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Research Papers: Forced Convection

An Approximate Analytical Solution for Electro-Osmotic Flow of Power-Law Fluids in a Planar Microchannel

[+] Author and Article Information
Arman Sadeghi

 Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, P.O. Box: 11155-9567, Tehran, Iranarmansadeghi@mech.sharif.edu

Moslem Fattahi

 Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iranmoslemfattahi@che.sharif.edu

Mohammad Hassan Saidi1

 Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, P.O. Box: 11155-9567, Tehran, Iransaman@sharif.edu

1

Corresponding author.

J. Heat Transfer 133(9), 091701 (Jul 07, 2011) (10 pages) doi:10.1115/1.4003968 History: Received April 17, 2010; Revised April 07, 2011; Published July 07, 2011; Online July 07, 2011

The present investigation considers the fully developed electro-osmotic flow of power-law fluids in a planar microchannel subject to constant wall heat fluxes. Using an approximate velocity distribution, closed form expressions are obtained for the transverse distribution of temperature and Nusselt number. The approximate solution is found to be quite accurate, especially for the values of higher than ten for the dimensionless Debye-Huckel parameter where the exact values of Nusselt number are predicted. The results demonstrate that a higher value of the dimensionless Debye-Huckel parameter is accompanied by a higher Nusselt number for wall cooling, whereas the opposite is true for wall heating case. Although to increase the dimensionless Joule heating term is to decrease Nusselt number for both pseudoplastic and dilatant fluids, nevertheless its effect on Nusselt number is more pronounced for dilatants. Furthermore, to increase the flow behavior index is to decrease the Nusselt number for wall cooling, whereas the contrary is right for the wall heating case. Depending on the value of flow parameters, a singularity is observed in the Nusselt number values of the wall heating case.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of the physical problem, coordinate system and electric double layer

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Figure 2

Transverse distribution of dimensionless EDL potential at different values of K

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Figure 3

Comparison between the approximate and exact velocity distributions at different values of K (a) n=1 and (b) n=1/3

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Figure 4

Transverse distribution of dimensionless velocity at different values of n

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Figure 5

Transverse distribution of dimensionless temperature at different values of S (a) n=0.5 and (b) n=2

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Figure 6

Transverse distribution of dimensionless temperature at different values of K (a) n=0.5 and (b) n=2

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Figure 7

Transverse distribution of dimensionless temperature at different values of n (a) S=-5 and (b) S=5

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Figure 8

Nusselt number versus 1/K at different values of S (a) n=0.5 and (b) n=2

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Figure 9

Nusselt number versus 1/K at different values of n (a) S=-1 and (b) S=1

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Figure 10

Nusselt number as a function of n at different values of S

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Figure 11

Nusselt number as a function of n at different values of K (a) S=5 and (b) S=-5

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