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Research Papers: Micro/Nanoscale Heat Transfer

Effect of Rarefaction, Dissipation, and Accommodation Coefficients on Heat Transfer in Microcylindrical Couette Flow

[+] Author and Article Information
Latif M. Jiji

Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031jiji@ccny.cuny.edu

J. Heat Transfer 130(4), 042404 (Mar 17, 2008) (8 pages) doi:10.1115/1.2818763 History: Received July 31, 2006; Revised April 04, 2007; Published March 17, 2008

This paper examines the effects of rarefaction, dissipation, curvature, and accommodation coefficients on flow and heat transfer characteristics in rotating microdevices. The problem is modeled as a cylindrical Couette flow with a rotating shaft and stationary housing. The housing is maintained at uniform temperature while the rotating shaft is insulated. Thus, heat transfer is due to viscous dissipation only. An analytic solution is obtained for the temperature distribution in the gas filled concentric clearance between the rotating shaft and its stationary housing. The solution is valid in the slip flow and temperature jump domain defined by the Knudsen number range of 0.001<Kn<0.1. The important effect of the momentum accommodation coefficient on velocity reversal and its impact on heat transfer is determined. The Nusselt number was found to depend on four parameters: the momentum accommodation coefficient of the stationary surface σuo, Knudsen number Kn, ratio of housing to shaft radius rori, and the dimensionless group [γ(γ+1)](2σto1)(σtoPr). Results indicate that curvature, Knudsen number, and the accommodation coefficients have significant effects on temperature distribution, heat transfer, and Nusselt number.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Cylindrical Couette flow

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Figure 2

Velocity distribution showing partial inversion at Kn=0.05 and total inversion at Kn=0.1

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Figure 3

Velocity distribution showing partial inversion at Kn=0.1

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Figure 4

Effect of σui and σuo on the intersection point of velocity profiles

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Figure 5

Full, partial, and no velocity inversion effect on temperature distribution

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Figure 6

Effect of Knudsen number, σui, and σuo on temperature distribution in air, γ=1.4, Pr=0.7

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Figure 7

Inversion of Knudsen number effect as σto is reduced from 1.0 (Fig. 6) to 0.5 for air, γ=1.4, Pr=0.7

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Figure 8

Effect of the energy accommodation coefficient on temperature distribution in air, γ=1.4, Pr=0.7

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Figure 9

Effect of σuo and curvature on Nusselt number for Kn=0.1 in air, γ=1.4, Pr=0.7

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Figure 10

Effect of σuo, σto, and curvature on Nusselt number for Kn=0.1 in air, γ=1.4, Pr=0.7

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Figure 11

Effect of σuo and curvature on Nusselt number for Kn=0.01 in air, γ=1.4, Pr=0.7

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Figure 12

Surface heat flux variation with σui and σuo

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