A New Approach for Modeling Electro-Osmotic Flow Micro-Cooling Systems

Abstract:

The problem of entropy generation due to heat transfer in an electro-osmotic flow with circular type area section micro-channels for small values of electro-kinetic parameter κα (where κ is the Debye length and a is the radius of the micro-channel) is investigated analytically. The momentum and energy conservation equations in cylindrical coordinates for an electro-osmotic flow are derived in non-dimensional form. The momentum equation is solved and velocity distribution in terms of modified Bessel function of the first kind is obtained. An approximation is used for the Bessel function of first kind. Considering the approximate velocity profile, the energy equation including viscous dissipation effects is solved to obtain the temperature distribution in terms of parametric values of the electro-kinetic parameter and the Brinkman number. A uniform surface heat flux boundary condition is considered. The importance of this investigation is development of an engineering simple method of design for electro-osmotic circular micro-electronic cooling systems and possible optimizations of these kinds of flows with respect to the second-law of thermodynamics through the micro-coolers.

• Periodical: Advanced Materials Research (Volume 705)
• Pages: 393-399
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.705.393
• Online since: June 2013
• Authors: Alireza Taklifi, Abbas Aliabadi
• Keywords: Circular Micro-Channel, Electro-Osmotic Flow, Micro-Cooling Systems

References

[1] G.F. Naterer, 2005, "Embedded converging surface microchannels for minimized friction and thermal irreversibilities", Int. J. of Heat Mass Transfer,48:1225–1235.

DOI: 10.1016/j.ijheatmasstransfer.2004.10.016

[2] G.F. Naterer, 2004, "Adaptive surface microprofiling for microfluidic energy conversion", J. Thermophys. Heat Transfer, 18(4).

DOI: 10.2514/1.8728

[3] S. Yu and T.A. Ameel, 2001, "Slip flow heat transfer in rectangular microchannels", Int. J. of Heat Mass Transfer, 44(22):4225–4234.

DOI: 10.1016/s0017-9310(01)00075-8

[4] C. Y. Zhao, and T. J. Lu, 2002, "Analysis of microchannel heat sinks for electronics cooling," Int. J. Heat Mass Transfer, 45(24): 4857–4869

DOI: 10.1016/s0017-9310(02)00180-1

[5] W. A. Khan and M. M. Yovanovich, 2008, "Analytical modeling of fluid flow and heat transfer in microchannel/nanochannel heat sinks", J. Thermophys. Heat Transfer, 22(3):352–359.

DOI: 10.2514/1.35621

[6] C. K. Chen, H. Y. Lai, C. C. Liu, 2011," Numerical analysis of entropy generation in mixed convection flow with viscous dissipation effects in vertical channel", Int. Comm. Heat Mass Transfer. 38(3): 285-290.

DOI: 10.1016/j.icheatmasstransfer.2010.12.016

[7] N. Guerroudj, H. Kahalerras, 2010," Mixed convection in a channel provided with heated porous blocks of various shape", Energy Conversion Management., 51: 505-517.

DOI: 10.1016/j.enconman.2009.10.015

[8] K. Hooman and A. Ejlali, 2007," Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature", Int. Comm. Heat Mass Transfer. 34: 408–419.

DOI: 10.1016/j.icheatmasstransfer.2006.10.008

[9] A. H. A. Al-Salim, 2008," Buoyancy effects on entropy generation due to laminar mixed convection in vertical channels", thesis for the degree of Master of Science in mechanical engineering, King Fahad university of Petroleum & Minerals.

[10] A. Jain and M. K. Jensen, 2007, "Analytical modeling of electrokinetic effects on flow and heat transfer in microchannels", Int. J. Heat Mass Transfer, 50:5161-5170.

DOI: 10.1016/j.ijheatmasstransfer.2007.07.005

[11] M. Liu, Y. Liu, Q. Guo, J. Yang, 2009, "Modeling of electroosmotic pumping of nonconducting liquids and biofluids by a two-phase flow method", J. Electroanalytical Chemistry, 636:86-92.

DOI: 10.1016/j.jelechem.2009.09.015

[12] N. Vasu and S. De, 2010, "Electroviscous effects in purely pressure driven flow and stationary plane analysis in electroosmotic flow of power-law fluids in a slit microchannel", Int. J. Eng. Sci., 48:1641-1658.

DOI: 10.1016/j.ijengsci.2010.08.015

[13] L. Zhao, L.H. Liu, 2010," Entropy generation analysis of electro-osmotic flow in open-end and closed-end micro-channels", Int. J. of Therm. Sci.., 49: 418-427.

DOI: 10.1016/j.ijthermalsci.2009.07.009

[14] A. H. Epstein, 2003," MILLIMETER-SCALE, MEMS GAS TURBINE ENGINES", Proceedings of ASME Turbo Expo 2003, Atlanta, Georgia, USA.

DOI: 10.1115/gt2003-38866

[15] L. Jiang, J.C. Mikkelsen, J.M. Koo, L. Zhang, D. Huber, S. Yao, A. Bari, P. Zhou and J.G. Santiago, 2002," Transient and sub-atmospheric performance of a closed-loop electroosmotic microchannel cooling system", THERMES 2002 Workshop, Santa Fe, New Mexico, USA.

DOI: 10.1109/tcapt.2002.800599

[16] O. R. Bakaraju, 2009," Heat transfer in electro-osmotic flow of power-law fluids in micro-channels", thesis for the degree of Master of Science in mechanical engineering , Cleveland State university.

[17] M. Gerendas and R. Pfister, 2000, "Development of a very small aero-engine," ASME Paper 2000-GT-0536, ASME Turbo Expo, Munich, Germany.