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Research Papers: Heat and Mass Transfer

Heat Transfer Analysis of Mixed Electro-osmosis Pressure-Driven Flow for Power-Law Fluids Through a Microtube

[+] Author and Article Information
Chien-Hsin Chen

Department of Mechanical Design Engineering,
National Formosa University,
Huwei, Yunlin 632, Taiwan
e-mail: chchen@nfu.edu.tw

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 3, 2015; final manuscript received April 5, 2016; published online April 26, 2016. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 138(8), 082001 (Apr 26, 2016) (10 pages) Paper No: HT-15-1160; doi: 10.1115/1.4033350 History: Received March 03, 2015; Revised April 05, 2016

In this work, convection heat transfer for combined electro-osmotic and pressure driven flow of power-law fluid through a microtube has been analyzed. Typical results for velocity and temperature distributions, friction coefficient, and Nusselt number are illustrated for various values of key parameters such as flow behavior index, length scale ratio (ratio of Debye length to tube radius), dimensionless pressure gradient, and dimensionless Joule heating parameter. The results reveal that friction coefficient decreases with increasing dimensionless pressure gradient, and classical Poiseuille solutions can be retrieved as the dimensionless pressure gradient approaches to infinite. To increase the length scale ratio has the effect to reduce Nusselt number, while the influence of this ratio on Nusselt number diminishes as the pressure gradient increases. With the same magnitude of dimensionless Joule heating parameter, Nusselt number can be increased by increasing both the flow behavior index and dimensionless pressure gradient for surface cooling, while the opposite behavior is observed for surface heating. Also, singularities occurs in the Nusselt number variations for surface cooling as the ratio of Joule heating to wall heat flux is sufficiently large with negative sign.

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Figures

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Fig. 2

Normalized velocity profiles for Γ = 1 and for different values of n and δ

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Fig. 3

Mean fluid velocity normalized with generalized Smoluchowski velocity (a) Um versus n for Γ = 1 and four values of δ and (b) Um versus Γ for δ = 0.01 and seven values of n

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Fig. 4

Friction coefficient as a function of Γ for different values of n when δ = 0.01

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Fig. 5

Temperature profiles for Γ = 1, G = 1, two values of δ, and three values of n

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Fig. 6

Temperature profiles for δ = 0.001, Γ = 1, different values of n, and for (a) G = −5 and (b) G = 5

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Fig. 7

Fully developed Nusselt number as a function of Γ for δ = 0.001 and different values of n: (a) surface cooling with G = −5, (b) no Joule heating (G = 0), and (c) surface heating with G = 5

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Fig. 8

Temperature profiles for δ = 0.001, n = 1.5, different values of Γ, and for (a) G = −5 and (b) G = 5

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Fig. 9

Nusselt number as a function of Γ for three values of δ, three values of G: G = −2 (constant wall temperature), G = 0 (no Joule heating), G = 2 (surface heating) when (a) n = 0.8 and (b) n = 1.2

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Fig. 10

Variation of fully developed Nusselt number with n for δ = 0.005, Γ = 1, and for different values of G

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Fig. 1

Normalized velocity profiles for δ = 0.05 and for different values of n and Γ

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