Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T01:59:59.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermally Fully Developed Electroosmotic Flow of Power-Law Fluids in a Circular Microchannel

Published online by Cambridge University Press:  07 August 2013

Y.-J. Sun ,
Y.-J. Jian ,
L. Chang  and
Q.-S. Liu
Y.-J. Sun
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China
Y.-J. Jian*
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China
L. Chang
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China School of Mathematics and Statistics, Inner Mongolia University of Finance and Economics, Hohhot, Inner Mongolia 010051, China
Q.-S. Liu
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China
*
*[email protected]
Get access

Abstract

This study presents a thermally fully developed electroosmotic flow of the non-Newtonian power-law fluids through a circle microchannel. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including the Poisson Boltzmann equation, the modified Navier Stokes equation and the energy equation is developed. The semi-analytical solutions of normalized velocity and temperature are derived. The velocity profile is computed by numerical integrate, and the temperature distribution is obtained by finite difference method. Results show that the velocity profiles depend greatly on the fluid behavior index n and the nondimensional electrokinetic width K. For a specified value of K, the axial velocity increases with a decrease in n, and the same trend for the effect of K on the velocity can be found for a specified value of n. Moreover, the dimensionless temperature is governed by three parameters, namely, the flow behavior index n, the nondimensional electrokinetic width K, and the dimen-sionless Joule heating parameter G. The variations of radial fluid temperature distributions with different parameters are investigated.

