd=0.667)

Figure 10

Isothermal lines at different instants for a silicon disk with water as the cooling fluid (Re=450, Ek=4.25×10−4, β=0.5, b/dn=0.5, rp/rd=0.667, and qw=125 kW/m2)

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