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Research Papers: Micro/Nanoscale Heat Transfer

Friction Numbers and Viscous Dissipation Heating for Laminar Flows of Water in Microtubes

[+] Author and Article Information
Mohamed S. El-Genk1

Chemical and Nuclear Engineering Department, and Institute for Space and Nuclear Power Studies, University of New Mexico, Albuquerque, NM 87131mgenk@unm.edu

In-Hwan Yang

Chemical and Nuclear Engineering Department, and Institute for Space and Nuclear Power Studies, University of New Mexico, Albuquerque, NM 87131

1

Corresponding author.

J. Heat Transfer 130(8), 082405 (Jun 04, 2008) (13 pages) doi:10.1115/1.2909617 History: Received July 02, 2007; Revised October 03, 2007; Published June 04, 2008

The friction numbers for laminar flows of water in microtubes, determined from the temperature rise due to the viscous dissipation heating assuming a velocity slip, show a strong dependence on the diameter and aspect ratio. The calculated values compare well with those determined from experimental data for water flows in glass and diffused silica microtubes (16101μm in diameter D and aspect ratios LD=4991479). With a slip, the friction number almost exponentially decreases as D decreases and, to a lesser extent, as LD increases. For D>400μm, the friction number approaches the theoretical Hagen–Poiseuille for macrotubes (64) when LD>1500, but higher values at smaller LD. The developed semiempirical analytical expression for calculating the friction number is in good agreement with the numerical and experimental results. The results suggest the presence of a velocity slip in the experiments and the plausible presence of a thin nanolayer at the walls of the microtubes. For D>200μm, this layer, if exists, is estimated to be 18.9nm, but increases to 21.5nm for D<200μm, when R¯e=800 and LD=1479.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Friction numbers for microtubes and microchannels

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Figure 2

Effect of entrance condition on viscous heating of water flow in microtubes

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Figure 3

Effect of slip length on viscous heating of water flow in microtubes

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Figure 4

Experimental measurements confirming slip at the wall of 50μm diameter microtube

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Figure 5

Experimental measurements confirming slip at the wall of 70μm diameter microtube

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Figure 6

Experimental measurements confirming slip at the wall of 101μm diameter microtube

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Figure 7

Additional measurements confirming slip at the wall of microtubes

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Figure 8

Effect of slip length on friction number for water flows in microtubes

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Figure 9

Comparisons of theory with experimental data of Celata (1) and Celata (2)

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Figure 10

Effects of D and L∕D on friction number for laminar flow of water in microtubes

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Figure 11

Effect of neglecting entrance thermal development on friction number

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Figure 12

Correction factor for thermal flow development at inlet of microtubes

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Figure 13

Effect of accounting for thermal development at inlet of microtubes

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Figure 14

Velocity profile for laminar flow in a microtube with a slip at the wall

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Figure 15

Thickness of thin gas layer at microtube walls

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