Keywords

Circular microchannelElectroosmotic flowPower-law fluidsJoule heating
Type
Research Article
Information
Journal of Mechanics , Volume 29 , Issue 4 , December 2013 , pp. 609 - 616
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Hunter, R. J., Zeta Potential in Colloid Science, Academic, San Diego (1981).Google Scholar
2.Karniadakis, G., Beskok, A. and Aluru, N., Micor-flows and Nanoflows: Fundamentals and Simulation, Springer, New York (2005).Google Scholar
3.Burgreen, D. and Nakache, F. R., “Electrokinetic Flow in Ultrafine Capillary Slits,” Journal of Physics and Chemistry, 68, pp. 1084–1091 (1964).Google Scholar
4.Rice, C. L. and Whitehead, R., “Electrokinetic Flow in Narrow Cylindrical Capillaries,” Journal of Physics and Chemistry, 69, pp. 4017–4023 (1965).Google Scholar
5.Kang, Y. J., Yang, C. and Huang, X. Y., “Elec-troosmotic Flow in a Capillary Annulus with High Zeta Potentials,” Journal of Colloid and Interface Science, 253, pp. 285–294 (2002).Google Scholar
6.Hsu, J. P., Kao, C. Y., Tseng, S. and Chen, C. J., “Electrokinetic Flow Through an Elliptical Microchannel: Effects of Aspect Ratio and Electrical Boundary Conditions,” Journal of Colloid and Interface Science, 248, pp. 176–184 (2002).CrossRefGoogle ScholarPubMed
7.Yang, C. and Li, D., “Electrokinetic Effects on Pressure-Driven Liquid Flows in Rectangular Microchannels,” Journal of Colloid and Interface Science, 194, pp. 95–107 (1997).Google Scholar
8.Patankar, N. A. and Hu, H. H., “Numerical Simulation of Electroosmotic Flow,” Analytical Chemistry, 70, pp. 1870–1881 (1998).CrossRefGoogle ScholarPubMed
9.Santiago, J. G., “Electroosmotic Flows in Microchannels with Finite Inertial and Pressure Forces,” Analytical Chemistry, 73, pp. 2353–2365 (2001).CrossRefGoogle ScholarPubMed
10.Jian, Y. J., Yang, L. G. and Liu, Q. S., “Time Periodic Electro-osmotic Flow through a Microannu-lus,” Physics of Fluids, 22, p. 042001 (2010).CrossRefGoogle Scholar
11.Yang, R. J., Fu, L. M. and Hwang, C. C., “Elec-troosmotic Entry Flow in a Microchannel,” Journal of Colloid and Interface Science, 244, pp. 173–179 (2001).Google Scholar
12.Jian, Y. J., Liu, Q. S. and Yang, L. G., “AC Electroosmotic Flow of Generalized Maxwell Fluids in a Rectangular Microchannel,” Journal of Non- Newtonian Fluid Mechanics, 166, pp. 1304–1314 (2011).Google Scholar
13.Yang, C., Li, D. and Masliyah, J. H., “Modeling Forced Liquid Convection in Rectangular Microchannels with Electrokinetic Effects,” International Journal Heat and Mass Transfer, 41, pp. 4229–4249 (1998).Google Scholar
14.Zhao, C., Zholkovskij, E., Masliyah, J. H., and Yang, C., “Analysis of Electroosmotic Flow of Power-Law Fluids in a Slit Microchannel,” Journal of Colloid and Interface Science, 326, pp. 503–510 (2008).Google Scholar
15.Chen, C. H., “Electroosmotic Heat Transfer of Non-Newtonian Fluid Flow in Microchannels,” Journal of Heat Transfer, ASME, 133, p. 071705 (2011).CrossRefGoogle Scholar
16.Horiuchi, K. and Dutta, P., “Joule Heating Effects in Electroosmotically Driven Microchannel Flows,” International Journal Heat and Mass Transfer, 47, pp. 3085–3095 (2004).Google Scholar
17.Horiuchi, K., Dutta, P. and Hossain, A., “Joule-Heating Effects in Mixed Electro-osmotic and Pressure-Driven Microflows under Constant Wall Heat Flux,” Journal of Engineering Mathematical, 54, pp. 159–180 (2006).Google Scholar
18.Sharma, A. and Chakraborty, S., “Semi-Analytical Solution of the Extended Graetz Problem for Combined Electroosmotically and Pressure-Driven Microchannel Flows with Step-change in Wall Temperature,” International Journal Heat and Mass Transfer, 51, pp. 4875–4885 (2008).Google Scholar
19.Liao, Q., Zhu, X. and Wen, T. Y., “Thermal Effects on Mixed Electro-osmotic and Pressure-Driven Flows in Triangle Microchannels,” Applied Thermal Engineering, 29, pp. 807–814 (2009).Google Scholar
20.Shi, Y., Zhao, T. S. and Guo, Z. L., “Simplified Model and Lattice Boltzmann Algorithm for Mi-croscale Electro-osmotic Flows and Heat Transfer,” International Journal Heat and Mass Transfer, 51, pp. 4875–4885 (2008).CrossRefGoogle Scholar
21.Nithiarasu, P. and Lewis, R. W., “A Short Note on Joule Heating in Electro-osmotic Flows: A Consistent Non-dimensional Scaling,” International Journal of Numerical Methods for Heat & Fluid Flow, 18, pp. 919–931 (2008).CrossRefGoogle Scholar
22.Xuan, X. C., Xu, B., Sinton, D. and Li, D. Q., “Electroosmotic Flow with Joule Heating Effects,” Lab Chip, 4, pp. 230–236 (2004).Google Scholar
23.Hsieh, S. S. and Yang, T. K., “Electroosmotic Flow in Rectangular Microchannels with Joule Heating Effects,” Journal of Micromechanics and Microengineering, 18, p. 025025 (2008).Google Scholar
24.Deen, W. M., Analysis of Transport Phenomena, University Press, New York (1998).Google Scholar
25.Masliyah, J. H. and Bhattacharjee, S., Electroki-netic and Colloid Transport Phenomena, Wiley-Interscience, Hoboken, New Jersey (2006).Google Scholar
26.Chen, C. H., “Thermal Transport Characteristics of Mixed Pressure and Electroosmotically Driven Flow in Micro- and Nanochannels with Joule Heating,” Journal of Heat Transfer, ASME, 131, p. 022401 (2009).CrossRefGoogle Scholar